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Crafting Cases

The Definitive Guide to Issue Trees

Introduction, issue trees: the secret to think like a mckinsey consultant and always have a clear, easy way to solve any problem.

Ask any McKinsey consultant what’s the #1 thing you should learn in order to solve problems like they do and you’re gonna get the same answer over and over again:

“You’ve gotta learn to create Issue Trees.”

Issue Trees (also known as “Logic Trees” and “Hypothesis Trees”) are THE most fundamental tool to structure and solve problems in a systematic way.

Mastering them is a requirement if you want to get a job in a top consulting firm, such as McKinsey, Bain and BCG.

But even if you’re not applying for a job at these firms, they’re a powerful tool for any job that requires you to solve problems .

In fact, Issue Trees are the main tool top management consultants use to solve the toughest multi-billion dollar problems their clients have.

This guide will teach you how to create and use Issue Trees.  

I will give a focus on case interviews  but you can use this skill in any other problem solving activity. I personally use it everyday at work.

(Which means what you’ll learn here is gonna be useful for far more than merely getting a job.)

About the author

I’m Bruno Nogueira.

I’m an ex-McKinsey consultant and I have learned to think using issue trees the hard way.

There were no good resources to learn this back when I was applying for the job.

Even within McKinsey there was no formal training. People just expected you to “get it” on the job.

After leaving the Firm, I’ve spent a few years coaching people to get a job in consulting, and I learned to teach this skill the only way possible: by actually teaching it!

Along with my partner Julio, I have taught 1000’s of people to break down problems in a structured way using issue trees.

And today I’m gonna teach you  how to do this.

In this guide you'll learn:

Issue Tree Fundamentals

Three Techniques To Build Issue Trees

Six Principles For AMAZING Issue Trees

Issue Tree Examples

Common Mistakes and Questions

How To Practice Issue Trees

BONUS CHAPTER

Applying Issue Trees On The Job

Issue trees are the blueprint of how McKinsey (and other) consultants think.

They make your thinking process more rigorous and much, much more clear.

Unfortunately they didn’t teach you this well enough (if at all) in school.

They don’t even teach this in most Business Schools.

But if you learn to harness their power, you’re set to case interview success (and a career where every problem can be easily solved).

How I learned about Issue Trees

A bit of a personal story first…

I first learned about Issue Trees from a friend who was working in management consulting. It was back when I was applying for a job at McKinsey, Bain and BCG.

This friend told me Issue Trees were the #1 thing I had to learn in order to do well on the interview and land a top consulting job.

And so, the first thing I did was to look for examples of Issue Trees.

And I found stuff like this…

Not exactly rocket science, right?

But then I thought… “Alright,  what if my problem is not a profit problem?  Or what if I need to dig a little deeper than that?”

It didn’t take me long to find people on the internet telling me that you could use Issue Trees to solve any  problem!

Here’s how they illustrated this important point:

Let’s be honest with ourselves here… This is NOT the best way to teach something!

And so I kept looking around. 

I wanted to see realistic examples of real Issue Trees consultants use to solve their client’s problems.

And if I was lucky, I hoped to find some explanation on why each example was structured the way it was.

Here’s the kind of stuff I found looking up on Google again:

And now I was left wondering how to get from Point A (the simple profit Issue Tree from the beginning of this orange box) to Point B (the behemoth you see above).

And I also wondered if getting to this behemoth was actually the kind of thing I wanted in the first place. Would it help me in a real interview?

So I gave up on the internet and decided to learn Issue Trees from those who know it best: real consultants. That’s who I learned to build Issue Trees from.

But I know that most people don’t have access to real consultants with the time to teach them things. 

And it never stopped bothering me the fact that the internet had no decent resource to teach people of a skill that I use multiple times a day (and even make a living out of).

This is why I wrote this guide.

The 4 things you need to "get" to understand Issue Trees

Before we jump into the nitty-gritty of how to create and use your Issue Trees, I want to give you a high-level view. This high-level view is what we’ll cover in this chapter.

I’m gonna show you four ways to look at Issue Trees so you can get an intuitive understanding of them.

And I’m gonna show you that through an example of a realistic Issue Tree. 

They are a "map" of your problem

The first thing you need to know about Issue Trees is that they’re nothing more than a “map” of the problem.

Not just any map, but a clear  and rigorous  map. 

We’re gonna achieve those two goals by using a principle called “MECE”. (Don’t worry about it now, we’re gonna get you covered later on).

So suppose you’re an executive in a Telecom Company in charge of B2C mobile services (that is, cell phone services for regular people like you and me).

Imagine you have a client retention problem. That means too many clients are unsubscribing for your services/plans. 

How would you figure out what’s causing this problem?

Well, a smart executive would build a “map” of all the possible things that might be going on. This map is your Issue Tree and “the things that might be going on” are your hypotheses.

I’ll show you one of these, but before I do that, I will ask you to do one 15-second task:

**Action step: grab a piece of paper and make a list of all the hypotheses that pop-up into your head of why customers might be unsubscribing for this Telco’s mobile services.**

Now, take a look at this Issue Tree.

If I did my job right, every hypothesis you had fits one of the “buckets” in this tree.

How do I know that?

Well, I used the MECE principle I mentioned above to build this tree. This means every “part” of the problem is here and that each “part” is different/independent from each other. 

We’re gonna get back to this later.

The second thing to notice is that there are probably whole categories of problems you didn’t even think of when you wrote out your list of hypotheses.

You’ve probably thought about customers hiring a competitor service because they hate us for a variety of reasons (unreliable service, poor customer service) and you’ve probably thought about them leaving us because they were lured by competition somehow (low prices, free phones).

And if you’re savvy on the telecom industry, you might have even though about customers moving to pre-paid services.

But if my intuition is good, you have probably forgotten about at least a couple of categories within the “They’re being forced out” branch. 

For example, you might’ve forgotten to think that they may be cancelling subscriptions on purpose because they’re leaving a market.

Simple – I’ve done thousands of cases with hundreds of candidates to consulting jobs and most people forget about those.

The third thing to notice is that I didn’t even mention any specific hypotheses that you might have written on your piece of paper, things such as:

• We’ve increased our prices and our competitors have dropped theirs
• There were failures in our billing provider and a bunch of people were overcharged and got mad at us
• Our network was down for several days due to a problem within our IT systems, leaving people offline
• A problem in the banking system caused us not to receive several payments, which triggered subscriptions to be cancelled automatically

But still, all of these hypotheses (and thousands of others) would fit into one of the eight categories at the right-end of the Issue Tree.

All of this is to say that an Issue Tree is a map of the problem you have to solve.

Just like a good map it covers the whole problem area (you wouldn’t want a map of just a part of the territory you’re exploring).

And just like a good map, it doesn’t go into the slightest details (the specific hypotheses), but focuses on the broad aspects of your problem  (the categories).

No adventurer should explore a territory without a good map.

And no smart problem solver should start solving a problem without a good Issue Tree.

Issue Trees are the tool for "dividing and conquering"

Issue Trees are more than a mere map. They’re a very useful one at that.

For those of you who are not warfare strategy geeks like me, “divide and conquer” is a military strategy based on attacking not the whole of the enemy’s forces at once, but instead, separating them and dealing with a part of their forces one at a time.

It’s much easier to deal with one cockroach a hundred times than with a hundred cockroaches at once (sorry for the nasty imagery for all cockroachofobics out there).

Anyway, this strategy goes back into the times of Sun Tzu (the ancient Chinese philosopher who wrote “Art of War”).

And it so happens that this “divide and conquer” strategy is not only good for dealing with military opponents, but also GREAT for dealing with Big, Hairy, Complex problems.

It’s very difficult to deal with a “customer retention problem” like our Telco Executive is facing right now without making this problem more specific first.

But if you try making it more specific without the help of an Issue Tree (or a “problem map”), you’re gonna end up with one of two things:

(1) An incomplete list of possible hypotheses (like the one you probably wrote down on your piece of paper)

(2) A HUGE list with hundreds, even thousands of hypotheses (which, at the end of the day, you don’t even know if it’s complete anyway)

Issue Trees allow you to divide the problem and work on it one part at a time.

Or, if you’re a Telco Executive like our friend from point #1, you can delegate this work to other people now that the problem is neatly divided.

Here’s an example of how you can divide the problem into tasks and delegate its parts:

On the left side are the 8 buckets at the end of our Issue Tree. These are the eight potential problem areas.

And in orange are the six tasks our executive must do to know what’s causing the problem. 

Many of them are actually just requests to other people within the company because when you use “divide and conquer” you get to give work to other people (which by the way, it’s a great way to grow your career quickly).

Depending on what they find Task #1, you may be able to stop there. Or you may need to do all 6 tasks and then some more as you find new, unexpected information.

Now, I know that this Telco Executive doesn’t seem like a really good professional when I put the Issue Tree and the tasks that way. He doesn’t even know the basics about what’s going on in his company!

But let’s pretend for a second that he was just hired and he’s not at fault for not knowing his company’s basic numbers.

Or that he’s actually a management consultant instead of an executive, and that he was hired to give this company’s executives an unbiased perspective of why customers are leaving.

Now things make more sense!

But the point is that the Issue Tree allows you to create a plan to solve the problem, just like a map allows you to create a route to get from Point A to Point B.

Issue Trees are excellent for prioritization

Not only Issue Trees let you have a “map” of the problem and help you create a “route” on how to solve it, they also give you the ability to anticipate a lot of stuff that could happen along that route.

And anticipation = prioritization.

(Or 80/20, for those of you who love the buzzwords).

Because Issue Trees lay out the underlying structure  of your problem, they help you with two things:

(1) Get data structured in a way that helps you quickly find out where the problem is

(2) Anticipate what happened with a moderate to high degree of confidence even before you get data.

Let’s tackle each of these individually.

(1) Issue trees help you get data structured in a way that’s helpful to prioritize the problem.

Suppose you’re the Telco Executive and you’ve built your Issue Tree.

Remember how his Task #1 was to ask the Business Intelligence unit of his company for hard data about what’s going on?

Let’s assume they came back with the data below – how would you prioritize the problem?

The way I see it:

Of the 6.5 thousand extra people who unsubscribed this year compared to last year, the vast majority came (4.5) from a system failure. This is not acceptable and this should be the area this executive should tackle first.

But there’s also another area that calls my attention: our biggest source of customer churn – them going to competitors – has increased from 7k per year to 10k per year.

This person (and the company) has two different problems, and getting data in a structured format via the Issue Tree makes this very clear.

(2) Issue Trees help you make a really good guess of what might be going on even before you get any data

Suppose this company’s Business Intelligence division is not that intelligent and has no data to provide.

In fact, suppose this company has such a problem with data gathering that they can’t get structured data for pretty much anything.

This would make this problem a nightmare to solve.

With no structured data, this exec (or his subordinates) would need to do a lot of legwork to test each category of hypotheses:

• To know if customers are hiring a competitor service, we’d need to call a large sample of them and ask
• To know if a problem in our processes caused customers’ subscriptions to be accidentally cancelled, we’d need to map out all our processes that could’ve caused that and evaluate each one individually

You get the idea!

But Issue Trees are a map of the problem. And as any good map, we can use it to see what parts of the terrain seem to be more important than others.

Here’s an example of how to do that even if you have no data:

Obviously you need to use logical reasoning and a bunch of assumptions to prioritize one of these categories as more likely than others. 

But in the absence of data that’s actually the best way to work!

So if I were this executive and there was no data, I’d try to work smart and start testing the most likely hypotheses.

This means I’d give more priority to the ones related to customers leaving us willingly. 

It customers were being forced out we’d have crazy call centers full of customer complaints and the executive would probably know about it already. We’d probably have some lawsuits already!

I won’t go into the weeds of how to prioritize as we already cover that in our courses (including our free 7-day course on case interview fundamentals) but for now it’s cool to know that Issue Trees are the tool  that enables you to prioritize effectively because it gives you a clear map of the problem.

You can have "problem trees" and "solution trees"

Last thing about Issue Trees that you must know to grasp what they are even before we can go into the specifics on how to build them is that you can have “Problem Trees” and “Solution Trees”.

Or, as I like to call them, “Why Trees” and “How Trees” .

“Why Trees”, also known as “Hypothesis Trees” are the one we’ve been working with so far.

You have a PROBLEM and you want to know WHY it’s happening. Then you create a tree with all categories of HYPOTHESES of why it happened.

Just like we did with our executive trying to fix the customer retention problem he is facing.

(By the way, this is why you can call them “problem trees”, “why trees” or “hypotheses trees”.)

But you can also use Issue Trees to map out SOLUTIONS.

This makes them really useful.

A consultant who can figure out what’s causing a problem every single time is a pretty good asset to the team.

But to have a consultant that not only can do that, but who can also figure out the best solutions to those problems every single time  is even better!

So let me show you how a “Solution tree” or a “How tree” is different from a “Problem tree”. 

Suppose our Telco Executive character did NOT have a customer retention problem. Everything is fine and clients aren’t unsubscribing from this company’s services more than the normal rate.

But, naturally, they still have some level of customer churn.

Let’s say that they want to make that level even better than it is today.

And then the executive team gets together for a meeting to “brainstorm” some ideas on how to reduce customer churn rates so they can grow revenues more.

What most people in this meeting are doing is to throw ideas on a whiteboard.

• “Hey, perhaps we can improve our customer service.”
• “Hey, maybe we should offer faster internet.”
• “Hey, what if we put people into long-term contracts?”

But our Telco Executive is smarter than that. He has learned how to make Issue Trees with his friend, a McKinsey consultant. And he puts his learnings into practice.

**Action step: grab a piece of paper and build an Issue Tree with the CATEGORIES of potential ideas/solutions  this company could have to improve their customer retention.**

Now, word of warning: this “solution Issue Tree” is NOT perfect.

If you try, you can probably come up with an idea that could improve customer retention that doesn’t fit any of these categories.

And the reason for that is that it’s much harder to map out all types of possible solutions to a problem than to map out all types of possible causes to a problem.

But in case you do come up with an idea that doesn’t fit any of these categories, you can easily abstract what “type” of solution is this and then create a category for it.

Now, you might be thinking – “Bruno, why do I want to use Issue Trees for mapping out types of solutions? Why not just Brainstorm freely?”

There are three reasons for that:

(1) Your ideas are gonna be way more organized

This helps you communicate your ideas with others.

And it also helps you organize everyone’s ideas into a coherent whole.

And then better prioritize those ideas and even “divide and conquer” the implementation of them. You know, all the good stuff Issue Trees allow you to do.

(2) Creativity from constraints

This is counter-intuitive, but bear with me.

There’s significant research showing that having some constraints make people MORE creative, not less. (You can see some of the core ideas here ,  here and here .)

And we know that intuitively!

Well, try to create a short story in your head.

Nothing comes to mind, right?

Now try to create a short story that involves an English guy, a French woman, a train trip and a few bottles of wine.

It’s actually easier  to do the second, even though there are many more constraints.

Now, if I ask you to generate ideas on how to improve customer retention in a Telco company you’ll probably be able to generate 5-7 ideas until they start to become scarce.

But if I ask you to generate ideas on how to improve customer service in a Telco you’ll also  be able to generate 5-7 ideas until they become scarce. Even though improving customer service is just a sub-set of the things you can do to improve customer retention.

And then I could ask you to generate ideas on how to make it financially costly to unsubscribe and you might be able to give me a few ideas as well.

Each of the last two questions was a branch of our issue tree from above.

And because our Issue Tree above has 7 different branches, if you’re able to generate 5 ideas for each, that’s 35 ideas!

I’ve never met a person that can generate that many ideas with just the prompt question (how to improve customer retention) and without building an Issue Tree first.

Our brains seem to get confused with that many ideas.

But if you add structure (forced constraints), you can think freely about each part without worrying about missing something.

Which leads me to the 3rd reason why you will want to use “solution Issue Trees” whenever you need to brainstorm ideas…

(3) They force you to see whole categories of ideas you wouldn’t have seen before.

This takes a bit of practice, but once you’re able to see how each category fits the whole, you might see parts of the whole that you weren’t even seeing before.

Take the “Make it costly to unsubscribe” category for example.

When I came up with it, I was thinking about financial costs. You know, contracts and stuff.

But when I saw the word “financial” coming up in my mind, I immediately noticed that there could also be “non-financial” costs, such as having to go to a physical retail store to cancel the service or losing your dear phone number that you had for 8 years and all your friends and business connections have.

I didn’t have these “non-financial costs” ideas before I create the category for them.

Which is another big advantage for using Issue Trees to come up with solutions for your problems. You can see the larger picture.

So, what’s our take away from all this?

Simple. Issue Trees are a “map” to your problem that help you prioritize what’s important and “divide and conquer” to solve it more effectively. 

And you can use them to map out solutions as well.

Oh, and by the way, I almost forgot…

One really powerful thing you can do is to use “Problem Trees” to find the problem and once you found it, use a “Solution Tree” on your newfound problem.

So, remember how we used a “Why Tree” to find out that one of our Telco Executive’s problems was that his customers were leaving to the competitor?

Now we could use a “How Tree” to figure out potential solutions to stop our customers from switching to the competitors even though they don’t really like us and the competitor is offering a better offer than we are.

I’ll leave this Issue Tree for you to build.

And you’ll be able to build it using the techniques you’ll learn in the next chapter!

Three Techniques to Build Issue Trees

You can have all the theory in the world, but if you don’t put it into practice you’re not gonna solve any of the world’s toughest problems (nor get a job offer at McKinsey, BCG or Bain).

In this chapter we’ll go deeply into the mechanics of how to build quality Issue Trees.

More specifically, we’ll go through three practical techniques that you will be able to apply in your next case interview or executive meeting to structure any problem.

The structure of an Issue Tree

Issue Trees are a “problem structuring” tool.

That means you can structure problems using them.

But even Issue Trees have an underlying structure to them. It gets a bit “meta” and abstract, but the point is that every Issue Tree shares some similarities with other Issue Trees.

Knowing these common characteristics is the starting point to being able to successfully build them, so I’m gonna go over that in this short section.

And I’ll be quick, I promise.

(Note: I’m gonna give names to some stuff so that you and I can talk more effectively over the rest of the guide, but you don’t have to memorize those names nor use them in case interviews.)

So we seem to always keep coming to this MECE thing, don’t we?

We have a whole article series on that , and I highly recommend you to go through it. 

You can do so right now and then come back to this guide or you can read this guide first and then go there to understand how to make each part of your Issue Tree MECE.

Now, I don’t want to break your reading flow here…

So, before you open a new tab on your browser and get into another rabbit hole, let me explain what MECE is in simple terms.

MECE means Mutually Exclusive, Collectively Exhaustive and it is a basic principle of organizing ideas that was popularized by ex-McKinsey Barbara Minto (from the book on the Pyramid Principle, you might have heard of that) but  goes back to the ideas of Aristotle  (yes, the greek one!).

It basically means your reasoning has no gaps (Collectively Exhaustive, all parts together exhaust the whole) and no overlaps (Mutually Exclusive, one part is different and independent from the other).

Easy, right?

Well, kind of. Most problems out there are harder than drawing rectangles. 

So, to give you a better idea of how to apply the MECE principle to a business problem, here’s an image from our article on  The 5 Ways to be MECE  of different MECE ways to break down the same problem:

No need to worry about understanding this whole image right now, but the idea behind it is that (i) there are 5 types of ways to break down the problem in the image’s title (or any other problem) in a MECE way, and (ii) you can build different structures within each type.

An Issue Tree is built using a lot of these MECE structures. You also need to know how to pick among different options when you find more than one way to break down a problem..

I’m gonna link to the article on the 5 Ways to be MECE again  because it’s the best way to learn about MECE in a practical way. Instead of a bunch of theory, I show actual techniques you can apply right now to any problem in that article.

Anyway, enough with MECE. Let’s jump into the actual techniques to build Issue Trees.

Technique #1: Create a Math Tree

Math Equations are ALWAYS MECE.

Equations have no gaps and no overlaps (otherwise they wouldn’t be equations).

Which is why I used rectangles within rectangles to explain MECE above. Rectangles are huge in mathematics if I remember my high school math right.

Anyway, one easy way to create MECE trees is to take advantage of that and ALWAYS break down the next level using a math equation.

Obviously you can only do that if your problem is numerical.

But since most business problems are  numerical, we’re in luck!

I’m gonna show you how to do this in a “slideshow” kind of way because I wanna show you in a very step-by-step fashion, so be prepared to click on the arrow button more than a few times:

Creating math trees as a way to create Issue Trees isn’t hard at all once you get some practice.

But some of its nuances can be deceiving. Most people see them done and think they can easily do it, but it all goes downhill when they actually grab a piece of paper and attempt to do these trees.

So, here are four methods to actually create your “mini-equations” to break down each bucket:

#1. Use a proven formula

Most of the time you don’t need to reinvent the wheel.

If you know a formula that fits the problem well, just use it!

The most common one here is the classical Profits = Revenues – Costs, but there are others as you can see on the image below…

You don’t need to memorize any formulas for your case interviews, as you can use the other methods and they will work.

But knowing some of these, especially the most basic ones does help a lot.

#2. The "Dimensional Analysis" method

This one’s my favorite!

Just find one direct “driver” of the variable you want to break down – a driver is a “fundamental cause” for that variable.

For example, one direct “driver” or “cause” of revenues is the “# of customers” you have. If you get more customers, these new customers  directly cause your revenues to increase.

Then, use dimensional analysis to find its mathematical complement. If you want “REVENUES” and you have “# OF CUSTOMERS”, you need to multiply that by REVENUE/CUSTOMER.

Just like in your high school physics class, customers on the numerator will cancel out with customers on the denominator and you’ll be left with REVENUES as a metric – exactly the one you’re aiming for.

This method is amazing because it lets you break down almost any metric into a formula really quickly – the only thing to be careful with is to not lose meaning in the process and end up with a formula that is mathematically right but doesn’t make any sense to actual human beings.

#3. The Funnel method

This works wonders when the target metric is a percentage or is the end result of a funnel.

Take one example from e-commerce: Conversion Rate.

This is the % of visitors in your website that buy from you. How can you break that down?

Simple, you multiply the steps of the funnel from visitor to buyer.

Funnels are everywhere: Sales, Product Development, Process Optimization. 

All you have to do is to find these funnels and then break them into stages.

#4. Use a sum of segments

This is my least favorite method because it doesn’t go too much into the structure of the problem, but simply slices it out.

However, it can be useful.

For example, if you’re working with a conglomerate and their profits are down, it might be useful to segment that conglomerate into its different businesses.

Or if you’re trying to understand a company’s market share drop in a certain category, it might be useful to just break it down into the market shares of its product lines.

If you’ve read  the article on the 5 Ways to be MECE  and you’ve been paying attention, you might have noticed that method #1, “Using a proven formula” and #2, “Dimensional Analysis” will get you an Algebra Structure. 

Method #3, “The Funnel Method” will get you a Process Structure. 

Finally, method #4, “Sum of segments” will get you a Segmentation type of structure.

If you haven’t read the article, don’t worry about these names – they are some of the ways to be MECE we teach there. I’m just helping the folks who did read it already to make the connections.

So, summing up. You can use any of these four methods to create a “mini equation” and you combine these “mini equations” to create a “Math Tree”, which is the first technique to build and Issue Tree.

And it’s a technique that works great with numerical variables, but doesn’t really work if you have a different type of problem to solve.

So, to tackle non-numerical problems – or even to make better  Issue Trees for numerical problems – let’s move on to the most powerful technique in your Issue Tree toolkit: layering the 5 Ways to be MECE.

Technique #2: Layering the 5 Ways to be MECE

Technique #1 works great because math is ALWAYS MECE and because creating equations isn’t too hard.

But not every problem is numerical and can be structured using equations alone.

And even to those problems that are numerical, doing a Math Tree isn’t always the best way to go about structuring them.

Here’s where Technique #2 comes in – instead of layering “mini equations” on top of each other, we’re gonna layer “mini MECE structures” on top of each other, regardless of them being equations or not.

Remember, we were confident to use math equations to build Issue Trees because they are always MECE. But from first principles what we need is MECE structure, not necessarily mathematical ones.

And where are we gonna find these “mini MECE structures”? 

Easy, with the 5 Ways to be MECE. These are 5 specific techniques we’ve developed that guarantee a MECE structure.

I’ll make your life easier in case you want to read about that now and link to  the article  we wrote about them.

But here’s a quick recap:

The process of building Issue Trees by layering the 5 Ways to be MECE is itself very very similar to the process to create Math Trees.

Step #1: Define the problem specifically  (no need to be a numerical variable here).

Step #2: Break down the first layer using one of the 5 Ways to be MECE.

Step #3: Get to the 2nd (and 3rd, and 4th) layers by breaking down each bucket into another “mini MECE structure” that comes from the 5 Ways to be MECE as well.

I’ll show you the exact process to create an Issue Tree by layering the 5 Ways to be MECE through the example below:

Layering the 5 Ways to be MECE is my go-to method to create Issue Trees and break down problems or finding solutions.

I use it every day of my life, either on paper or just in my head.

And I used to use it everyday when I worked at McKinsey as well (even though I was doing it unconsciously – no one there had explicitly told me there were five  ways to be MECE).

Now, let me address one thing that comes up often… One thing that may have crossed your mind as you were going through the three steps above regarding the Issue Tree is “well, but this is so obvious” .

That thought may have crossed your head in each break-down of a bucket or just when looking at the whole Issue Tree.

And here’s my take on it: a well-structured problem SHOULD look obvious – at least in hindsight .

How Elon Musk changes the world structuring problems in "obvious" ways

(I swear to you it’s interesting, but you can skip this green box if you want and/or understand why MECE Issue Trees are super important even when they’re “obvious”)

You’ve probably heard of Elon.

In case you haven’t, he’s this guy…

And he’s created these companies…

So, the guy basically transformed the payments industry, the automotive industry, the aerospace industry and is transforming the tunneling and the solar power industry.

But how does he do that?

Well, anyone who does that much has many “secret sauces”, but one of the special things Musk has is to think things from first principles.

In this fantastic blog post  (from one of my favorite blogs), a guy who had access to Musk breaks down exactly how he thinks.

But let’s analyze one specific instance: how he came up with “The Boring Company”, a company that was created to dig tunnels more efficiently and solve the traffic problem in Los Angeles.

There are two underlying logics to the company:

Simple logic, but a really strong reasoning about why tunnels are probably the best way to solve the traffic problem.

(And it actually is the only way that’s ever worked so far – demand for roads keep increasing no matter how many Uber rides people take, building more roads doesn’t seem to make a difference in most cities and no one’s ever been able to make flying cars… But most people in large cities take the subway/metro system every single day.)

Notice that we’re basically dividing the problem into supply and demand and then dividing “road” capacity into on ground, flying and underground. 

There’s no rocket science here (pun intended).

Alright, but there’s still a problem with tunnels: they’re expensive to make. So, is it possible to make them cheaper? Here comes Elon’s Logic #2 to build The Boring Company:

Again, no rocket science here (although a bit of tunneling science).

If you want to understand better how Musk thinks, I recommend  this article  and  this TED Talk .

Now, onto what matters for us: 

(1) Most traffic specialists know that trying to reduce demand is an uphill battle and that expanding road capacity is mostly fruitless.

(2) Most people in the auto/aerospace industry know that flying cars are a very far away dream

(3) Most people in the tunneling industry understand the cost drivers of a tunnel.

And yet, no one looked at the big picture and questioned things from first principles.

You need an Issue Tree to do that, even if it’s an obvious one.

I’m not saying Elon Musk draws Issue Trees for a living, but I know  he has them in his head because he talks like he has one – I “took” both trees I showed you above from his own words.

Takeaway from the green box: Issue Trees are “obvious” because they’re drawn from first principles.

And this means if you want to think from first principles, draw Issue Trees.

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Technique #3: creating decision trees.

In the realm of Microsoft Excel, the most basic kind of logic you can do is using math operators. That is,  adding, subtracting, multiplying and dividing.

If you wanna go a step further you can use what they call “boolean operators”: AND functions, OR functions and so on.

And if you want to go a third step further, you can use “conditional operators”, the most famous of which are IF functions.

Decision Trees are basically regular Issue Trees with “conditional operators”, IF-THEN functions.

Now, let me translate into plain English for all the non-Excel nerds out there…

(Or should I say “future Excel nerds? I mean, this is a site for aspiring management consultants!)

When you do a Math Tree, the only way you have to relate the variables to each other is through math symbols. E.g.: Revenues = Price * Quantity. There is a mathematical relationship among everything in your Issue Tree.

It is great to have math because math is always MECE, but it is also limiting. What about everything that can’t fit an equation?

Enter Technique #2: Layering the 5 Ways to be MECE.

If you pay attention to it, everything that’s not in a mathematical relationship in that technique is joined logically by “AND” or “OR” relationships.

For example, we can find better employees ‘at the schools we already recruit in’ OR ‘in new schools’.

Another example, we can make new recruits better before their first project ‘by training them before they start’ AND/OR ‘as soon as they start working for us’.

Decision Trees are just like regular Issue Trees but they add another layer of logic to it: IF-THEN statements.

I won’t go into too much detail on how to build them because (1) it’s an advanced skill to be able to anticipate all the if-then logic required to take a decision before you even start exploring the problem, and (2) you don’t need to be able to do this to get a job at McKinsey, BCG or Bain if you can use the other two techniques well.

But I will give you a simple example below so you can see what I mean.

And if you want to learn more about this,  here’s a timeless article from Harvard Business Review on Decision Trees.

There are also different types of decision trees.

For example, you can create a decision tree for an investment opportunity that considers the probabilities of different events to happen in order to calculate the expected value (there’s an example of this in the HBR article I’ve shared above).

Or you can create decision trees for WHY and HOW problems where you use IF-THEN statements to say where would you focus and prioritize if certain conditions applied.

(An example of the last phrase is this: in a case on “How should a restaurant grow revenues”, you can say that IF it has lines/too much demand, THEN you would focus on increasing capacity through expansion or increased productivity, and that IF if doesn’t have enough demand, THEN you would focus in customer acquisition and retention initiatives.)

Decision Trees can get really complicated even for simple decisions, so I would NOT recommend you to start learning with them. 

Focus on Techniques #1 and #2 to solve WHY and HOW problems.

For “decision-making”-type problems, we recommend you to learn Conceptual Frameworks first. We teach how to structure these problems using Conceptual Frameworks in our free course on case interview fundamentals.

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Six Principles for AMAZING Issue Trees

Man does not live by bread alone.

And Issue Trees need more than being “technically correct”

If Issue Trees had a “soul”, it would live in the six principles outlined in this short chapter.

In fact, if you follow the principles from this chapter, you don’t even need to use any of the three techniques I showed you on the last chapter.

And if you MASTER these principles, you might be able to come up with your own techniques. 

(And if you do come up with a “fourth technique”, please shoot me an e-mail telling me about it).

Separate different problems early on

Some restaurants that want to grow revenues should work on getting more clients. Others have too much demand and should work on expanding their operations to handle that and sell more.

Most companies that have employee attrition problem have some problem that makes people wanna leave their jobs. Others are just firing too many people.

And a violence crisis in a country could be caused by criminals. But it could very well be caused by a really violent police system as well.

The common factor between the last three situations is that each one could be caused by two COMPLETELY DIFFERENT PROBLEMS.

Separate them early on your Issue Tree because trying to fix the two things together will only lead to confusion. Not good.

Build each part ONE AT A TIME

Most people who see a huge Issue Tree for the first time are overwhelmed.

Of course they are! 

They see this huge logical structure (that takes time to digest) and wonder if they’ll be able to do the same when they need to.

What they’re missing is that these trees are built one step at a time .

First you get the problem question and your only concern  is to define it well.

Then your only concern  is to break it down into a first layer.

Then you get each bucket from the first layer and your only concern  should be to break each down into a “mini MECE structure”.

One bite at a time, you will eat the whole metaphorical elephant.

Each part must be MECE

I’ve talked about MECE before in this article, but I’ll do it one last time.

ME = Mutually Exclusive =  No overlaps  between the parts of your structure = your structure is as clear as the blue sky for another person to understand.

CE = Collectively Exhaustive =  No gaps  in the way you break each part of your structure down = your structure is rigorously correct.

MECE is tough for most people, but you can use  the 5 Ways to be MECE  as a checklist of structures you can use to be MECE. 

That means it’s not gonna be as hard for you and you have more chances of getting the offer than the other people. Good for you!

Each part must be relevant and add INSIGHT to the problem

There are many MECE ways to break down any problem.

Choose the one that’s more relevant. The one that adds more insight to the problem.

For example, one of the Issue Trees from Chapter 2 was about improving the quality of new recruits in a consulting firm. Within “making the selection better”, I could’ve broken it down into “Stages 1, 2, 3” and so on of the selection process. 

That would’ve been “technically correct” and “MECE”, but it would bring absolutely no insight to the table. 

Because it wouldn’t be problem-specific .

Here are two resources to help you make your structures more insightful and problem-specific:

The first is  a Youtube video on how to make better revenue trees.  It shows how to create more insightful revenue trees but you can apply the same principles to any type of Issue Tree.

The second is “The Toothbrush Test”, a numerical measure so you can get a proxy of how insightful one structure is compared to another. You can watch the video  here  or read the article  here .

Each part must be eliminative and help you FOCUS to the problem

An Issue Tree that is built in a way that allows you to ELIMINATE all the non-problems and focus on the one thing that’s driving the issue is way more useful than one that does not allow you to do that.

Say you’re a soft drinks company concerned that you’re selling less soda.

Here are two ways to structure the first layer of that Issue Tree:

(1) Drop in general soda consumption OR Drop in market share

(2) Customers less willing to buy product OR Competition getting stronger OR Company doing poor marketing or supply chain OR Distribution channels not exposing our product

Which one’s better?

Well, according to this fifth principle, (1) is better because it allows you to get data and eliminate a whole branch (unless the problem comes from both, of course).

Eliminative Issue Trees help you FOCUS the problem and waste less time (that means more 80/20 for you).

The key to be eliminative is to make each bucket FALSIFIABLE. 

Falsifiable means you can find a test that, given a certain result , guarantees that the problem is not on that bucket.

This falsifiability is what makes Issue Trees “hypothesis testing” structures. If you want to be a hypothesis-driven problem solver you need to include falsifiability in your structures whenever you can.

However, this does not mean every single structure  you create must follow this principle.

There are times where falsifiability is impossible , and that means you should focus your efforts in being the most insightful as you can (Principle #4).

It is usually in these situations where you’ll want to use a qualitative, conceptual framework. You can learn more about this in the free course we offer on case interview fundamentals. In the Frameworks module of the course we will show you exactly when to use conceptual frameworks and how to create them.by 

Clarify what you need in each layer you build

You might be shy, but hey, overcome that shyness!

You don’t need to do guesswork to build your structures. You can ask first.

Actually, doing guesswork when you could’ve asked a simple question and eliminated confusion will harm your performance.

Say you’re breaking down how a consulting firm could hire better junior consultants. You’re trying to break down how they select candidates, but you’re not sure how their recruiting process is currently like…

Say to your interviewer: 

“Hey, I want to break it down into the stages of the selection process but I don’t know what those stages are. Here’s what’s on my mind… Does it make sense or did I miss something?”

If you’re doing Issue Trees to solve a problem in your work, this principle is even more important. You can’t structure what you don’t understand, so when in doubt ask questions and understand it better!

Sometimes these principles will enter in conflict with one another.

You might need to choose between being more eliminative and being more insightful.

You might feel in doubt of whether you should be fully exhaustive (MECE) or just add the relevant stuff.

And when principles enter in conflict, experience and judgement are here to save the day. 

Seeing real examples of real people that know what they’re doing making Issue Trees to solve case interview problems is invaluable to get that experience.

Which is why I will show you in-depth examples in the next chapter, including videos of me going through the thought process of building Issue Trees with you.

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When I was preparing for my case interview I looked for good Issue Tree examples all around.

I found none .

I don’t want you to go through the same, so here I’m gonna go all in and not only show you great Issue Trees but also show you, in video, how I think through each step of building them.

I’ll show you everything that goes through my mind as well as the specific nuances that make them great.

I will use different examples so you can see how the principles and techniques apply to different types of situations.

And I will do exactly what I’d do in a real case interview on when solving a real problem at work.

The only thing I’ll avoid doing is using Decision Trees.

Because it’s much much harder to get to a MECE result using them, let alone explain why it’s MECE. I’d be only showing off instead of actually helping you learn how the principles apply and what makes a great Issue Tree. 

Not my style!

Example #1 - Airline fuel costs surge

This first example is of a fairly easy case question that would lead many well-prepared candidates to failure.

It’s funny how some problems can be easy  to real consultants and yet hard  even for candidates who have done 50+ cases.

Here’s why this happens: the business problem isn’t hard to solve from a first principles perspective (which is how good consultants tend to think) but they’re a bit unusual or too specific to an industry. 

Most candidates who haven’t internalized the principles of solving problems well feel overwhelmed when they get a case completely unrelated to anything they’ve seen before.

Even worse is when this problem doesn’t fit the half a dozen frameworks these candidates have memorized by heart.

Here’s a video of this first example. I highly recommend you to try to structure this Issue Tree by pausing the video right after I clarify the case question and then compare your structure and your thinking process with mine.

If you don’t have access to audio or can’t watch a video right now, you’ll be able to keep reading and grasp the main insights as well, although I highly recommend you come back to watch this later!

So, what’s interesting about this Issue Tree example is that I have structured the first two layers of the tree as a Math Tree (Technique #1) and then I used the “Opposite Words” technique and the “Conceptual Frameworks” technique to build layers 3 and 4.

You can do that too!

Here’s the whole Issue Tree if you weren’t able to watch the video: 

There were three main take aways from this structure:

Takeaway #1: Break down a numerical problem mathematically as long as the math remains meaningful/insightful – then get more layers using qualitative “mini-MECE-structures”

As with most thing problem-solving related, this is not a rule written in stone.

There are a few numerical problems that are best structured with a qualitative structure. And you don’t always need to do the qualitative layers afterwards.

But usually the best way to break down a math problem initially is to break it down into an equation first, as you’ll be able to quantify how each driver contributed to the problem.

And usually the equation alone won’t be enough to bring you to the meaningful stuff. 

In this case, for example, if we were only mathematical in our structuring we would have missed important elements that show real world business intuition, such as “maintenance”, “aircraft weight” and “mix of aircraft in the fleet”.

Takeaway #2: Stop each branch when it can reasonably  explain the source of the problem

I have stopped some parts of my tree in Layer 2, other parts in Layer 3 and others in Layer 4.

How did I make this call?

A lot of people have asked me this in the past: how can I know that my Issue Tree is done? How many layers do I need?

The rule of thumb is to stop when your buckets can reasonably explain the problem.

For example, on Layer 2 you have a bucket which is “# of trips flown has risen”. This can reasonably explain why fuel costs might have risen. It’s pretty logical – if you fly more trips, your fuel costs will rise as well.

Now, one could ask “why has the # of trips flown risen” and if that’s the actual problem going on, I as a consultant would want to know that. But that’s getting granular, you don’t need to go that far unless the problem is proven to be there.

If I told my mom or someone on the street that an airline’s fuel costs have risen because the # of trips have risen, they’d accept the answer and probably not question it further (and they certainly would tell me I’m a weirdo for caring about an airline’s fuel costs).

Now, if I told my mom or a random guy on the street that fuel costs have risen because liters of fuel per km flown have risen they would: (1) think I’m really really weird, and (2) not take that answer as it is.

Even if I used more accessible language and said that this airline’s fuel efficiency was down, they’d still ask me “why is it down”? (That is, assuming my mom is actually interested about airlines).

If I had stopped that branch on the 2nd layer, I wouldn’t be telling the whole story. 

And so I went a level deeper.

Now, on the 3rd layer if I say that fuel efficiency is down because we’re using less efficient types of aircraft, most people would be satisfied with that answer. I can stop the Issue Tree here.

But in the case we’re flying the same aircraft, most people would NOT be satisfied. They’d be like “Hey, you’re telling me you’re less fuel efficient even though we’re flying the same aircraft? How come?”

And so we dig a level deeper on that one. Maybe the aircrafts are flying with more weight. Or we’re doing less maintenance. Or we’re flying at lower altitude and facing denser atmosphere. Or our pilots are changing speed all the time. 

Most people would take any of those as sufficient answer. Which means we don’t need to dig a level deeper.

Takeaway #3: You can still go deeper in the buckets you need

If the last take away gives you an idea on where to stop structuring the Issue Tree, this one gives you permission to dig deeper than that.

Say your interviewer tells you the problem is that this airlines is flying their planes heavier and asks why that might be. Well, weight was at the end of our tree, right? But we can still investigate the reasons behind that increased weight.

Here I would segment the things that add weight to airplanes into their categories: people, cargo, equipment, fuel itself (we may be flying with excess fuel and thus spending more fuel to carry fuel itself).

Or say that the interviewer tells you that fuel prices have gone up even though we’re buying the same product from the same supplier. 

Why that might be happening?

Well, either this supplier’s cost has gone up (because crude oil is up in price, for example) or their margins are higher (because we’re not negotiating as well, for example). We could dig deeper into each one of these factors if need be.

The point here is that even though you need somewhere to stop your Issue Tree (otherwise you’d spend the whole day building 15 layers), you also need to be aware that you can go as deep as you need to in the specific parts of your structure that the problem really is.

You find where the problem really is by getting data, numerical or not, for each part of your structure.

Example #2 - Overwhelmed consultant productivity

Real consultants have their own personal problems to solve as well.

And often time they will solve them with Issue Trees!

They’re a great way to see what your options are.

So before you look into this example, I want you to do an exercise:

**Action step: grab a piece of paper and write down all ideas you have to become more productive in case you were overwhelmed with work as a consultant**

What you’ll see from this exercise is that if you just “freely brainstorm” ideas to improve productivity on paper, you’ll end up with a huge list of (probably) unconnected action steps that are hard to estimate impact and to prioritize.

But if you had built an Issue Tree to organize those ideas , you’d get something much closer to an actual system to improve productivity.

Here’s what I mean by that:

This tree is solving a more qualitative problem than Example #1, but the techniques still work.

You define the problem really specifically at first.

And then you layer different “mini MECE structures” using the techniques from the 5 Ways to be MECE.

Here’s the final Issue Tree in case you couldn’t watch the video:

Of course your tree can still be different than this one and still be correct.

How do you know if it’s correct or not?

Well, simple: are you adhering to the key principles? Are you using the techniques I have shown you in this guide?

If so, your Issue Tree is good to go!

Example #3 - Help a government solve illiteracy in children

This is an interesting example because it focuses specifically on Principle #1: Separating different problems early on.

In fact, the whole Issue Tree is built by separating different problems over and over again.

Because the problem to be solved has many different possible root-causes that are completely different from each other.

Once you watch the video, you’ll see that the way the Issue Tree is constructed in a very intuitive way. 

However, give this problem to most people and they aren’t able to structure it. They’ll spit out ideas and hypotheses without order nor an overarching logic.

Check it out how to help a government solve illiteracy in its children that go to public schools:

If you couldn’t watch the video, I’ll put an image of the Issue Tree bellow.

Notice how each layer is basically the previous bucket divided into two completely distinct problems.

The value of building Issue Trees like this is that you get a map of all types of possible root-causes. It’s also pretty easy to do so!

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Common mistakes and questions.

I’ve helped hundreds of people learn to build Issue Trees.

In the process I’ve seen them making thousands of Issue Trees. And probably somewhere north of tens of thousands of mistakes.

Making mistakes if part of the learning process.

But you don’t have to make all those mistakes yourself because you can learn from theirs!

In this chapter I will show you the most common mistakes people make (with real Issue Trees, from real candidates) and also answer some of the most common questions that arise as you learn to build them.

What you can learn from the key mistakes of real Issue Trees from real candidates

When I first wrote the  5 Ways to be MECE article  I had a little challenge in the end of it.

I challenged people to send me a structure for a specific business problem that could happen in a case interview: 

“Imagine you’re doing a project with Amazon and they’re complaining about a surge in theft in their warehouses – what could be causing this surge in theft?”

And so I got dozens and dozens of real Issue Trees from real candidates for the same problem.

What’s fascinating is that all these candidates had three things in common:

(1) They were having trouble with creating MECE structures for their cases (or else why would you read a huge guide on how to be MECE?).

(2) They had just read a huge guide with different techniques to be MECE and instructions on how to build Issue Trees using these techniques.

(3) They were dedicated enough to take my challenge, spend 10-20 minutes building their best Issue Trees and sending them to me.

Still, even with all those things going for them, most of their Issue Trees had mistakes. Mistakes you and I can learn from.

So in this section I’m gonna show you their trees, point out their key mistakes and show you the feedback I sent them.

#1 - Anastasia and the sin of ignoring problem definition

The first Issue Tree I wanna show you was sent by Anastasia.

Here it is:

Seems like a quite good Issue Tree, right? 

I mean, it describes quite well the process of a warehouse.

Well, not quite.

There are a few mistakes that this Issue Tree makes in terms of MECEness, some parts could be more insightful, etc. But the most important mistake here is that Anastasia ignored the specificity of the problem.

Much of this Issue Tree isn’t about theft – it is about losing items in general. So she’s talking about damage, negligence, machine mistake, etc.

Go back to the image above and click the right arrow to see all the areas of this tree that are not about theft at all.

Most of the tree is not talking about theft at all!

What that means is that she’s talking a lot about things unrelated to the problem and leaving a lot of important things out. It also implies that she wasn’t listening to the problem.

This is the #1 thing I’d tell Anastasia to focus on and the #1 thing I’d tell you to make sure you’re not messing up.

Now, Anastasia’s structure also has a #2 thing that I’d tell her to focus on if problem definition weren’t a problem: look for root causes. 

While she makes an excellent description of how the warehousing process is and thus is able to map out where  the problem might be, she never talks about the why.

You know, things like security systems and lack of penalties and having warehouses in areas with a lot of crime. The types of things you might expect for a WHY question…

#2 - How Anne messed up with layer ordering

This Issue Tree is actually quite good!

But it has three main mistakes. Can you guess what they are?

Well, I gave you the main one in the title.

Anne’s first layer shouldn’t be a first layer. 

Because geographical location is not all that important. The different geographical areas of the problem aren’t the most relevant way to break it down.

What’s more, even if it were, why divide by continent? Why not small vs. big cities? Or low income vs. high income areas? Or high-crime vs. low-crime areas?

Anyway, I think it’s an excellent idea to mention that you’d like to see in which warehouses is the problem more prevalent. But what I would’ve done is to put that as a side note to an Issue Tree that actually digs into the potential causes of the problem, not as the main course.

She could’ve done an Issue Tree of causes for one  warehouse and then said at the end: “and then I’m gonna look at these causes for all warehouses we have, segmented by geographical area, warehouse size, how old they are, etc”.

And what would this Issue Tree that digs into the potential causes look like? 

Well, very much like Anne’s example Issue Tree for American warehouses (which I guess she would replicate for other continents as well).

Now, you might be thinking: what are the other two mistakes she made?

Well, one is that she offered solutions to each root-cause of the problem. That’s not a mistake in itself. In fact, I loved it. But the problem is that she was a bit too early on that – she should’ve gone a layer deeper into the why  each thing happened.

Keep in mind the case question was a WHY question and not a HOW question. 

And what she did was to suggest, for example, that if internal thieves who had the intention of stealing were responsible for the surge in theft, then they should run better checks.

What she should’ve done instead was to say that if that was the cause, then that caused happened because (a) they’ve stopped doing background checks, (b) background checks have worsened in quality or (c) background checks were never good at stopping that but that was never a problem beforehand. And then perhaps dig even deeper into the cause.

But she offered solutions before she got to the root cause, and that may hurt because she may be solving the wrong problem.

And the last mistake she did was one related to problem definition.

Everything she mentioned was related to the amount  of theft. But we don’t know if that’s the problem. It’s not clear on the case question (on purpose). Maybe the problem is the value  stolen.

So, she would’ve done much better by showing that in her structure. Maybe there are more thefts (in which case her issue tree is valid) and maybe the amount stolen per theft is higher (and because she didn’t consider this, she missed a whole part of the problem).

#3 - Guillaume and the "aggregator fallacy"

There are many problems with the Issue Tree below, for instance:

• A regional segmentation early on when that’s not a really relevant factor to explain the problem (as in Mistake #2)
• This regional segmentation isn’t even MECE (there are emerging countries in Europe and he forgot all developed countries in Asia)
• A lack of $ value of theft (again, as in Mistake #2)
• The way he breaks down a process structure to explain a surge in # of thefts per warehouse isn’t very insightful/relevant

But I want to call your attention to one other mistake which is related to causal effects. I call it “the aggregator fallacy”.

Can you spot it?

Let me ask you one thing… If the number of gas stations raise in a city by 2X in a year, will sales of gas increase by 2X as well?

Will they even increase by 10 or 20%?

Not necessarily!

More gas stations don’t drive  more demand for fuel (unless there’s very few, high priced gas stations in town, but let’s leave extreme scenarios aside).

Yes, there might be 2X the number of gas stations because demand skyrocketed. But it could also be the case that gas stations were a really profitable business and entrepreneurs entered this market even thought there was no increase in demand. 

It could also be the case that some people who don’t know what they’re doing entered the market even though demand didn’t increase and profits weren’t that high (and everyone’s losing money now).

So if you were to find out if demand for gas increased in a town one MECE structure you could use is “# of gas stations * avg. amount of gas sold per station”, but that wouldn’t be the best one.

Because # of gas stations don’t drive  demand – more cars and more usage per car does.

The same thing is happening with Guillaume’s structure. 

More warehouses don’t drive more theft. They don’t cause  more theft.

Say, for example if Amazon had restructured their operations and they had switched from 10 huge warehouses to 100 smaller ones, with the goal of having faster delivery. Would it be ok for theft to increase 10X? Would it even be ok for it to increase by 50 or 100%?

Probably not, right? 

Amazon’s carrying the same number of items, they have roughly the same number of employees (considering internal theft) and if they have their security systems in place, they’re not necessarily more attractive to external burglars (if anything, it’s harder to steal a smaller warehouse than a huge one).

More warehouses shouldn’t cause more thefts. The warehouse is not a driver of stealing just as the gas station is not a driver of demand for gas.

The warehouse and the gas station are merely aggregators  of something. The warehouse aggregates products to be shipped (or stolen) and the gas station aggregates fuel to be sold (or not sold in case of a flat demand).

Which is why I call this mistake “the aggregator fallacy” – thinking that because the aggregator has increased that it has caused your problem.

Instead, try to build your Issue Trees with some causal relationship in mind. In the case of the gas station problem, that’d be “# of cars * fuel used per car”.

In the Amazon theft case, you could use “# of products in the warehouse * theft rate” if you assume that more products cause more demand for burglars or “avg. crime rate where Amazon warehouses are located * % of those crimes that are in Amazon’s warehouse” in case you assume that overall crime rate is a given and you can only control your exposure to it.

#4 - Jimi, the unMECE

Again many problems with this Tree. 

You can mistake-hunt later at your own pace, so I’ll just point out to the ONE FATAL MISTAKE YOU SHOULD NEVER MAKE:

Jimi wasn’t MECE on the first layer of his Issue Tree.

In part because he insisted on using a conceptual framework (the hardest of the 5 Ways to be MECE) without needing to do it (as a theft problem is a numerical problem).

In part because he didn’t know how to create a MECE conceptual framework (as we teach in our courses).

And this would’ve gotten Jimi rejected from a real case interview at McKinsey, BCG, Bain or any other firm.

And it would probably get him fired if he was in charge of Amazon’s warehouses.

Don’t be like Jimi.

Always be MECE (and especially so on the first layer)!

#5 - Was Natalia rejected due to a simple mistake?

I actually like this Issue Tree quite a bit.

It’s well built, although there are a couple of problems.

And it’s interesting because Natalia, the lady who built this tree had been rejected from a Bain and a BCG final round before. She was preparing to try again. That means she was good enough to actually get to the final round but made some mistakes that prevented her to get the offer.

Maybe her mistakes were showing in her Issue Tree? 

Perhaps… Let’s take a look:

There are two great mistakes with this tree.

One we’ve talked before – Natalia went for a conceptual structure to break down the “Warehouse facility factors” bucket and had trouble building it. There’s overlap between “Security” and “Information Confidentiality”. Also, there are many things not considered here (including theft caused by internal employees).

But the one mistake I wanna call your attention to is much less obvious. It’s more a nuance than a mistake.

It is on the first layer.

The way she build it is much better than many alternatives: there’s external factors (crime) and internal factors (the warehouse itself).

HOWEVER, it’s really really tough to test  which one is causing the surge in theft. These things look measurable but they’re not really.

Because measuring overall crime is a pain. And getting that data, an even higher pain.

Just to give you an example: what crime data should we consider to prove/disprove the fact that external crime has risen? Should it be overall criminal incidents? Thefts only? Warehouse thefts, specifically?

Also, how regional should the data be? Neighborhood? City? State?

And because you can’t measure “warehouse facility factors”, it’s hard to exclude a whole branch of the tree. Which means this tree is not very “eliminative”, because the factors in the first branch aren’t falsifiable.

Now, I’m being really picky here just to make a critical point to you. 

Maybe in a real interview Natalia would’ve been able to come up with a test that would reliably eliminate a whole branch. 

And maybe the problem could be solved without that kind of rigorous testing (e.g. maybe they completely switched their security personnel and had security holes in the process, so the cause would be obvious).

But if the situation was harder, more nuanced it would be tough to Natalia to actually diagnose the issue.

And whether she would be able to actually do it in real life is the #1 question in the interviewer’s mind.

Her first layer is not bad, but there are other MECE structures as insightful as this one that would also be more testable, more falsifiable.

And in a final round that could make all the difference.

Commonly Asked Questions

Learning from the mistakes of others is a great way to accelerate your learning curve!

But still, you might have some questions in your head.

Here are some of the questions I have been asked about Issue Trees throughout the years (and the best answers I have to those)…

Issue Trees are one structuring technique but they’re not the only one.

So there are actually two questions within this one: (1) How do I know if I should use a structure to solve the problem and (2) How do I know if I should use an Issue Tree or another technique.

Great questions!

Let’s start with #1…

You should use a structure to solve a problem, well, when you want to solve it in a structured way.

And when’s that? 

Well, whenever you want to be able to foresee the steps to the solution of the problem. 

That is, when you must have a due date of when the problem’s going to be solved (which is whenever you have a boss or a client, for example) or when you want to distribute the problem for other people to solve it (your employees or an outsourced company, for example).

That means almost always, especially in the professional world, where people have bosses, employees and clients.

Question #2 is a bit trickier to answer…

There are other structuring techniques – ways to break down the problem – that you can use. So, when to use Issue Trees and when to use the others?

Basically there are two scenarios: either you want to split the problem into components of the problem, or you want to look at the problem from different angles/points of view  without actually splitting it.

If the first, use an Issue Tree; if the last, use another tool (such as a conceptual framework, as we teach in our free course on case interviews).

How to know which one you want is a bit more complicated and would take an article on its own to explain. 

If you want the full details, check out our free course that you can find in our homepage or throughout this article, but here’s the long story short: if you want focus, efficiency and logic onto a well-defined problem use an Issue Tree and if you want awareness and insight onto a messy problem, use a tool like a conceptual framework.

A lot of people who teach case interviews say you should start with a hypothesis.

And they say that because MBB consulting firms (MBB stands for McKinsey, BCG and Bain) work in a hypothesis-driven approach. That means they come up with hypotheses and test them to find the truth (much like in the scientific method).

Being hypothesis-driven is tricky because you also have to be structured and MECE. 

So, how do you make your hypotheses MECE?

Well, one way some people figured out is to build a MECE tree and just throw the word hypothesis around. If it were in a case investigating why profits have fallen, this would sound something like this:

“My hypothesis if that profits have fallen because sales are down. To know if that’s true we need to look at sales and costs.”

Notice how there’s ZERO value add to using the word “hypothesis” in the phrase above. If the guy had just asked for sales and cost data he’d ask the same questions, do the same analysis and reach the same conclusion.

If you just want to use the word hypothesis like that, go for it, but there’s absolutely no need to do it. If your buckets are MECE and  testable with data, you can just lay out your Issue Tree with no “hypothesis” and test the buckets.

However if you can’t make your structure MECE/testable, you might need to use a hypothesis, but it’s a completely different type hypothesis than the one I’ve shown you above. Instead of being just a random guess with the word hypothesis on it, it must have a structure which we teach in the “Hypothesis Testing” module from our free course.

Great question, glad you asked that!

Clarifying questions are the questions you use to define the problem so you can create your structure / Issue Tree.

You use them to understand the problem better.

If the answer to a question you ask could potentially lead you to solve the problem then the question is a part of the structure of the problem and should be within your Issue Tree.

Drawing Issue Trees on paper is good practice whether you’re in a case interview, helping a client or solving your own problems.

The reason for that is that having it on paper makes it easier to communicate the ideas and frees up space in your mind so you can actually think about each part of the problem.

Not drawing the tree is kind of like memorizing a map – it’s helpful, but the whole purpose of the map is to be there when you need it without you having to know anything by heart.

But drawing does take a bit of time and in answering certain questions in case interviews, interviewers want you to be quick and may even ask you not to use paper . THIS DOES NOT MEAN YOU’RE ALLOWED TO BE UNSTRUCTURED.

It basically means they want to see if you can be structured and communicate your ideas in a structured way even when you don’t have a lot of time to think through a structure and draw it on paper.

Issue trees are a representation of how a consultant thinks. That means consultants think in Issue Trees . 

They communicate using these trees as the underlying structure of the ideas they’re thinking through.

So if you don’t have time at all to think, you don’t have to draw your Issue Tree on paper, but you still must communicate as if you were going through one.

This is a super common question, and a highly context dependent one.

If you’re in an interview and it’s a more conversational, back-and-forth style, you should use less layers and get data so you know where to focus on (and dig deeper on that one).

If you’re in a more structured rigid interview format without a lot of back-and-forth, you should use more layers and they may never give you data.

The first scenario will typically happen at BCG and the second at McKinsey. Other firms will depend more on office / interviewer.

But this is not a rule. I’ve gotten the first scenario at McKinsey (final rounds) and the second at BCG. This means you’ll have to feel the situation a bit, or even ask the interviewer what they prefer.

But there’s a rule of thumb: no less than 2 layers and no more than 5 layers, regardless of format.

Because with just one layer you’re not really structuring the problem. You’re not showing a map of the situation. And with more than 5 layers the time it takes to build each layer grows while the value each layer brings diminishes. Your interviewer can always ask you to dig deeper in a certain bucket if they want you to (and they often do).

That’s true!

Drivers are “underlying causes”, and Levers are “potential things you can do to fix the situation”.

You use drivers for WHY problems and Levers for HOW problems.

If you build a good WHY tree and a good HOW tree for the same problem you’ll see the similarities and differences between drivers and levers (and you can actually go back to Item #4 in Chapter 1, where I did just that).

Simple example: if costs in a factory have increased and you want to decrease them, “material costs” could be a driver of the problem AND a lever to solve it, “taxes” could be a driver but not a lever (because you can’t change it) and outsourcing could be a lever to solve it but not a driver of the problem.

Drivers must be potential causes to the problem and Levers should be under your control.

If each part is MECE, your structure is MECE.

To know if each part is MECE, read  the 5 Ways to be MECE .

And to know if your conceptual framework is MECE, check out our free course on case interview fundamentals.

Also, don’t obsess too much. There’s usually a bit  of overlap between areas and no framework is FULLY exhaustive. You want to aim for “as MECE as possible”, not perfection.

Take their hint and go do it!

Interviewers are there to help you. If they tell you the problem is elsewhere, it probably is.

That doesn’t mean there’s absolutely nothing  happening in the parts of the structure you were working on, but it does mean that they want to test your problem solving skills in the other part, not in the one you’re at.

If you got stuck, it’s either building  your issue tree or using  your issue tree.

If you got stuck building  your issue tree, that means you need more and better practice. There’s a whole section on how to practice in this guide (and it’s the part that’s coming next).

If you’re in the interview already, however, there’s no time left to practice. So, what do you do?

My advice: keep it simple.

Take a breath, rethink the case and create a very simple, down-to-earth structure that can solve the problem. Not a good time to be sophisticated and elaborate when you’re stuck.

Now, if you already have your tree and you got stuck using it, here’s what you should do:

Eliminate as many parts of your tree as possible and find out everything that is NOT a part of the problem .

It’s much easier to say something is not a problem than to say for certain that something else is.

Use this process of elimination to your favor. Doctors use it all the time to save people’s lives (they call it a differential diagnosis) and you can too to save your own butt in your interviews.

How to Practice Issue Trees

Practice makes perfect.

Or, as a teacher used to say, “Practice makes permanent”.

(Which means poor practice is worse than no practice).

You can have all the theory in the world, you can have seen all the examples and still not be able to perform when the time to use this tool comes.

Which means that reading this guide is useless if you don’t apply it into practice.

In this chapter, I’ll show you how.

4 ways to practice Issue Trees

I could just tell you to go practice Issue Trees.

But then this chapter wouldn’t exist!

Just kidding 🙂

Here’s the thing, telling people to go practice Issue Trees is what we did when we started our case interview coaching practice.

But it didn’t really work.

Most people would just memorize  the common profit trees you see out there and try to apply them to different problems. The problem with that is that they weren’t building their ability to create  new trees for new problems.

Other people would feel stuck. They’d get bogged down into the details and be afraid to do it wrong and waste their time. Or they wouldn’t know where to start.

So what did we do?

Over time we created different techniques for people to practice trees. Each one has a different function and they’re synergistic – the more techniques you use, the more you’ll learn.

Here are my four favorite ones:

As you can see there is a logic for the four types of practice I will suggest. (And yes, as a former consultant I can’t get over with 2×2 matrices.)

Case-specific practice  is important because this type of practice is very targeted to what you’ll find in your case interviews.

But you also need more generic day-to-day practice  because that will train your mind to always think in a structured way . Even when you’re in the bus. Even when you’re hanging out with your family. Even when the interviewer asks you that informal question about the time where you studied abroad.

On the vertical axis, you’ll find the type of problem you will be practicing with.

You need to practice with real problems you’ve tried to solve before  because you are (or were) emotionally invested in them. You know nuances about them that you wouldn’t know about a random problem and you care (or have cared) about solving them. That gives you the rigor and confidence to structure problems with all the nuances and details they need.

But you also need to practice with hypothetical problems , problems you’ve never considered before. Why? Because that gives you the flexibility and confidence to structure any  problem, even those you have never seen before! 

It helps you be more creative and trains you to face the unknown. What’s the point of learning to structure problems if you can’t face new problems, after all?

Using the four techniques I’ll show you, you will get all four types of practice. 

Actually, because this is a 2×2 matrix, practicing with three of these techniques should be enough to get you really good at this, so if you don’t like any of these, feel free to skip one of them if you want.

Practice #1: Creating "deep trees"

The first type of practice is that of creating very deep Issue Trees for hypothetical problems, simulating one you would do in a case interview if you had 20-30 minutes to think or one you would do in a real project.

The process is rather simple:

(1) Think of a problem (business or public sector) that someone might have to solve. It could be a WHY problem or a HOW problem.

(2) Create a multilayered Issue Tree to solve the problem. Aim for at least 6 layers and try to create even more than that as you get more practice.

What you’ll notice is that the first few layers are going to be quite easy, especially if the problem you chose to structure is a common one.

However, as you go deeper you’ll find that it gets harder and harder.

Because when you get deep into your Issue Tree you must deal with much more specific problems, problems that you might have never considered in your life before.

The deepest layers are the ones that teach you the most.  

Everyone knows how to break down “profits” in a MECE way. Few people can break down “improving customer retention” in a MECE way. Even fewer can find a MECE structure on how to increase customer friction to leave to a competitor.

This exercise works wonders because most cases start really broad but they eventually get to really specific issues, such as “increasing customer friction to leave”, “outsourcing job tasks”, “reducing perceived purchase risks” and things like that.

Here’s an example of a “deep tree” for the “How to reduce costs in a widget manufacturing plant?” problem:

Hey, I’m the first to say this tree isn’t perfect, especially in the last couple layers. It’s really hard to create MECE structures to “buying terms and conditions” and other specific things like that.

And I only covered the “material costs” part, otherwise it wouldn’t fit the screen.

But I wanted to show you one example just do you could see how deep you should go when doing this kind of practice.

Practice #2: Restructuring past cases

Remember the last case you did? The one you messed up on the initial structure?

How much better would your structure be if you had 20-30 minutes to do it?

There’s a simple way to find out…

Restructure that case with as much time as you want!

This is a really good way to practice Issue Trees because (1) you internalize what you’ve learned in the case and (2) you can structure it with unlimited time and without being nervous.

Plus, let’s be honest, you keep telling yourself that your structures aren’t as good as they could be because you don’t have a lot of time to build them and you’re nervous.

But is that really the case?

Try it out!

This practice is as simple as the name suggests, but there is ONE NUANCE…

You will  feel tempted to overemphasize the parts of the case your interviewer directed you to and underemphasize other areas.

So, for example, if you had a profitability case and the case ended up being about cutting labor costs in a telecom company, you will tend to make your structure much more robust in the labor costs part than in the rest of the tree.

DON’T DO THAT.

Instead, build a robust tree all around.

Maybe this case was about labor costs, but the next one could be on infrastructure costs and the one after that could be on pricing. Build a robust structure all around that simulates what you would’ve done had the interview gone in any of those directions.

Be prepared for every situation.

Practice #3: Solving real work problems

Got a problem at work?

Work like a consultant and build an Issue Tree first and foremost!

Have to hit a certain target in an organization you work at or collaborate with?

Break that metric down into an Issue Tree and find the best lever to focus on.

Have a school assignment?

Try to build an Issue Tree for it.

By doing these things you will incorporate Issue Trees in your daily work and study. 

Sometimes I even create them as I read a book to better organize its ideas. And as I do that, I end up with the whole structure and all the important ideas of a book in just one page.

Practice #4: Creating "mental trees"

Remember I said you can do 3 out of the 4 types of practices in this chapter and still do fine?

Well, don’t skip this one.

Mental trees exercise a different muscle than the other practices, because it happens all in your head.

It’s kind of like mental math but for Issue Trees.

And it’s a skill that every consultant can do , and so should you.

So what are “mental trees”?

It’s simple. As you go through your day you will notice things. You will be curious about things. You will wonder how to fix certain problems or why they happen in the first place.

You’ll have questions such as:

• “How could this restaurant generate more demand?”
• “What could the city do to improve its transport system?”
• “Why is the doctor always late for the appointment?”
• “What will TV networks do to generate more revenue now that everyone’s on Youtube and Instagram?”

And as you have these questions, use these opportunities to create Issue Trees in your head.

Not huge ones, 2 or 3 layers is fine.

But do that and try to keep them in your head as you generate hypotheses for each bucket. At first this is gonna be really hard, but once you get the hang of it it will be a breeze.

And once it’s easy, you’ll be able to use Issue Trees whenever you need them.

This practice is especially important for final rounds because partners will often tell you to discuss a problem without using paper. (And they do expect you to structure it).

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Applying issue trees on the job.

If you’ve read this far, you’ve learned how to use the most versatile tool in solving business (and many other) problems.

And if you’re like me, you want to now maximize the value you got from learning this!

Issue Trees can help you be a better problem solver, but also to present your ideas better, to bring more and better insights and even to be a better manager.

In this chapter I’ll show you 5 direct, on-the-job applications of Issue Trees that you can use if you’re a consultant, if you work in industry and even if you have started your own business.

Issue Trees can be used in every facet of your job

Before we even jump into examples of direct applications of how to use Issue Trees on the job, let me make a bold claim: Issue Trees can be used in every  facet of your job.

You know that saying about how everything looks like a nail to the guy who has a hammer?

Well, don’t think of Issue Trees as hammers. 

They’re more like Swiss army knives or Microsoft Excel. It’s a tool with many functions.

And you can use it as a consultant, but also as an executive, as an entrepreneur and more. I once taught my dad who is a doctor how to use it and he’s now better able to explain his thought process and diagnostics to his patients.

Why am I telling you all this?

Just so you know that the 5 on-the-job applications I’m about to show you are some  of the things you can do with Issue Trees. 

With a bit of creativity you can do much more.

Application #1 - As a map to solve a specific problem

If you’ve spent any time at all as a knowledge worker in your career (that’s most analyst and management positions at most companies), you know how it feels to be stuck with a problem.

Most business problems start with a very simple, almost trivial, question, but as you dig deeper you start seeing all the nuances you feel overwhelmed. 

It’s very different from the experience of solving a problem in business school, where all the information you’ll need (and all the info you’ll get) is in a neat 10-20 page case.

Anyway… When you feel overwhelmed, when you feel like there’s too much nuance to handle and when you feel like there’s so many directions to go what you need is a map. A high-level view of the problem with its distinct parts laid out in front of you so you can put numbers, hypotheses and plans to act in each part.

What you need is an Issue Tree.

Years ago I worked in a Venture Capital firm here in Brazil. They had just entered the market and wanted to invest in e-commerce.

My task was to figure out what types of e-commerce businesses would thrive in the country so they could invest well. Would it be auto-parts? Maybe fashion? Or perhaps food delivery?

It was an overwhelming task for me. There’s so many things you can do with e-commerce.

So what I did was to build two Issue Trees. One with our options and another with the high level criteria I’d want to see in each option for it to become a successful e-commerce.

Something like this:

Now, the real trees I did were a bit more sophisticated than this. They had:

• More layers and a more MECE structure for the verticals
• Other criteria for success not shown here
• Prioritization so we could find the most important information first and eliminate whole verticals quickly

But you can get the idea… I got both of these trees and put into a spreadsheet and now I had a map of the problem that I could work on.

Because I used Issue Trees to create this map, I assured that the thinking was clear and rigorous, that I would be able to work efficiently by eliminating bad options quickly and that I’d bring insight to the table.

It also removed all overwhelm and made my work much more efficient. I no longer had to consider all the factors at once in my head. All I had to do now was to fill out a table with the best information I could get and see the results.

Application #2 - As a guide to brainstorm solutions

Brainstorming solutions to common business problems is a nervous activity.

Everyone wants to show the best solution, and people want to show common sense AS WELL AS creativity. It’s a tough spot to be in.

On top of that, people typically brainstorm solutions to problems that are urgent and critical (why fix what’s not broken?) and this is usually done in meetings, which adds to the pressure.

But that’s not all… In most meetings, solution generation happens in a haphazard way – completely different ideas are mentioned in the spam of a few minutes and it’s hard to even evaluate which are the best ones.

The result? The best solutions rarely win and it’s common that people don’t even reach a consensus on which should be implemented.

So, what’s the antidote?

You guessed it: Issue Trees.

If you have a solution generating meeting (or if you’re doing it by yourself) and you can find a HOW tree that reaches consensus (not actual solutions, but the structure of the problem) at the beginning of the meeting, you can then lead the discussion forward, helping people generate solutions for each bucket of your tree and then prioritizing those in an organized fashion.

Also, doing it this way tends to bring out more, better ideas – for the same reason why dividing the problem brings more creativity in case interviews. It’s easier to get 5 ideas per bucket than 40 for the problem as a whole.

I’ve been to both kinds of solution-generating meetings. One feels like a pointless chaos and the other gives you certainty that the problem will be solved from minute one.

Application #3 - As a way to structure a presentation

Structuring a presentation is the kind of thing that gets most people CRAZY.

You have to consider your audience, how to capture and keep attention, storytelling, getting your point across quickly and being to the point and so many other conflicting goals.

But here’s a simple way to do it: use the Issue Tree of the problem as a basis to how your presentation is organized.

This works because your Issue Tree is a map of your problem. And maps are great ways to make people understand a complex thing with simplicity and accuracy.

Let me show you an example of how to do this…

Remember the Telco executive from Chapter 1 that had a problem because his customers were unsubscribing from their services? I’ll help you remember it, it’s been a while…

Now, imagine he had to present what’s happening to the executive committee. It needed to be a short and to the point presentation that was compelling as well.

Not a full solution to the problem, but a presentation showing what happened.

What would you do in his place?

Here’s what I’d do:

Slide 1: A chart showing the high level problem (overall unsubscriptions have raised from 10.5 to 17 thousand clients, with an increase of 2,000 from clients willing to unsubscribe and 4,500 from clients being forced out). 

I’d also add something that pointed out that the cause of the clients being forced out (the main problem) was a problem in the systems.

In other words, Slide 1 would be “High-level view” + “root-cause of main problem”. Everything the committee needs to understand the situation.

Slide 2: A chart detailing the root-cause of the main problem, with all details needed to understand why it happened. This would include numbers and qualitative things about that system problem.

Slide 3: A chart showing that even though we only lost 2,000 extra customers because they wanted out, we actually lost 3,000 to competition. I’d show the numbers (2nd Layer at “They wanted to unsubscribe” bucket) and show that there is potential there.

Slide 4: I’d turn back to the system’s problems and start talking about solutions. I’d show what was done, what is being done and what’s next to prevent it from happening again.

Slide 5: I’d show next steps to understand how to retain more customers vs. competition. This is a less urgent problem so I’d leave it at that.

That’s it, simple and straightforward.

And it all comes because I have a simple and straightforward Issue Tree that helps me solve and explain the problem in simple and straightforward ways.

Application #4 - As a guide to research best practices

We’ve all had that hurried boss that passes through your desk and casually mentions: “Hey, you should try to find some best practices around X”.

X can be anything he or she is concerned about: doing better presentations, sharing internal documents, improving productivity at work, getting more clients.

And the problem with that is that it’s really really hard to research that. If you just type “best practices for X” in google, chances are you’ll get some really generic, obvious tips.

One thing I’ve learned to do at McKinsey was to research best practices for each component  of X. So instead of looking for best practices around “getting more clients”, I could research best practices to “get more leads” and “increasing conversion rate”.

And then I could break down those components even further and look for best practices for each sub-component.

Guess what’s the tool you need to get all the components in a logical manner? Yes, Issue Trees!

A normal best practice for X’s sub-sub-component usually is a great insight to improve X, so by simply doing this exercise you will come off way ahead of your peers as the go-to person for insights on how to improve your company.

Application #5 - As a way to generate KPIs and indicators

In case you don’t know the lingo, KPIs are you “Key Performance Indicators”.

They’re a business’ dashboard. The numbers you have to look at to see how healthy your business is.

But how do you create KPIs?

Well, in three simple steps:

1) You define your goals

2) Your break down your goals into the sub-components that must be true for you to achieve them

3) You figure out indicators for each prioritized sub-component. (Without the “prioritized” part, these indicators wouldn’t be “Key”)

So for example,  if you’re studying for consulting interviews and you want to see how your preparation is going , here’s an example of how to create KPIs you can track:

Each bullet point could be a KPI. Some of these are numbers to track, others are Yes/No KPIs.

I am not saying nor implying every candidate should use all these KPIs to prepare, but notice how nuanced you can get when you use a MECE Issue Tree to create KPIs.

Most candidates just track the # of cases they did, without even caring for the quality of those. 

No wonder why most get rejected. 

It’s like a company that just tracks how many products it has sold without concerning about margins, customer retention rates, customer satisfaction, quality control and so on.

You can get any Issue Tree from this article and transform it into a list of KPIs to track within each important bucket. 

There’s certainly an art on which ones are better to track (because you don’t want to end up with 35 different KPIs) but just generating them out of a MECE Issue Tree allows you to have at least one indicator to every important part of the problem, leaving no blind spots in your master dashboard.

What's next?

Issue Trees are one, but not the only  tool MBB consultants use to solve their client’s problems.

There are actually 6 types of questions interviewers ask in case interviews, to test on the 6 most important tasks consultants perform in real client work. 

You can learn about those questions and the specific tools, techniques and strategies management consultants from McKinsey, BCG and Bain use to solve business problems by joining our free course on case interviews!

By joining our course, you’ll get access to:

• Step-by-step methods to solve the 6 (and only six) types of questions you can get in case interviews
• The “Landscape Technique” to create conceptual frameworks from scratch (this is the technique you need when Issue Trees fail to help you)
• Tons of practice drills so you can apply your knowledge

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MECE Framework McKinsey

  “MECE,” pronounced “me see,” an acronym for “mutually exclusive and collectively exhaustive,” is a popular mantra at McKinsey. If you manage to get a position at McKinsey, or at any other MBB for that matter, you are likely to have to handle huge amounts of data. Chances are that your boss will ask you to ensure that you organize your data in an “MECE manner.” “Be more ‘MECE’ in your approach,” she might say. In fact, even at your case interview, you likely used the MECE principle. You might not have got the green signal if you hadn’t.  

Introduction and definition

MECE is a method of grouping information into elements that are mutually exclusive (ME) and collectively exhaustive (CE). In other words, it is a process by which information—ideas, topics, issues, solutions—is arranged or, put in “MECE buckets,” with no overlapping between buckets and with each item having a place in one bucket only (ME), and with the buckets including all possible items relevant to the context.

A simple example of the MECE principle would be the classification of the population into age groups. Here, dividing the population into two groups, one group of people above, say, 60, and another group below 60, would be based on the MECE principle. The entire population would be either above or below 60 (ME, with no overlapping between the two buckets) and with all people included in one or the other bucket (CE).

However, a categorization of the population into one group of, say, people below 60 and another of people between 50 and 70 would not be based on MECE. People between 50 and 60 would be in both “buckets” (not ME) and some people would not be in either bucket (so not CE).  

How is it used?

Strategy consultants use the MECE framework (Issue Tree, Decision Tree, Hypothesis Tree) to segregate a client’s problems into logical data categories that can be analyzed systematically and minutely by their staff involved with the project. The framework is notably used at McKinsey, where data from clients’ businesses is organized on the basis of MECE. Well-known frameworks, such as Cost-Benefit Analysis, 4Cs, and Porter’s Five Forces have the MECE principle at their core.

Let’s discuss three popular MECE frameworks.  

How is the MECE framework used to solve clients’ issues at consultancies? One method consultants use is to create an “issue tree” to arrange all the information that they have and divide this information into all possible issues and sub-issues.

An issue tree is particularly helpful for solving large and complex problems as it facilitates splitting them up into smaller, solvable problems. “Issue trees” get their names from their structure—narrow at the top with the problem statement, and wider towards the bottom, even as each level accommodates more specific sub-issues or smaller problems. However, some “trees” are also created left to right, but the principle remains the same.

A common type of cases in which a MECE issue tree is used is profitability cases. Suppose the problem statement is “My restaurant is not profitable.” An issue tree is created, starting with the problem statement at the treetop.

The various sub-levels of the tree would answer the question “How to make the restaurant profitable?” in broad, intuitive ways: “Increase revenue” and “Reduce costs.” The lower levels would also answer the question “How?”

The second level, with sub-issues of the first level, would answer the questions “How to increase revenue?” (under “Increase revenue”) on the one hand and “How to reduce costs?” on the other. The answers under “Increase revenue” would be “Increase the number of orders” and “Increase the prices of items.” The answers under “Reduce costs” would be “Reduce salary expenditure,” “Reduce rental,” and “Reduce raw material expenses.”

On the third level, the issue tree would tackle the question “How to Increase the number of orders?” One way to increase orders would be to shift the restaurant to a busier area and another would be to launch a marketing campaign so that the restaurant becomes more widely known. On the other main branch, under “reduce salary expenditure,” options such as “fire redundant workers” could be mentioned, as also “shift to a less expensive locality” under “reduce rental”, and “change the vendors,” under “reduce raw material expenses.”

How does an issue tree help? It enables consultants to consider all options separately and exclusively and suggest the best option to the client. It helps create a common understanding among team members about the problem-solving framework and focus team efforts. It smoothens work distribution among team members.

Often, consultants who create an issue tree may need to “trim branches,” which means doing away with options that are not worth pursuing after a detailed initial consideration. In the example of the issue tree, given above, about how to increase the profitability of a restaurant, increasing prices may not be an option for various reasons, and that “branch” of the issue tree may be left out or “trimmed.”

Decision tree

A decision tree is a tree-shaped graphical representation of decisions and potential outcomes of those decisions, and is used to determine a course of action. A decision tree helps users understand the comparative advantages and disadvantages of each decision and outcome.

A decision tree is often drawn from left to right. It starts with a specific decision denoted by a small square. “Branches,” or lines, are drawn to the right from the square, representing each potential option. If the option is a new decision, a square is drawn, and from it, new branches are drawn, representing new options. At the end of each branch, a circle is drawn if the result of the option is unclear. If the option leads to a decision that helps bring about a solution, the branch is left blank. A triangle is also used to signify the end of a branch or path to a potential solution.

Like an issue tree, a decision tree is exhaustive in its inclusion of decision, outcomes, options, and scenarios. A user of a decision tree looks at each of them and chooses the best option.

Hypothesis tree

Another method to structure a problem is to develop a hypothesis tree, which is the graphical representation of all MECE hypothesis that elucidates the problem. It is, in a way, similar to an issue tree, where a problem is broken down into its components, which makes identifying and solving it easier. But while an issue tree splits up each problem into issues and sub-issues, a hypothesis tree organizes a problem around hypotheses, and often offers a more direct approach than an issue tree.

Developing MECE hypotheses

First, understand the problem thoroughly. What are you trying to solve?

Second, write down the problem statement. Take care to ensure clarity in the statement so that there is no ambiguity.

Third, list the options to solve the problem, using a MECE tree. See that the options do not overlap (that they are mutually exclusive) and that no option has been left out (that they are collectively exhaustive).

Fourth, consider each option individually. Consider the pros and cons. Leave out those that are illogical and include any new insight as an option as you understand the problem better.

Fifth, select the best option and present it to the client.  

Clarity pays

Good management consultants use the MECE structure for problem-solving. A piece of advice they like to give to aspiring consultants is to learn to use the MECE principle for not only structuring problems but also communicating solutions, whether they are attending a case interview at MBB or sitting across the desk from a client.

Creating a MECE hypothesis helps clarifies a problem. It’s like having a road map when you are lost in unknown territory. If your approach to structuring a problem is “not MECE,” “it is probably messy,” as they say.   In order to truly understand MECE, you’ll first need a solid foundation of business. Which is what we teach in our popular online course. It covers other important strategy concepts (including powerful problem solving frameworks), as well as the wider range of super-essential business topics. Check it out here Mini MBA

  Resources: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

What is a hypothesis tree and how do you make one?

An essential productivity tool any business professional should have in their tool belt is the hypothesis tree.

Emily Branch

Problem-solving

One of the challenges of delivering presentations is creating visual aids that help your listeners understand in a more intuitive way.

Experienced presenters accumulate a repertoire of tools: word clouds, tree maps, issue trees, etc., but one essential tool any business professional should have in their tool belt is the hypothesis tree .

Hypothesis trees are useful visualizations for communicating different ideas, explanations, or theories about a central topic in a visually clear and logically cohesive way. This guide will teach you what a hypothesis tree is, when you should use one, and how you can create your own.

Key Takeaways:

• A hypothesis tree is a counterpart to an issue tree.
• Hypothesis trees are useful for visualizing a problem and conceptualizing solutions.
• Prezent helps companies put theory into practice in their presentations.

What is a hypothesis tree?

A hypothesis tree starts with the problem you’re trying to solve. From that central issue, a hypothesis tree visually connects various explanations (or hypotheses) to the issue in question. Each hypothesis can have its own sub-hypotheses and sub-sub-hypotheses in as much detail and variety as you need.

The key feature of a hypothesis tree is that it applies the scientific method to business scenarios. Each hypothesis is a falsifiable, testable explanation for the problem at hand, and by evaluating these individual branches with logical or practical tests, you gain greater insight into your company and your path forward.

Both visually and conceptually, hypothesis trees resemble issue trees . While issue trees start with a complex problem and break it down into simpler and simpler components, a hypothesis tree starts with a complex question and pursues simpler and simpler solutions. Because of that similarity, some businesspeople refer to issue trees as “diagnostic trees” and hypothesis trees as “solution trees.”

When should you use a hypothesis tree?

At some point in their life, everybody has experienced a presentation (in the workplace, school, online, etc.) that was so jam-packed with abbreviations, lingo, and convoluted analogies that they left feeling like they understood even less than they went in with.

When it comes to components of a presentation , a good rule of thumb for speakers is to use special tools when it makes things simpler, not when it makes things more complex.

This applies to special terminology, examples, and visual aids: the right visual aid should make your job easier, not harder. When it comes to presentations before you can persuade your audience to agree with you, you first have to make them understand what you’re trying to convey, and hypothesis trees are an easy and effective way to visually demonstrate solutions to an issue.

Not only are hypothesis trees helpful visual aids for increasing understanding, but they’re also useful tools for helping your audience conceptualize and test solutions. In the international bestseller, The McKinsey Mind , authors Ethan Rasiel and Paul N. Friga go as far as to claim that a hypothesis tree can solve a problem in a single meeting.

This is great news for presenters but also great news for your colleagues. You should use hypothesis trees to help your audience understand your topic and when they can help conceptualize and test solutions to a problem.

Putting ink to paper

As you’re preparing for a presentation , you’ll identify situations that call for a hypothesis tree. The first step to creating your tree is to identify the problem you are trying to solve and what a solution for that problem would look like.

For example, if your workplace has unusually high printer paper usage, your central issue may be, “We can lower our paper usage.” Take that central issue and put it in a box:

From there, consider possible hypotheses: What could lead to lowering paper usage? Is your company printing redundant documents? Are you using paperwork for things you already have digital records of? Consider all the solutions to your issue.

If you’re leading a meeting, it would be helpful to consider these solutions ahead of time and prepare them as part of your presentation.

But hypothesis trees are more than presentation tools. They’re valuable collaboration drivers. 

At this point, you may prepare an answer ahead of time or collect feedback and brainstorm possible hypotheses as a collaborative activity.

Whether you prepare hypotheses yourself or collect ideas from the room, you can organize those theories either vertically or horizontally from your central issue, but for visual clarity, they should be in alignment with each other. For example:

In this hypothesis tree, there are two main hypotheses: we can implement more paperless storage , and we can reduce redundant documents. Crucially, both of these hypotheses are falsifiable, meaning that you can test their validity, and if they are false, you can prove them false.

How would you prove them false? By disproving their sub-hypotheses. For instance, to disprove the statement “we can lower our paper usage,” you would have to disprove both “we can implement more paperless storage” and “we can reduce redundant documents.” 

To disprove “we can implement more paperless storage,” you would have to disprove both “we can store checklists digitally” and “we can create a paperless application process.”

In this way, hypothesis trees not only provide a framework for searching for potential solutions to a problem (too much paper usage) but also a way of testing those solutions.

Make the most of your presentations with Prezent

Humans have been telling stories since we developed the tools to paint on cave walls. Stories aren’t just the purview of fiction or entertainment. They’re essential for building relationships, making decisions, and conducting business.

As the Canadian Broadcasting Corporation puts it: “Storytelling is not just entertainment. It’s a fundamental part of being human.”

Storytelling belongs in business, and Prezent is on a mission to make presentations efficient, dynamic, collaborative, structured, and proficient.

To learn how Prezent can help, contact us to see how Prezent can work for you.

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Issue Trees – What Are They and How Do You Use Them?

Issue trees are a useful approach to breaking down a problem statement into component parts that can more easily be acted upon. In consulting teams, it’s often done in the first couple of weeks of a project. It enables the team to structure the project in a way that people can be assigned to specific “workstreams” and that the team can align their hypotheses to make predictions about which elements might have the biggest impact.

I like the definition that McKinsey Mind uses for issue trees:

The issue tree, a species of logic tree in which each branch of the tree is an issue or question, bridges the gap between structure and hypothesis. Every issue generated by a framework will likely be reducible to sub issues, and these in turn may break down further. An issue tree is simply the laying out of issues and subissues into a MECE visual progression. By answering the questions in the issue tree, you can very quickly determine the validity of your hypothesis.

It’s a good definition but it’s also chock-full of jargon and we’re not a fan of jargon (or at least egregious uses of it) here are StrategyU The simplest way of thinking about an issue tree is as a way of breaking down a complex problem into many possible explanations of what is going wrong.

What Do They Look Like And How Do You Use Them ?

Issue trees are often created visually in PowerPoint but can also be in the form of financial models. The type of issue tree we are concerned about are the ones that help us structure our central problem or mission. For example, most companies are focused on increasing profitability. We might frame this “problem” in the form of a question, “Company profitability is declining, what are the ways to improve it?”

We can then start to brainstorm different ways that profitability might be increased. At the higher levels, you want to be as broad as possible such that you can break the tree down further and get more specific the deeper you go. You’ll also want to try to use MECE . Our initial issue tree might look like this:

From there we can go deeper. What are the different ways we can increase revenue. It’s best to just start listing ideas and then start thinking about how to synthesize them, organize them, and yes, make sure they are MECE!

You might develop the next leg of your tree:

This tree is not perfect and the answers at the lowest level are not collectively exhaustive for all the possibilities for increasing revenue and decreasing costs. However, for a specific company, these may be the relevant issues, meaning that they are the ones that you are able to invest money on, tweak and that might have a positive impact.

The next step is to develop analyses or experiments that you can perform to validate or quantify how much impact can be generated by focusing in each of these areas

How Issue Trees Are Linked With Problem Solving

At StrategyU we are fans of the SCQA process to define problems and develop hypotheses. This approach enables us to have a rigorous problem-solving approach to business problems instead of starting with the solution in mind from the beginning. This approach works best when you are open-minded and flexible. The first test of the issue tree is when you are doing the initial research and analysis after you structure the problem. This is step two of the consulting process :

At this point, you will likely get some quick feedback on your initial problem statement such as:

• Have we defined the problem appropriately or are there deeper issues?
• Have we identified the relevant issues and areas in which we can make a difference?
• What kind of initial tests have we done are are we designing to confirm if the issues and questions are right?

This is a frustrating, iterative process and within a consulting team, you are often revisiting the issue tree and problem statement over and over again throughout a project.

How To Use This In Your Company

You should have a good understanding of the “levers” that help your company continue to grow, increase its profitability, and improve over time. Spend long enough in any company and you start to realize that there are a narrow set of metrics everyone makes decisions around. Except unless you’ve mapped this out explicitly, there will likely be many different definitions and interpretations of what you are optimizing for.

Using a template like follows and coming up with the high-level issues and areas within the business you are focusing on can be clarifying. You can also add specific types of analyses and information that you use to help you solve or improve in these areas:

This can also be rolled out across your org chart. Let’s imagine a company realizes that it doesn’t have much room to lower costs anymore and it wants to focus exclusively on increasing revenue. They can do this in two ways (assuming they aren’t adding new products). They can increase the price per order or they can increase volume. They may when want to break this down into different sub-issues.

In reality, you’d want to collect a lot of data and verify that the way you are breaking things down is correct. The numbers often surprise companies. They realize that an area of focus (increasing # of customers, for example) is not as big of an impact on the bottom line as other areas.

The only way to figure this out is to map out all of the possibilities of your issues and then validate them with real data.

This is the same thing that consulting teams do when they work for companies.

In my course, Think Like A Strategy Consultant, you have to complete an issue tree for a case example featuring Facebook’s transition from desktop to mobile and I’ll walk you through the process step-by-step which also providing you feedback if you want. Learn more here .

Do you have a toolkit for business problem solving? I created Think Like a Strategy Consultant as an online course to make the tools of strategy consultants accessible to driven professionals, executives, and consultants. This course teaches you how to synthesize information into compelling insights, structure your information in ways that help you solve problems, and develop presentations that resonate at the C-Level. Click here to learn more or if you are interested in getting started now, enroll in the self-paced version ($497) or hands-on coaching version ($997). Both versions include lifetime access and all future updates.

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Issue Tree in Consulting: A Complete Guide (With Examples)

What’s the secret to nailing every case interview ? Is it learning the so-called frameworks? Nuh-uh.

Actually, that secret lies in an under-appreciated, yet extremely powerful problem-solving tool behind every real consulting project . It’s called the “issue tree”, also known as “logic tree” or “hypothesis tree” – and this article will teach you how to master it.

Table of Contents

What is an issue tree?

An issue tree is a pyramidal breakdown of one problem into multiple levels of subsets, called “branches”. It can be presented vertically (top-to-bottom), or horizontally (left-to-right). An issue tree systematically isolates the root causes and ensures impactful solutions to the given problem.

The issue tree is most well-known in management consulting , where consultants use it within the “hypothesis-driven problem-solving approach” - repeatedly hypothesizing the location of the root causes within each branch and testing that hypothesis with data. Once all branches are covered and root causes are found, impactful solutions can be delivered.

The issue tree is only part of the process used in case interviews or consulting projects. As such, it must be learned within the larger context of consulting problem-solving, with six concepts: problem, root cause, issue tree, hypothesis, data & solution , that strictly follow the MECE principle .

Every problem-solving process starts with a well-defined PROBLEM...

A problem is “well-defined” when it is attached with an objective. Let’s get straight to a business problem so you can get a good perspective on how it is done. So here’s one:

Harley-Davidson, a motorcycle company, is suffering from negative profit. Find out why and present a solution.

Now we’ve got our first piece of the tree:

 ...then tries to find its ROOT CAUSES…

To ensure any solution to the problem is long-lasting, consultants always look for the root cause.

Problems are often the last, visible part in a long chain of causes and consequences. Consultants must identify the very start of that chain – the root cause – and promptly deal with it to ensure that the problem is gone for good.

The diagram is a simple representation. Real problems can have multiple root causes. That’s where the issue tree comes to the rescue.

Since Harley has been reporting losses, it tried to decrease cost (in the simplest sense, profit = revenue - cost) by shutting down ineffective stores. As you may have imagined, it wasn’t very effective, so Harley set out to find the real source of the problem.

...by breaking it down into different BRANCHES of an issue tree

An issue tree ensures that all root causes are identified in a structured manner by breaking the problem down to different “branches”; each branch is in turn broken down into contributing sub-factors or sub-branches. This process is repeated through many levels until the root causes are isolated and identified.

For this problem, Harley deducted that losses must be due to decreasing revenue or increasing cost. Each branch is in turn segmented based on the possible reasons

For a branch to be included in the issue tree, there must be a possibility that it leads to the problem (otherwise, your problem-solving efforts will be wasted on the irrelevant).

To ensure that all possibilities are covered in the issue tree in a neatly organized fashion, consultants use a principle called “ MECE ”. We’ll get into MECE a bit later.

A HYPOTHESIS is made with each branch…

After we’ve developed a few branches for our issue tree, it’s time to hypothesize, or make an educated guess on which branch is the most likely to contain a root cause. 

Hypotheses must adhere to 3 criteria:

It must follow the issue tree – you cannot hypothesize on anything outside the tree 

It must be top-down – you must always start with the first level of the issue tree

It must be based on existing information – if your information suggests that the root cause is in branch A, you cannot hypothesize that the root cause comes from branch B

Once a hypothesis is confirmed as true (the root cause is inside that branch), move down the branch with a lower-level hypothesis; otherwise, eliminate that branch and move sideways to another one on the same level. 

Repeat this process until the whole issue tree is covered and all root causes are identified.

Harley hypothesized lower revenue is either due to losing its customers because they came to competitors or they weren’t buying anymore, or it couldn’t attract new buyers

But wait! A little reminder: When solving an issue tree, many make the mistake of skipping levels, ASSUMING that the hypothesis is true instead of CONFIRMING  it is. 

So, in our example, that means from negative profit, we go straight into “losing old customers” or “can’t attract new customers” before confirming that “decreasing revenue” is true. So if you come back and reconfirm “decreasing revenue” is wrong, your case is completely off, and that’s not something consultants will appreciate, right?

Another common mistake is hopping between sub-branches before confirming or rejecting one branch , so that means you just jump around “losing old customers” and “can’t attract new customers” repeatedly, just to make haste of things. Take things very slowly, step-by-step. You have all the time in the world for your case interview.

But testing multiple sub-branches is possible, so long as they are all under the same branch and have the same assessment criteria.

So for our example, if you are assessing the sales of each motorcycle segment for Harley, you can test all of them at once.

The hypothesis is then tested with DATA... 

A hypothesis must always be tested with data.

Data usually yield more insights with benchmarks – reference points for comparison. The two most common benchmarks in consulting are historical (past figures from the same entity) and competitor (figures from similar entities, in the same timeframe).

Using “competitor benchmark” to test if competitors are drawing away customers, Harley found that its competitors are also reporting losses, so it must be from something else!

...to find an ACTIONABLE SOLUTION

After the analyzing process, it’s time to deliver actionable solutions. The solutions must attack all the root causes to ensure long-lasting impact – if even one root cause remains untouched, the problem will persist.

Remember to deliver your solutions in a structured fashion, by organizing them in neat and meaningful categories; most of the time, solutions are classified into short-term and long-term.

So Harley found that it is losing its traditional customer base - old people, as they were the most vulnerable groups in the pandemic, so they stopped buying motorcycles to save money for essentials, or simply didn’t survive. 

Harley also found that it can’t attract new, younger buyers, because of its “old-school” stigma, while also selling at premium price tags. So the short-term solution is setting more attractive prices to get more buyers; and the long-term solution is renewing itself to attract younger audiences.

Our case was a real problem for Harley-Davidson during the pandemic, whose sales plummeted because its target audience were either prioritizing essentials, or dead. So now, Harley has to change itself to attract younger people, or die with its former customer base. 

What Is MECE and How Is It Used in an Issue Tree?

A proper issue tree must be MECE, or “ Mutually Exclusive, Collectively Exhaustive .” Mutually exclusive means there’s no overlap between the branches, and collectively exhaustive means all the branches cover every possibility. This is a standard all management consultants swear by, and together with the issue tree, a signature of the industry. 

To answer whether an issue tree is MECE or not, you need to know all the basic and “advanced” rules of the MECE principle, and we’ll talk about those here. If you want a more comprehensive guide on MECE, check out our dedicated article on MECE .

Basic rule #1: Mutually exclusive

Adherence to this rule ensures that there will be no duplicated efforts, leading to maximum efficiency in problem-solving. It also allows the consultant to isolate the root cause more easily; otherwise, one root cause may manifest in multiple branches, making it harder to pinpoint.

For example, an apparel distributor trying to find out the cause of its decreasing unit sales may use the cleanly-separated product segments: High-end, mid-range, and entry-level. A non-mutually exclusive segmentation here would be: high-end products and footwear.

Basic rule #2: Collectively exhaustive

A collectively exhaustive issue tree also covers only the relevant factors - if one factor is not related to the problem, it must not be included. 

If the aforementioned apparel distributor omits any of the product segments in its analysis, it may also ignore one or a few root causes, leading to ineffective problem-solving. But even if it produces runway-exclusive, not-for-sale pieces, those are not included in the issue tree because they don't contribute to unit sales.

Advanced rule #1: Parallel items

This rule requires that all items are on the same logical level.

High-end, mid-range, and entry-level are three parallel and MECE branches. But if we replace the first two with “high-and-mid-range”, the whole issue tree becomes non-parallel and non-MECE, because the new branch is one level higher than the remaining “entry-level” branch.

Advanced rule #2: Orderly List

This rule requires that all items are arranged in a logical order.

So for our apparel distributor, the branches can be arranged as high-mid-low or low-mid-high. Never go “high-low-mid” or “mid-low-high”, because this arrangement is illogical and counter-intuitive.

Advanced rule #3: The “Rule of Three”

The ideal number of branches on any level of the issue tree is three - the most intuitive number to the human mind.

Three items are often enough to yield significant insights, while still being easy to analyze and follow; segmentations into 2 or 4 are also common. 5 is acceptable, but anything more than that should be avoided.

Our apparel distributor may have dozens of product lines across the segments, but having that same number of branches in the issue tree is counter-intuitive and counter-productive, so we use the much more manageable 3 segments.

Advanced rule #4: No Interlinking Items

There should be minimal, and ideally no connections between the branches of the issue tree. 

If the branches are interlinked, one root-cause may manifest itself in multiple symptoms across the tree, creating unnecessary confusion in the problem-solving process.

Variants of an issue tree

Beside the “why tree” we used to solve why Harley was reporting losses, there are two other common trees, the “which tree” and the “how tree.” The which tree answers which you should do among the choices, and the how tree answers how you should do something.

Why tree helps locate and attack root causes of a problem

We’ve shown you how a why tree could be used to break down a problem into smaller pieces to find the root causes, which involves several important concepts, but in short there are 3 things you need to do:

Locate root causes by narrowing down your search area. To quickly locate root causes, use breakdown by math, process, steps or segment, or any combination of those. We’ll talk about that a bit later

Identify root causes from what you’ve hypothesized. Remember, all hypotheses must be tested with data before reaching a conclusion

Suggest solutions to attack the root causes to eliminate the problem for good. However, sometimes the root causes cannot be solved effectively and efficiently, so we might also try to mitigate their effects

Which tree helps make the most suitable decision

The which tree is a decision-making table combining two separate issue trees – the available options, and the criteria. The options and criteria included must be relevant to the decision-maker. When considering choosing X over something, consultants might take a look at several factors:

Direct benefits: Does X generate more key output on its own?

Indirect benefits: Does X interact with other processes in a way that generates more key output?

Costs: What are the additional costs that X incur?

Risks: Can we accept the risks of either losing some benefits or increasing cost beyond our control?

Feasibility: Do we have enough resources and capability to do X?

Alternative: Are there any other alternatives that are better-suited to our interests?

Additionally, the issue tree in “Should I Do A or B” cases only contains one level. This allows you to focus on the most suitable options (by filtering out the less relevant), ensuring a top-down, efficient decision-making process.

How tree helps realize an objective

The how tree breaks down possible courses of action to reach an objective. The branches of the tree represent ideas, steps, or aspects of the work. A basic framework for a how tree may look like this:

Identify steps necessary to realize the objective

Identify options for each steps

Choose the best options after evaluations

Again, like the two previous types of issue trees, the ideas/steps/work aspects included must be relevant to the task. 

A restaurant business looking to increase its profitability may look into the following ideas:

Consulting frameworks – templates for issue trees

Don’t believe in frameworks….

In management consulting, frameworks are convenient templates used to break down and solve business problems (i.e. drawing issue trees).

So you might have heard of some very specific frameworks such as the 4P/7P, or the 3C&P or whatever. But no 2 cases are the same, and the moment you get too reliant on a specific framework is when you realize that you’re stuck.

The truth is, there is no truly “good” framework you can use. Everyone knows how to recite frameworks, so really you aren’t impressing anyone.

The best frameworks are the simplest, easiest to use , but still help you dig out the root causes.

“Simplest, easiest to use” also means you can flexibly combine frameworks to solve any cases, instead of scrambling with the P’s and the C’s, whatever they mean.

“Simplest, easiest to use” frameworks for your case interviews

There are 5 ways you can break down a problem, either through math, segments, steps, opposing sides or stakeholders.

Math : This one is pretty straightforward, you break a problem down using equations and formulae. This breakdown easily ensures MECE and the causes are easily identified, but is shallow, and cannot guarantee the root causes are isolated. An example of this is breaking down profits = revenues - costs

Segments : You break a whole problem down to smaller segments (duh!). For example, one company may break down its US markets into the Northeast, Midwest, South and West regions and start looking at each region to find the problems 

Steps : You break a problem down to smaller steps on how to address it. For example, a furniture company finds that customers are reporting faulty products, it may look into the process (or steps) on how its products are made, and find the problems within each steps

Opposing sides : You break a problem down to opposing/parallel sides. An example of this is to break down the solution into short-term and long-term 

Stakeholders: You break a problem down into different interacting factors, such as the company itself, customers, competitors, products, etc. 

To comprehend the issue tree in greater detail, check out our video and youtube channel :

Scoring in the McKinsey PSG/Digital Assessment

The scoring mechanism in the McKinsey Digital Assessment

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Case Interview End-to-End Secrets Program

Elevate your case interview skills with a well-rounded preparation package

A case interview is where candidates is asked to solve a business problem. They are used by consulting firms to evaluate problem-solving skill & soft skills

Case interview frameworks are methods for addressing and solving business cases.  A framework can be extensively customized or off-the-shelf for specific cases.

MECE is a useful problem-solving principle for case interview frameworks with 2 parts: no overlap between pieces & all pieces combined form the original item

Hacking the Case Interview

An issue tree is a structured framework used to break down and analyze complex problems or questions into smaller components. It is a visual representation of the various aspects, sub-issues, and potential solutions related to a particular problem.

Issue trees are commonly used in business, consulting, problem-solving, and decision-making processes.

If you’re looking to better understand issue trees and how to use them in consulting case interviews or in business, we have you covered.

In this comprehensive article, we’ll cover:

• What is an issue tree?
• Why are issue trees important?
• How do I create an issue tree?
• How do I use issue trees in consulting case interviews?
• What are examples of issue trees?
• What are tips for making effective issue trees?

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course . These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

What is an Issue Tree?

An issue tree is a visual representation of a complex problem or question broken down into smaller, more manageable components. It consists of a top level issue, visualized as the root question, and sub-issues, visualized as branches and sub-branches.

• Top Level Issue (Root Question) : This is the main problem or question that needs to be addressed. It forms the root of the tree.
• Sub-issues (Branches) : Underneath the top level issue are branches representing the major categories or dimensions of the problem. These are the high-level areas that contribute to the overall problem.
• Further Sub-issues (Sub-branches) : Each branch can be broken down further into more specific sub-issues.

Issue trees generally take on the following structure.

Issue trees get their name because the primary issue that you are solving for can be broken down into smaller issues or branches. These issues can then be further broken down into even smaller issues or branches.

This can be continued until you are left with a long list of small issues that are much simpler and more manageable. No matter how complicated or difficult a problem is, an issue tree can provide a way to structure the problem to make it easier to solve.

As an example, let’s say that we are trying to help a lemonade stand increase their profits. The overall problem is determining how to increase profits.

Since profits is equal to revenue minus costs, we can break this problem down into two smaller problems:

• How can we increase revenues?
• How can we decrease costs?

Since revenue is equal to quantity times price, we can further break this revenue problem down into two even smaller problems:

• How can we increase quantity sold?
• How can we increase price?

Looking at the problem of how to increase quantity sold, we can further break that problem down:

• How can we increase the quantity of lemonade sold?
• How can we increase the quantity of other goods sold?

We can repeat the same procedure for the costs problem since we know that costs equal variable costs plus fixed costs.

• How can we decrease variable costs?
• How can we decrease fixed costs?

Looking at the problem of how to decrease variable costs, we can further break that down by the different variable cost components of lemonade:

• How can we decrease costs of lemons?
• How can we decrease costs of water?
• How can we decrease costs of ice?
• How can we decrease costs of sugar?
• How can we decrease costs of cups?

The overall issue tree for this example would look like the following:

In this example, the issue tree is a special kind of issue tree known as a profit tree.

Why are Issue Trees Important?

Issue trees are helpful because they facilitate systematic analysis, managing complexity, prioritization, generating solutions, identifying root causes, work subdivision, roadmap generation, and effective communication.

Systematic analysis : Issue trees guide a systematic analysis of the problem. By dissecting the problem into its constituent parts, you can thoroughly examine each aspect and understand its implications.

Managing complexity : Complex problems often involve multiple interrelated factors. Issue trees provide a way to manage this complexity by organizing and visualizing the relationships between different components.

Prioritization : Issue trees help in prioritizing actions. By assessing the importance and impact of each sub-issue, you can determine which aspects of the problem require immediate attention.

Generating solutions : Issue trees facilitate the generation of potential solutions or strategies for each component of the problem. This allows for a more comprehensive approach to problem-solving.

Identifying root causes : Issue trees help in identifying the root causes of a problem. By drilling down through the sub-issues, you can uncover the underlying factors contributing to the main issue.

Work subdivision : Issue trees provide you with a list of smaller, distinct problems or areas to explore. This distinction makes it easy for you to divide up work.

Roadmap generation : Issue trees layout exactly all of the different areas or issues that you need to focus on in order to solve the overall problem. This gives you a clear idea of where to focus your attention and work on.

Effective communication : Issue trees are powerful communication tools. Visualizing the problem in a structured format helps in explaining it to others, including team members, stakeholders, or clients.

How Do I Create An Issue Tree?

Creating an issue tree involves several steps. Here's a step-by-step guide to help you through the process:

Step 1: Define the top-level issue

Start by clearly articulating the main problem or question that you want to address. This will form the root of your issue tree.

Step 2: Identify the branches (sub-issues)

Consider the major sub-issues that contribute to the overall problem. These will become the branches of your issue tree. Brainstorm and list them down.

There are four major ways that you can break down the root problem in an issue tree. You can break down the issue by stakeholder, process, segments, or math.

• Stakeholder : Break the problem down by identifying all stakeholders involved. This may include the company, customers, competitors, suppliers, manufacturers, distributors, and retailers. Each stakeholder becomes a branch for the top-level issue.
• Process : Break the problem down by identifying all of the different steps in the process. Each step becomes a branch for the top-level issue.
• Segment : Break the problem down into smaller segments. This may include breaking down the problem by geography, product, customer segment, market segment, distribution channel, or time horizon. Each segment becomes a branch for the top-level issue.
• Math : Break a problem down by quantifying the problem into an equation or formula . Each term in the equation is a branch for the top-level issue.

Step 3: Break down each branch

For each branch, ask yourself if there are further components that contribute to it. If so, break down each branch into more specific components. Continue this process until you've reached a level of detail that allows for meaningful analysis.

Similar to the previous step, you can break down a branch by stakeholder, process, segment, or by math.

Step 4: Review and refine

Take a step back and review your issue tree. Make sure it accurately represents the problem and its components. Look for any missing or redundant branches or sub-issues.

Step 5: Prioritize and evaluate

Consider assigning priorities to different sub-issues or potential solutions. This will help guide your decision-making process.

How Do I Use Issue Trees in Consulting Case Interviews?

Issue trees are used near the beginning of the consulting case interview to break down the business problem into smaller, more manageable components.

After the interviewer provides the case background information, you’ll be expected to quickly summarize the context of the case and verify the case objective. After asking clarifying questions, you’ll ask for a few minutes of silence to create an issue tree.

After you have created an issue tree, here’s how you would use it:

Step 1: Walk your interviewer through the issue tree

Once you’ve created an issue tree, provide a concise summary of how it's structured and how it addresses the problem at hand. Explain the different branches and sub-branches. They may ask a few follow-up questions.

As you are presenting your issue tree, periodically check in with the interviewer to ensure you're on the right track. Your interviewer may provide some input or guidance on improving your issue tree.

Step 2: Identify an area of your issue tree to start investigating

Afterwards, you’ll use the issue tree to help identify a branch to start investigating. There is generally no wrong answer here as long as you have a reason that supports why you want to start with a particular branch.

To determine which branch to start investigating, ask yourself a few questions. What is the most important sub-issue? Consider factors like urgency, impact, or feasibility. What is your best guess for how the business problem can be solved?

Step 3: Gather data and information

Collect relevant facts, data, and information for the sub-issue that you are investigating. This will provide the necessary context and evidence for your analysis.

Step 4 : Record key insights on the issue tree

After diving deeper into each sub-issue or branch on your issue tree, you may find it helpful to write a few bullets on the key takeaways or insights that you’ve gathered through your analysis.

This will help you remember all the work that you have done during the case interview so far. It’ll also help you develop a recommendation at the end of the case interview because you’ll quickly be able to read a summary of all of your analysis.

Step 5: Iterate and adjust as needed

As you work through the problem-solving process, be prepared to adjust and update the issue tree based on new information, insights, or changes in the situation.

Remember, creating an issue tree is not a one-size-fits-all process. It's a dynamic tool that can be adapted to suit the specific needs and complexity of the problem you're addressing.

Step 6: Select the next area of your issue tree to investigate

Once you have finished analyzing a branch or sub-issue on your issue tree and reached a satisfactory insight or conclusion, move onto the next branch or sub-issue.

Again, consider factors like urgency, impact, or feasibility when prioritizing which branch or sub-issue to dive deeper into. Repeat this step until the end of the case interview when you are asked for a final recommendation.

What are Examples of Issue Trees?

Below are five issue tree examples for five common types of business situations and case interviews.

If you want to learn strategies on how to create unique and tailored issue trees for any case interview, check out our comprehensive article on case interview frameworks .

Profitability Issue Tree Example

Profitability cases ask you to identify what is causing a company’s decline in profits and what can be done to address this problem.

A potential issue tree template for this case could explore four major issues:

• What is causing the decline in profitability?
• Is the decline due to changes among customers?
• Is the decline due to changes among competitors?
• Is the decline due to market trends?

Market Entry Issue Tree Example

Market entry cases ask you to determine whether a company should enter a new market.

• Is the market attractive?
• Are competitors strong?
• Does the company have the capabilities to enter?
• Will the company be profitable from entering the market?

Merger and Acquisition Issue Tree Example

Merger and acquisition cases ask you to determine whether a company or private equity firm should acquire a particular company.

• Is the market that the target is in attractive?
• Is the acquisition target an attractive company?
• Are there any acquisition synergies?
• Will the acquisition lead to high returns?

New Product Issue Tree Example

New product cases ask you to determine whether a company should launch a new product or service.

• Will customers like the product?
• Does the company have the capabilities to successfully launch the product?
• Will the company be profitable from launching the product?

Pricing Issue Tree Example

Pricing cases ask you to determine how to price a particular product or service.

A potential issue tree template for this case could explore three major issues:

• How should we price based on the product cost?
• How should we price based on competitors’ products?
• How should we price based on customer value?

What are Tips for Making Effective Issue Trees?

Issue trees are powerful tools to solve complex business problems, but they are much less effective if they don’t follow these important tips.

Issue tree tip #1: Be MECE

MECE stands for mutually exclusive and collectively exhaustive. When breaking down the overall problem in your issue tree, the final list of smaller problems needs to be mutually exclusive and collectively exhaustive.

Mutually exclusive means that none of the smaller problems in your issue tree overlap with each other. This ensures that you are working efficiently since there will be no duplicated or repeated work.

For example, let’s say that two of the issues in your issue tree are:

• Determine how to increase cups of lemonade sold
• Determine how to partner with local organizations to sell lemonade

This is not mutually exclusive because determining how to partner with local organizations would include determining how to increase cups of lemonade sold.

In determining how to increase cups of lemonade sold, you may be duplicating work from determining how to partner with local organizations.

Collectively exhaustive means that the list of smaller problems in your issue tree account for all possible ideas and possibilities. This ensures that your issue tree is not missing any critical areas to explore.

For example, let’s say that you break down the issue of determining how to decrease variable costs into the following issues:

This is not collectively exhaustive because you are missing two key variable costs: sugar and cups. These could be important areas that could increase profitability, which are not captured by your issue tree.

You can read a full explanation of this in our article on the MECE principle .

Issue tree tip #2: Be 80/20

The 80/20 principle states that 80% of the results come from 20% of the effort or time invested.

In other words, it is a much more efficient use of time to spend a day solving 80% of a problem and then moving onto solving the next few problems than to spend five days solving 100% of one problem.

This same principle should be applied to your issue tree. You do not need to solve every single issue that you have identified. Instead, focus on solving the issues that have the greatest impact and require the least amount of work.

Let’s return to our lemonade stand example. If we are focusing on the issue of how to decrease costs, we can consider fixed costs and variable costs.

It may be a better use of time to focus on decreasing variable costs because they are generally easier to lower than fixed costs.

Fixed costs, such as paying for a business permit or purchasing a table and display sign, typically have long purchasing periods, making them more difficult to reduce in the short-term.

Issue tree tip #3: Have three to five branches

Your issue tree needs to be both comprehensive, but also clear and easy to follow. Therefore, your issue tree should have at least three branches to be able to cover enough breadth of the key issue.

Additionally, your issue tree should have no more than five branches. Any more than this will make your issue tree too complicated and difficult to follow. By having more than five branches, you also increase the likelihood that there will be redundancies or overlap among your branches, which is not ideal.

Having three to five branches helps achieve a balance between going deep into specific sub-issues and covering a broad range of aspects. It balances breadth and depth.

Issue tree tip #4: Clearly define the top-level issue

Make sure that you clearly articulate the main problem or question. This sets the foundation for the entire issue tree. If you are addressing the wrong problem or question, your entire issue tree will be useless to you.

Issue tree tip #5: Visualize the issue tree clearly

If you're using a visual representation, make sure it's easy to follow. Use clean lines, appropriate spacing, and clear connections between components.

Keep your issue tree organized and neat. A cluttered or disorganized tree can be confusing and difficult to follow.

Ensure that each branch and sub-issue is labeled clearly and concisely. Use language that is easily understandable to your audience.

Issue tree tip #6: Order your branches logically

Whenever possible, try to organize the branches in your issue tree logically.

For example, if the branches in your issue tree are segmented by time, arrange them as short-term, medium-term, and long-term. This is a logical order that is arranged by length of time.

It does not make sense to order the branches as long-term, short-term, and medium- term. This ordering is confusing and will make the entire issue tree harder to follow.

Issue tree tip #7: Branches should be parallel

The branches on your issue tree should all be on the same logical level.

For example, if you decide to segment the branches on your issue tree by geography, your branches could be: North America, South America, Europe, Asia, Africa, and Australia. This segmentation is logical because each segment is a continent.

It would not make sense to segment the branches on your issue as United States, South America, China, India, Australia, and rest of the world. This segmentation does not follow logical consistency because it mixes continents and countries.

Issue tree tip #8: Practice and get feedback

It takes practice to create comprehensive, clear, and concise issue trees. This is a skill that takes time to develop and refine.

When you initially create your first few issue trees, it may take you a long period of time and you may be missing key sub-issues. However, with enough practice, you’ll be able to create issue trees effortlessly and effectively.

Practice creating issue trees on different problems to improve your skills. Seek feedback from peers or mentors to refine your approach.

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What are the differences between issue trees and hypothesis trees, overview of answers.

• Date ascending
• Date descending

Issue trees are at the heart of the problem-solving approach. What you refer to in your question are two distict types: diagnostic trees (what you call issue tree --> "problem-based") and solution trees (what you call hypothesis tree --> "solution-based").

Generally speaking, an issue tree is a graphical breakdown of your key question. Trees have four basic rules:

• They consistently answer why or how questions (depending on your key question)
• They progress from the key question to the analysis as they move to the right
• Their branches are mutually exclusive and collectively exhaustive (MECE)
• They use an insightful breakdown

Diagnostic trees are for diagnosing your key question

Diagnostic trees help you search for all the possible causes of a problem. They give you the " WHY? ".You list these in logical groups on the first column to the right of your key question, ensuring that your groupings are MECE. As you progress to the right, you drill further down in the details of each grouping.

Solution trees are for actively looking for ways to correct your problem

With solution trees , you look for all the potential solutions to your problem. They give you the " HOW? ". As a general rule, you want to know the WHY before you get to the HOW , so if you don’t know the root cause(s) of your problem, find these first by means of a diagnostic tree.

For broader context, issue trees progress further into details until elements are sufficiently explicit. Then come the hypotheses, analyses and data sources. Once you have tested which solutions are viable, you are ready to select one, for instance by using a decision matrix (impact vs. doability).

Example Problem Tree for a household recycling issue:

Example Solution Tree for a household recycling issue:

Hope this helps!

In practical sense, they are similar.

Imagine building a framework for Market Entry where you look at 4 things as part of a I ssue Tree:

• Market Attractiveness
• Competitive Landscape

Then you break each one down in more details. You have an issue tree now. You can also state a hypothesis for your interviewer saying: My hypothesis is that our client can enter the Japenese Car Manufacturing market, given that

• There is a real Market
• We can win in this market
• The economics are favourable
• And the risks are acceptable

Then you basically test each of these 4 hypotheses by asking the interviewer questions around each bucket ot test it. Does this help? Best, Aws

We might count to the COGS as well factors such as the German Packaging Act (https://www.lizenzero.de/en/blog/german-packaging-act-in-the-uk-obligations-when-shipping-to-germany/) or in general any costs that arise during shipment.

Related Cases

Bain Case Style - Growth offensive at ChemCorp [NEW]

Kearney first round case - top chemicals, related case interview basics article(s).

The Issue Tree Framework can be used to break down the problems of a case to its components and significantly increase your speed during case interviews.

Similar Questions

Last round ey / presentation case interview issue tree practise, hard/complex profitability structure - help, what's the best way to structure a revenue growth case.

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Lindsay Angelo

Issue tree explained: the ultimate guide including examples [2024].

An issue tree is a tool used to visualize and solve complex problems. Commonly used in strategic thinking, it can be applied to a variety of business situations, such as when you are trying to solve complex issues, make a decision, untangle complex situations, or come up with a new idea. In this blog post, we will discuss what an issue tree is, the basic principles or basic rules and how to unleash the power of an issue tree in strategic thinking. We'll also provide some examples of how issue trees can be used and address some key questions.

What are issue trees?

Issue tree s, sometimes referred to as "issue maps", are a logical structure and powerful tool that help you to identify the different elements of a problem in order to help solve it. They are commonly used in hypothesis based problem solving and are actually considered a type of hypothesis tree . Issue trees start by defining what the problem is and then asking a series of "why" questions until you can't ask it anymore. The beauty of an issue tree is that it can be used to help solve virtually any problem. Simply put, it's problem-solving process.

When to use issue trees?

An issue tree is used when you’re trying to figure out what the root cause of a complex issue is or the WHY – for example, US growth rates are declining and you’re trying to figure out why – is it related to market trends? Is it product related? Is it brand related or customer experience related? For issue trees, you’re asking questions related to “WHY” something is happening, trying to get to the root of the problem, which will either validate or refute your hypothesis .

How to use issue trees?

There are three main steps to crafting multi-layer issue trees: 

The first step is to identify the main problem or issue that you want to address. Visually this comes to life at the top of your tree. For example, "sales have been steadily declining in Austin, Texas".

The second step is to define the problem space - said otherwise, to brainstorm causes or root issues to the problem. Visually this comes to life as sub-branches to your main problem statement at the top. For example, one branch might be "market trends are declining", another branch might be "lack of product innovation", while another might be "customer experience lacking". For each branch, you then want to ask "why" until you can't ask it any longer. This will inform your sub-branches. For example, under "market trends are declining", one sub-branch might be "competition higher", another might be "overall spend in the niche is declining", etc. Ultimately, you're trying to drill down to the root issues.

The third and final step is to identify what you think the root problem(s) are and outline the data or facts you need to find to either prove or disprove them. This is the same process used in hypothesis-driven thinking . This will inform your work plan or road map.

MECE principle (Mutually Exclusive Collectively Exhaustive)

Ultimately an issue tree should apply the MECE principle .  MECE is a popular decision-making process technique, created by McKinsey & Company vis a vis Barbara Minto . MECE is a great tool for analyzing and solving problems and stands for Mutually Exclusive and Collectively Exhaustive. In other words, it helps you break down a problem into smaller, more manageable pieces, similar to what you're doing with an issue tree. 

The 80/20 principle is another important principle when designing an issue tree. Also known as the Pareto Principle, the Law of 80/20 states that roughly 80% of outcomes come from 20% of inputs. An example of this is when 20% of your customers often represent 80% of your sales. Once you've identified the problem space or potential root issues, you can use 80/20 to hypothesize the most relevant issues or key issues.

Issue Tree Examples

Let's take a look at an example of how multi-layer issue trees can be used. To be clear, multi-layer issues trees normally encompass a 1st layer, a 2nd layer, a 3rd layer and onward. As displayed in graphic a, suppose there has been a decline in US growth rates. You might start by asking the following key questions: 

Is this issue market share related?

Is this issue product related?

Is this issue brand related?

The above components are known as "primary issues". Once you have asked these questions, you can then brainstorm all of the possible sub-issues that could branch off from each one. For example, if you're thinking that this issue is related to one of the product lines you may ask: Which product is causing the most damage? How are our distribution channels affecting this decline?

By asking these questions, you can start to develop a work plan to figure out which of these issues is correct. That will give you your complete issue tree.

A second example would be:

Problem: Profitability is down Potential issues/branches: Fixed costs are up, Variable costs are up  Sub-issues: For fixed costs --> Leasing costs are up, insurance costs are up, property taxes are up, labor costs are up, etc. Note: Fixed costs are those that remain the same regardless of volume. Variable costs -->  commissions are higher, packaging supplies are more expensive, piece-rate labor costs are higher, credit card fees are higher, etc. Note: Variable costs are those costs that fluctuate as volume fluctuates.

As you can see, issue trees are a great tool for your strategic thinking toolkit. Issue trees can also help if you're in the Consulting space preparing for an interview or onboarding. They're often at the crux of real case interviews and your employer will be looking at how you can apply them effectively to problem-solve. 

Looking to level up your strategic thinking? Sign up for a free hypothesis problem-solving guide that includes an issue tree template and hypothesis tree template that will help you take that first step into your strategic thinking journey. 

Decision Trees, Decision Trees, and more Decision Trees

Decision Trees are different from issues trees but are also a popular framework to apply when trying to solve a problem. Often people confuse decision trees and issue trees. To keep it simple, a decision tree is used as part of the decision-making process when you're trying to make a decision, an issue tree is used when you're trying to uncover a root cause. If you're a decision maker, both of these tools will help. 

Interested in learning more about issue trees and hypothesis-driven thinking ? Check out this blog !

Do Management Consultants use issue trees?

Yes, management consulting firms used them all the time - issue trees are a helpful tool within the umbrella of hypothesis driven problem-solving which is the bread and butter or many of the big fives consultancies including McKinsey and Company, Bain, BCG, and more. Preparing to ace your consulting interview? Dreams of joining a consulting firm? Leap frog business school and master your issue tree and hypothesis based problem solving skills through this Masterclass.

What is meant by an issue tree?

See above. In short, an issue tree is an important tool that can be used to help structure and organize the different elements of a relevant issue. It is often used in business settings to help identify the root cause (think, root cause analysis) of a problem or to develop potential solutions. If you are facing a complex problem, consider using issue trees to help you better understand the situation and to develop a plan of action for any real issue you might be facing. It's one of a variety of powerful business concepts that will make you a better strategic thinking and help you arrive at an actual solution. 

What is a root cause analysis and how does it relates to issue trees?

A root cause analysis is a process aimed at getting to the source of a problem - the goal is essentially the same as that of an issue tree.

Are there different types of issue trees? 

Yes, but that's a level 201 concept, not covered in this blog post.

What's the difference between an issue and solution tree?

Both solution trees and issue trees are useful tools for problem-solving. However, it’s important to know when to use each one. If you’re trying to find a quick fix to a simple problem, you are probably safe to bypass the issue tree and go directly to a solution tree. However, if you want to get to the bottom of a complex problem and be sure to find the root cause, then an issue tree is what you need. Both types of trees can be applied to work examples and also real-life examples that occur in everyday life.

How do I start an issue tree?

To start an issue tree, first identify the main problem. This will be your "trunk". From there, create a complete list of all the potential "why" questions that could contribute to this problem. These will be your 2nd layer of branches. There you have it - the start of your issue tree!

What makes a good issue tree?

There are a few key principles that make a good issue tree. First, as a rule of thumb, the initial structure of the tree should be comprehensive. It should cover all of the potential issues that could be causing the problem. Second, the tree should be organized in a way that is easy to understand, each branch of the tree clearly labeled and easy to follow. Finally, the tree should be concise. It should not include any unnecessary information or superfluous branches. By following these guidelines, you can ensure that your issue tree is effective and helpful in solving problems.

What is a profitability framework?

A profitability framework is a specific type of issue tree that's also used to measure and improve their profitability. The framework provides a clear and concise way to track progress, identify areas of opportunity, and make decisions that will improve the bottom line.  The benefits of using a profitability framework are numerous, but perhaps the most important is that it gives businesses a comprehensive view of the levers that drive financial performance. Facing a profitability issue? Trying to figure out where to allocate resources or how to grow the business? This framework will be your best friend.

What is a decision matrix?

We talked about decision trees above. A sister to the decision tree is the decision matrix which is a tool related to a decision tree that can be used to help make decisions. It can be used to compare potential ideas and to evaluate the pros and cons of each option. This is different from hypothesis driven thinking.

Does Business School teach issues trees or hypothesis driven thinking? 

Nine times out of ten, no they don't. it's a fundamental skill that's missed in the Business School curriculum but you can master it through taking this masterclass.

About the Author

Lindsay provides growth and advisory services to purpose-driven brands. Named a global innovation leader and Women to Watch, you will find her at the intersection of strategy, storytelling and innovation. When she’s not collaborating with clients, she’s hitting TEDx and other stages across North America to deliver keynotes on the future of consumerism , strategy and innovation. Prior to advising and providing strategy consulting services, Lindsay spent six years at lululemon crafting their global growth strategy, exploring new marketplace opportunities, strategizing new ideas and growing the company into the number one yoga wear player in the world. Her experiences culminate in what she refers to as her sweet spot - where strategy, innovation and insights intersect, where the rational meets the emotive, where facts meet insights and where logic meets creativity.

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.

There are 5 main steps in hypothesis testing:

• State your research hypothesis as a null hypothesis and alternate hypothesis (H o ) and (H a  or H 1 ).
• Collect data in a way designed to test the hypothesis.
• Perform an appropriate statistical test .
• Decide whether to reject or fail to reject your null hypothesis.
• Present the findings in your results and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.

The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.

There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).

If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.

Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.

Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.

In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.

In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).

The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .

In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.

In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.

However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.

If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”

These are superficial differences; you can see that they mean the same thing.

You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.

If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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• Who’s Joe?

“A fact is a simple statement that everyone believes. It is innocent, unless found guilty. A hypothesis is a novel suggestion that no one wants to believe. It is guilty until found effective.”

– Edward Teller, Nuclear Physicist

During my first brainstorming meeting on my first project at McKinsey, this very serious partner, who had a PhD in Physics, looked at me and said, “So, Joe, what are your main hypotheses.” I looked back at him, perplexed, and said, “Ummm, my what?” I was used to people simply asking, “what are your best ideas, opinions, thoughts, etc.” Over time, I began to understand the importance of hypotheses and how it plays an important role in McKinsey’s problem solving of separating ideas and opinions from facts.

What is a Hypothesis?

“Hypothesis” is probably one of the top 5 words used by McKinsey consultants. And, being hypothesis-driven was required to have any success at McKinsey. A hypothesis is an idea or theory, often based on limited data, which is typically the beginning of a thread of further investigation to prove, disprove or improve the hypothesis through facts and empirical data.

The first step in being hypothesis-driven is to focus on the highest potential ideas and theories of how to solve a problem or realize an opportunity.

Let’s go over an example of being hypothesis-driven.

Let’s say you own a website, and you brainstorm ten ideas to improve web traffic, but you don’t have the budget to execute all ten ideas. The first step in being hypothesis-driven is to prioritize the ten ideas based on how much impact you hypothesize they will create.

The second step in being hypothesis-driven is to apply the scientific method to your hypotheses by creating the fact base to prove or disprove your hypothesis, which then allows you to turn your hypothesis into fact and knowledge. Running with our example, you could prove or disprove your hypothesis on the ideas you think will drive the most impact by executing:

1. An analysis of previous research and the performance of the different ideas 2. A survey where customers rank order the ideas 3. An actual test of the ten ideas to create a fact base on click-through rates and cost

While there are many other ways to validate the hypothesis on your prioritization , I find most people do not take this critical step in validating a hypothesis. Instead, they apply bad logic to many important decisions . An idea pops into their head, and then somehow it just becomes a fact.

One of my favorite lousy logic moments was a CEO who stated,

“I’ve never heard our customers talk about price, so the price doesn’t matter with our products , and I’ve decided we’re going to raise prices.”

Luckily, his management team was able to do a survey to dig deeper into the hypothesis that customers weren’t price-sensitive. Well, of course, they were and through the survey, they built a fantastic fact base that proved and disproved many other important hypotheses.

Why is being hypothesis-driven so important?

Imagine if medicine never actually used the scientific method. We would probably still be living in a world of lobotomies and bleeding people. Many organizations are still stuck in the dark ages, having built a house of cards on opinions disguised as facts, because they don’t prove or disprove their hypotheses. Decisions made on top of decisions, made on top of opinions, steer organizations clear of reality and the facts necessary to objectively evolve their strategic understanding and knowledge. I’ve seen too many leadership teams led solely by gut and opinion. The problem with intuition and gut is if you don’t ever prove or disprove if your gut is right or wrong, you’re never going to improve your intuition. There is a reason why being hypothesis-driven is the cornerstone of problem solving at McKinsey and every other top strategy consulting firm.

How do you become hypothesis-driven?

Most people are idea-driven, and constantly have hypotheses on how the world works and what they or their organization should do to improve. Though, there is often a fatal flaw in that many people turn their hypotheses into false facts, without actually finding or creating the facts to prove or disprove their hypotheses. These people aren’t hypothesis-driven; they are gut-driven.

The conversation typically goes something like “doing this discount promotion will increase our profits” or “our customers need to have this feature” or “morale is in the toilet because we don’t pay well, so we need to increase pay.” These should all be hypotheses that need the appropriate fact base, but instead, they become false facts, often leading to unintended results and consequences. In each of these cases, to become hypothesis-driven necessitates a different framing.

• Instead of “doing this discount promotion will increase our profits,” a hypothesis-driven approach is to ask “what are the best marketing ideas to increase our profits?” and then conduct a marketing experiment to see which ideas increase profits the most.

• Instead of “our customers need to have this feature,” ask the question, “what features would our customers value most?” And, then conduct a simple survey having customers rank order the features based on value to them.

• Instead of “morale is in the toilet because we don’t pay well, so we need to increase pay,” conduct a survey asking, “what is the level of morale?” what are potential issues affecting morale?” and what are the best ideas to improve morale?”

Beyond, watching out for just following your gut, here are some of the other best practices in being hypothesis-driven:

Listen to Your Intuition

Your mind has taken the collision of your experiences and everything you’ve learned over the years to create your intuition, which are those ideas that pop into your head and those hunches that come from your gut. Your intuition is your wellspring of hypotheses. So listen to your intuition, build hypotheses from it, and then prove or disprove those hypotheses, which will, in turn, improve your intuition. Intuition without feedback will over time typically evolve into poor intuition, which leads to poor judgment, thinking, and decisions.

Constantly Be Curious

I’m always curious about cause and effect. At Sports Authority, I had a hypothesis that customers that received service and assistance as they shopped, were worth more than customers who didn’t receive assistance from an associate. We figured out how to prove or disprove this hypothesis by tying surveys to transactional data of customers, and we found the hypothesis was true, which led us to a broad initiative around improving service. The key is you have to be always curious about what you think does or will drive value, create hypotheses and then prove or disprove those hypotheses.

Validate Hypotheses

You need to validate and prove or disprove hypotheses. Don’t just chalk up an idea as fact. In most cases, you’re going to have to create a fact base utilizing logic, observation, testing (see the section on Experimentation ), surveys, and analysis.

Be a Learning Organization

The foundation of learning organizations is the testing of and learning from hypotheses. I remember my first strategy internship at Mercer Management Consulting when I spent a good part of the summer combing through the results, findings, and insights of thousands of experiments that a banking client had conducted. It was fascinating to see the vastness and depth of their collective knowledge base. And, in today’s world of knowledge portals, it is so easy to disseminate, learn from, and build upon the knowledge created by companies.

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Hypothesis-Driven Approach: Crack Your Case Like a Consultant

• Last Updated June, 2023

A hypothesis-driven approach in consulting is a structured method of problem-solving. Consultants formulate a hypothesis for the solution to a business problem, then gather data to support or disprove it. 

Cracking a case interview can be a daunting task, with a wide range of potential solutions and approaches to consider. However, using a hypothesis-driven approach is a systematic and effective problem-solving method. It will impress your interviewer and demonstrate your readiness for a career in consulting.

In this article, we will talk about:

• The definitions of a hypothesis and a hypothesis-driven approach
• The differences between a hypothesis-driven approach and a non-hypothesis-driven approach
• An example of how to solve a case using both approaches
• Our 5-step process for using a hypothesis-driven approach to solve consulting cases

Let’s get started!

What Is a Hypothesis & a Hypothesis-Driven Approach?

Differences between a hypothesis-driven approach vs. non-hypothesis-driven approach, our 5-step process for using the hypothesis-driven mindset to solve cases, other consulting tools that will strengthen your problem-solving.

In the realm of science, the term “hypothesis” is used to describe a proposed explanation for a question or phenomenon, based on limited evidence, as a starting point for further investigation. Similarly, consultants act as scientists or as doctors solving their clients’ business problems, constantly forming and testing hypotheses to identify the best solutions. 

The key phrase here is “starting point,” as a hypothesis is an educated guess at the solution, formed from currently available information. As more data is gathered, the hypothesis may be adjusted or even discarded entirely.

Nail the case & fit interview with strategies from former MBB Interviewers that have helped 89.6% of our clients pass the case interview.

Hypothesis-Driven Approach

Consultants are engaged to efficiently and effectively solve their clients’ problems and assist in making critical business decisions. With the vast amount of data available and an array of options to consider, it can be overwhelming to examine everything. Time constraints on projects make it imperative that consultants avoid getting bogged down in excessive analysis and questioning, without making meaningful progress toward a recommendation.

Instead, consultants begin by forming a hypothesis after gaining an understanding of the client’s problem and high-level range of possibilities. Then, they gather data to test the initial hypothesis. If the data disproves the hypothesis, the consultants repeat the process with the next best hypothesis. This method of problem-solving is commonly used by top consulting firms, such as McKinsey.

A non-hypothesis-driven approach is the opposite of a hypothesis-driven approach. Instead of forming a hypothesis, the individual makes a recommendation only after thoroughly evaluating all data and possibilities. This approach may rely on intuition, trial and error, or exhaustively exploring all options to solve the problem. This is not an efficient method for a case interview, where time is limited.

An analogy that illustrates the distinction between the two methods is to look at problem-solving as trying to find a needle in a haystack. A non-hypothesis-driven approach would involve randomly searching through the entire stack without any clear strategy. 

On the other hand, a hypothesis-driven approach would involve dividing the haystack into smaller piles, and systematically searching through one section at a time. The searcher would gather information from the person who lost the needle, such as their location when it was lost, to identify the most likely pile to search first. This not only saves time but also increases the likelihood of finding the needle. If the needle is not found in the initial pile, the search can then move on to the next most probable pile.

Solving a Case Interview Using the Hypothesis-Driven Approach vs. the Non-Hypothesis-Driven Approach

To further illustrate the advantages of a hypothesis-driven approach, let’s examine two different approaches to the same case interview example. We’ll compare and contrast these approaches, highlighting the key distinctions between them. By the end, you’ll have a clear understanding of the benefits of using a hypothesis-driven approach in problem-solving. 

The client is SnackCo, a consumer goods company that manufactures and sells trail mixes in the United States. Over the past decade, SnackCo has seen significant growth following the launch of premium trail mix products, capitalizing on the trend toward healthier snacking options. Despite this success, the company’s operations have remained unchanged for the past decade. SnackCo is asking for your help to improve its bottom line.

Let’s look at how two candidates, Alex and Julie, solve the same case.

The Non-Hypothesis-Driven Approach

After hearing this prompt, Alex jumps right into listing possible questions related to how to improve the bottom line.

Alex: I understand SnackCo wants to improve profitability. Here are some questions I want to look into. Has SnackCo’s retail prices remained the same in recent years?

Interviewer: No, SnackCo has adjusted prices quite closely to what competitive products are selling at.

Alex: Oh interesting. Are consumers willing to pay more for premium trail mix? Do we know if we are underpricing?

Interviewer: SnackCo’s Director of Sales strongly believes that they should not change product prices. He believes the consumers love the product and it is priced fairly. 

Alex: Got it. Has the client’s market share decreased?

Interviewer: No, the market share has increased over the years.

Alex: In that case, it seems like our growth is fine. Have the costs increased?

Interviewer: SnackCo has not made many changes to its costs and operations in the last decade. What are some ways we can help them look at their cost savings opportunities?

Although Alex is making progress and may eventually solve the case, his communication style gives the impression that he is randomly guessing at the sources of the problem, rather than using logical reasoning and structure to pinpoint the solution.

The Hypothesis-Driven Approach

Julie has prepared for her case interviews with My Consulting Offer’s coaches so she is well-versed in the hypothesis-driven approach. 

After hearing the same prompt, she takes a moment to write down the key issues she wants to dig into to solve this case and organizes her thoughts. 

Julie: For the goal of improving profitability, we could look at how to improve revenue or decrease costs. For revenue, we could look at if prices or volumes have changed. Since the client said they haven’t made any changes to the business operations in the last decade, I would like to start with a better understanding of their costs. However, before we begin, I want to confirm if there have been any changes to prices or volumes recently.

Interviewer: SnackCo’s Director of Sales strongly believes that they should not change product prices. They also believe the volumes have grown well as SnackCo is one of the market leaders now. 

Julie: Great. That confirms what I was thinking. It’s likely a cost problem. We could look at their variable costs, such as ingredients, or fixed costs, such as manufacturing facilities. Given that this is an established business, I would assume their fixed costs are likely consistent. Therefore, let’s start with their variable costs.

Interviewer: How should we think about variable costs?

Julie: Variable costs for SnackCo likely include ingredients, packaging, and freight. The levers they could pull to reduce these costs would be through supplier relationships or changing the product composition. 

Julie quickly identifies that variable costs are likely the problem and has a structured approach to understanding which opportunities to explore. 

Key Differences

The interviewer is looking for candidates with strong problem-solving and communication skills, which are the qualities of a good consultant. Let’s look at how the two candidates performed.

Problem-Solving

Alex’s approach to solving the client’s problem was haphazard, as he posed a series of seemingly unrelated questions in no particular order. This method felt more like a rapid-fire Q&A session rather than a structured problem-solving approach. 

On the other hand, Julie takes a structured and analytical approach to address profitability concerns. She quickly realizes that while revenue is one factor of profitability, it is likely costs that are the main concern, as they haven’t changed much in the last decade. She then breaks down the major cost categories and concludes that variable costs are the most likely opportunity for cost reduction. Julie is laser-focused on the client’s goal and efficiently gets to a solution.

Communication

Alex is not making a positive initial impression. If this were an actual client interaction, his questioning would appear disorganized and unprofessional. 

On the other hand, Julie appears more organized through her clear communication style. She only considers the most pertinent issues at hand (i.e., the client’s business operations and costs) and avoids going down irrelevant rabbit holes.

• Understand the client’s problem; ask clarifying questions if needed.
• Formulate an issue tree to break down the problem into smaller parts.
• State the initial hypothesis and key assumptions to be tested.
• Gather and analyze information to prove or disprove the hypothesis; do not panic if the hypothesis is disproven.
• Pivot the hypothesis if necessary and repeat step 4. Otherwise, make your recommendation on what the client can do to solve their problem. 

Other helpful tips to remember when using the hypothesis-driven approach:

• Stay focused on the client’s problem and remember what the end goal is.
• Think outside the box and consider new perspectives beyond traditional frameworks. The basic case interview frameworks are useful to understand but interviewers expect candidates to tailor to the specific client situation.
• Clearly communicate assumptions and implications throughout the interview; don’t assume the interviewer can read your mind.

A hypothesis-driven approach is closely tied to other key consulting concepts, such as issue trees, MECE, and 80/20. Let’s take a closer look at these topics and how they relate.

• Issue Trees

Issue trees, also known as decision trees, are visual tools that break down complex business problems into smaller, more manageable parts. In a consulting interview, candidates use the issue tree to outline key issues and potential factors in the client’s problem, demonstrating their understanding of the situation. This structure is then used to guide the case discussion, starting with the candidate’s best hypothesis, represented as one branch of the issue tree. For more information and examples of issue trees, check out our i ssue tree post. 

During the interview process, consulting firms look for candidates who can demonstrate a MECE (mutually exclusive and collectively exhaustive) approach to problem-solving, which involves breaking down complex issues into distinct, non-overlapping components. 

A MECE approach in case interviews involves identifying all potential paths to solving a client’s problem at a high level. This allows the candidate to form an initial hypothesis with confidence that no potential solutions have been overlooked. To gain a deeper understanding, read our comprehensive guide on the MECE case structure .

Consultants use the 80/20 rule, also known as the Pareto principle, to prioritize their efforts and focus on the most important things. This principle states that 80% of effects come from 20% of causes, which means a small number of issues often drive a large portion of the problem. By identifying and focusing on the key issues, consultants can achieve significant results with relatively minimal resources.

By following these tips and developing a solid understanding of the hypothesis-driven approach to case-solving, you will have the necessary tools to excel in your case interview. For more interview resources, check out Our Ultimate Guide to Case Interview Prep . 

– – – – –

In this article, we’ve covered:

• Explanations of a hypothesis and hypothesis-driven approach
• Comparison between a hypothesis-driven approach and a non-hypothesis-driven approach
• Examples of the same case using both approaches and the key differences
• Practical tips on how to develop a hypothesis-driven mindset to ace the case

Still have questions?

If you have more questions about the best degrees for a career in consulting, leave them in the comments below. One of My Consulting Offer’s recruiters will answer them.

Other people preparing to apply to consulting firms found the following pages helpful:

• Our Ultimate Guide to Case Interview Prep
• Types of Case Interviews
• Case Frameworks
• Hypothesis Trees

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Thanks for turning to My Consulting Offer for advice on the best majors for consulting. My Consulting Offer has helped almost 89.6% of the people we’ve worked with to get a job in management consulting. We want you to be successful in your consulting interviews too. For example, here is how Misha was able to get his offer from BCG.

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Understanding Evolution

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• The Tree Room

Trees are hypotheses

If you had read about the evolutionary history of whales in the 1970s or 80s, you might have seen a tree that looks something like that shown below left, which implies that whales are closely related to an extinct group of mammals called the mesonychids. Today, we know that the origin of whales is better represented by the tree on the right. Whales and water-loving hippos are closely related! Why the change? Because the discovery of new  DNA  evidence caused paleontologists to re-evaluate their interpretations of the  fossil  evidence, leading to a revision of our understanding of the evolutionary relationships in this group.

Furthermore, we know that this branch of the mammal’s evolutionary tree will continue to grow as paleontologists dig further into the fossil record. Most organisms that have ever lived on Earth (including most ancient relatives of whales) have gone extinct. As new fossil organisms are discovered, biologists will have to figure out where on this tree they fit. In fact, we will never know the  true  evolutionary history of  all  whale-relatives because of the incompleteness of the fossil record. Many organisms that belong on this tree have gone extinct without leaving a trace in the fossil record. However, it’s important to keep in mind that, although this tree is incomplete and some details may change as we discover new evidence, it is still a good representation of the relationships among these groups of organisms and is based on many different converging lines of evidence.

This example highlights a basic characteristic of evolutionary trees: they are  hypotheses  that have been tested with evidence. Because they are supported by so many lines of evidence, widely accepted phylogenetic trees are unlikely to have their branches rearranged (though new branches are likely to be added as species are discovered). However, a change in our understanding is always possible. If new evidence is discovered or old evidence is reinterpreted, we must adjust our views of evolutionary relationships to reflect those data. Ignoring evidence would be bad science!

This doesn’t mean that trees change all the time. On the contrary, many evolutionary trees are so well supported (and continue to be supported by newly discovered evidence) that they are very likely to represent the evolutionary relationships among the organisms included accurately. 4  For example, the idea that birds are a twig on the dinosaurs’ branch of the tree of life became widely accepted in the 1980s and 90s based on fossil and anatomical evidence. Subsequent decades have yielded evidence that further supports this hypothesis. Hundreds of feathered dinosaur fossils have been unearthed, and  proteins  extracted from a  Tyrannosaurus rex  fossil were found to be remarkably similar to those of a chicken. We’d all better get used to the idea that birds are part of the dinosaur lineage, because all the available evidence suggests that it is true and that the idea is here to stay! New feathered dinosaur species will certainly be discovered and we will need to add them to the tree, but such changes are very unlikely to shake our basic understanding of the close relationship between birds and dinosaurs.

4  Of course, any phylogenetic tree is likely to be incomplete because of the existence of now-extinct lineages that belong on the tree but that we simply don't know about.

Trees adapted from: Geisler, J.H., and J.M. Theodor. 2009. Hippopotamus and whale phylogeny. Nature 458:E1-E4; Naylor, G.J.P, and D.C. Adams. 2001. Are the fossil data really at odds with the molecular data? Morphological evidence for Cetartiodactyla phylogeny reexamined. Systematic Biology 50:444-453; Zhou, X., S. Xu, Y. Yang, K. Zhou, and G. Yang. 2011. Phylogenomic analyses and improved resolution of Cetartiodactyla . Molecular Phylogenetics and Evolution 61:255-264; Zelenitsky, D.K., F. Therrien, G.M. Erickson, C.L. DeBuhr, Y. Kobayashi, D.A. Eberth, and F. Hadfield. 2012. Feathered non-avian dinosaurs from North America provide insight into wing origins. Science 338:510-514.

Clades within clades

The anatomy of an evolutionary tree

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AP®︎/College Biology

Course: ap®︎/college biology   >   unit 7.

• Taxonomy and the tree of life
• Discovering the tree of life
• Understanding and building phylogenetic trees

Phylogenetic trees

• Building a phylogenetic tree

Key points:

• A phylogenetic tree is a diagram that represents evolutionary relationships among organisms. Phylogenetic trees are hypotheses, not definitive facts.
• The pattern of branching in a phylogenetic tree reflects how species or other groups evolved from a series of common ancestors.
• In trees, two species are more related if they have a more recent common ancestor and less related if they have a less recent common ancestor.
• Phylogenetic trees can be drawn in various equivalent styles. Rotating a tree about its branch points doesn't change the information it carries.

Introduction

Anatomy of a phylogenetic tree, which species are more related, some tips for reading phylogenetic trees, where do these trees come from, attribution.

• " Taxonomy and phylogeny ," by Robert Bear, David Rintoul, Bruce Snyder, Martha Smith-Caldas, Christopher Herren, and Eva Horne, CC BY 4.0 . Download the original article for free at http://cnx.org/contents/[email protected] .
• " Organizing life on Earth ," by OpenStax College, Biology, CC BY 4.0 . Download the original article for free at http://cnx.org/contents/[email protected] .

Works cited

• John. W. Kimball, "Taxonomy: Classifying Life," Kimball's Biology Pages, last modified December 16, 2013, http://www.biology-pages.info/T/Taxonomy.html .
• Jack R. Holt, "Polytomy," Dictionary of Terms,ast revised January 2, 2009, http://comenius.susqu.edu/biol/202/dictionary%20of%20terms/p/polytomy.htm .

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Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

What is Hypothesis Testing?

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. 

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

Defining Hypotheses

Key Terms of Hypothesis Testing

• P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
• Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
• Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
• Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing. 

One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

• Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
• t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
• Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
• F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

• If Test Statistic>Critical Value: Reject the null hypothesis.
• If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

• μ represents the population mean, 
• σ is the standard deviation
• and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

• t = t-score,
• x̄ = sample mean
• μ = population mean,
• s = standard deviation of the sample,
• n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

• i,j are the rows and columns index respectively.

Real life Hypothesis Testing example

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

• Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
• After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

• Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
• Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

• m  = mean of the difference i.e X after, X before
• s  = standard deviation of the difference (d) i.e d i ​= X after, i ​− X before,
• n  = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

• If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
• If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Hypothesis Testing

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05. 

• The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
• The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

• Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
• Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Limitations of Hypothesis Testing

• Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
• The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
• Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

2.What are the 4 components of hypothesis testing?

Null Hypothesis ( ): No effect or difference exists. Alternative Hypothesis ( ): An effect or difference exists. Significance Level ( ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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Different profiles of soil phosphorous compounds depending on tree species and availability of soil phosphorus in a tropical rainforest in French Guiana

• Albert Gargallo-Garriga 1 , 2 ,
• Jordi Sardans 3 , 4 ,
• Joan Llusià 3 , 4 ,
• Guille Peguero 3 , 4 ,
• Marta Ayala-Roque 2 ,
• Elodie A. Courtois 5 , 6 ,
• Clément Stahl 7 ,
• Otmar Urban 3 ,
• Karel Klem 3 ,
• Pau Nolis 8 ,
• Miriam Pérez-Trujillo 8 ,
• Teodor Parella 8 ,
• Andreas Richter 9 ,
• Ivan A. Janssens 5 &
• Josep Peñuelas 3 , 4  

BMC Plant Biology volume  24 , Article number:  278 ( 2024 ) Cite this article

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The availability of soil phosphorus (P) often limits the productivities of wet tropical lowland forests. Little is known, however, about the metabolomic profile of different chemical P compounds with potentially different uses and about the cycling of P and their variability across space under different tree species in highly diverse tropical rainforests.

We hypothesised that the different strategies of the competing tree species to retranslocate, mineralise, mobilise, and take up P from the soil would promote distinct soil 31 P profiles. We tested this hypothesis by performing a metabolomic analysis of the soils in two rainforests in French Guiana using 31 P nuclear magnetic resonance (NMR). We analysed 31 P NMR chemical shifts in soil solutions of model P compounds, including inorganic phosphates, orthophosphate mono- and diesters, phosphonates, and organic polyphosphates. The identity of the tree species (growing above the soil samples) explained > 53% of the total variance of the 31 P NMR metabolomic profiles of the soils, suggesting species-specific ecological niches and/or species-specific interactions with the soil microbiome and soil trophic web structure and functionality determining the use and production of P compounds. Differences at regional and topographic levels also explained some part of the the total variance of the 31 P NMR profiles, although less than the influence of the tree species. Multivariate analyses of soil 31 P NMR metabolomics data indicated higher soil concentrations of P biomolecules involved in the active use of P (nucleic acids and molecules involved with energy and anabolism) in soils with lower concentrations of total soil P and higher concentrations of P-storing biomolecules in soils with higher concentrations of total P.

Conclusions

The results strongly suggest “niches” of soil P profiles associated with physical gradients, mostly topographic position, and with the specific distribution of species along this gradient, which is associated with species-specific strategies of soil P mineralisation, mobilisation, use, and uptake.

Peer Review reports

Tropical forests are characterised by high biodiversity and biomass despite growing in strongly weathered soils. All tropical rainforests tend to have high productivity, rapid nutrient turnover, highly weathered soil, and low soil pH [ 1 ]. Tropical regions, such as those in Africa, Asia, and South America, have distinct geological histories that underlie the high biodiversity [ 2 ]. The distribution of plant species and soils are highly variable at local scales within tropical regions [ 3 ]. Several mechanisms have been proposed to explain the coexistence of many plant species in small areas in tropical forest i.e. the high biodiversity observed in tropical forests [ 4 , 5 ]. Many of these mechanisms include heterogeneous disturbances and systems of regeneration [ 6 ]. A diverse topography [ 7 ], species-specific defenses against herbivores [ 8 ], soil traits heterogeneity [ 9 , 10 , 11 ], and differences in nutrient availability [ 10 , 12 , 13 , 14 ] are the other most frequently discussed mechanisms.

The amount of P and its availability limits the productivity of many terrestrial and aquatic ecosystems [ 15 ]. Stocks of total soil P, the chemical forms of P, and P availability in the soil change as ecosystems age and develop, and these transformations can strongly influence ecosystem properties [ 16 , 17 , 18 ]. In particular, biological productivity in wet tropical forests is frequently limited by the availability of soil P [ 19 , 20 ]. Soil taxonomic studies (Soil Survey Staff 2006) classify most tropical forest soils as Oxisols, Ultisols, Alfisols, Inceptisols, or Entisols [ 21 ]. P in these soils usually occurs as organic P and as occluded inorganic forms as part of pedogenic minerals. Occluded forms of P are especially common in older soils (Oxisols, Ultisols, and Alfisols), which frequently have very low or negligible amounts of primary minerals in their profiles and low concentrations of orthophosphate, which is the chemical form of P directly available to plants [ 17 , 22 ]. In contrast, organic P can account for a considerable proportion of total P in tropical mineral soils, accounting for an average of 29 ± 3% of the total P in equatorial forests and in Panama (soil organic P in lowland tropical forests) [ 23 , 24 ].

The turnover of organic P is the primary source of P for microbes and plants (soluble inorganic phosphate ions) in tropical soils [ 25 , 26 ], even though several plant-soil processes can make organic and inorganic/occluded P available to plants, such as mobilisation by roots [ 27 ] or the chemical reduction of iron-phosphate complexes under anaerobic conditions [ 28 ]. Organic P in forest soils is derived from fresh organic matter (leaf litter), microbial biomass, and non-microbial biomass. In general there is evidence suggesting rapid decomposition of leaf litter in the humid tropics (< 1 year; [ 29 ], despite other studies have observed slower rates of leaf litter decomposition (> 1 year) [ 30 ]. Litter nonetheless provides most of the P that supports growth in strongly weathered tropical soils. This phenomenon of “ direct nutrient cycling ” in tropical forests is characterised by the fast release of biologically available phosphate to roots and mycorrhizae by the decomposition of leaf litter and the consequent fast absorption of P by microbes and plants, which is so rapid that the plant-soil P cycle closes, nearly preventing P from being lost via leaching or sorption to iron and aluminium oxides [ 31 ].

Knowledge of the various chemical types of soil organic P and of how plants and microbes use these forms of P is essential to better understand the global cycling and use of P in the plant-soil systems of tropical rainforests. 31 P nuclear magnetic resonance (NMR) is an excellent tool for studying soil organic P because it provides quantitative data and allows the comparison of the various chemical forms of P [ 32 , 33 , 34 , 35 ]. In fact, 31 P NMR allows to discern different molecules where P is present, molecules with different metabolic function such as phosphate mono- and di-esters such as nucleic acids, ATP or acilglyrates involved directly in metabolism pathways, metabolism control and energy transfer from molecules such as orthophosphate, pyrophosphates and polyphosphates, which are involved in P storage. For example, 31 P NMR in soil studies provides data on the proportion of diester P associated with changes in microbial P compounds [ 36 , 37 ] and the ratio of monoester P to diester P, information needed to characterise the lability and rate of turnover of soil organic P.

In these conditions of high species diversity under strong P limitation, we hypothesised, as suggested in previous reports [ 38 ], a long-term adaptation of sympatric species to maximise the capacity of taking up P while avoiding competition. We tested this hypothesis using 31 P NMR spectroscopy in a P metabolomics study to determine the allocation of P to different biological functions in the soil. Our objective was to investigate the variation in soil P profiles along topographic gradients in two tropical forests with highly diverse compositions of tree species for determining whether changes in the profiles of soil organic P were correlated with changes in the composition of tree species and/or with distinct topographic environments and sites. We hypothesised that tree species would use P in specific ways, because the species occupy different functional [ 39 ] and biogeochemical [ 40 ] niches. Biogeochemical niche hypothesis captures niche parameters through species-specific elemental composition and stoichiometry [ 40 , 41 , 42 , 43 ]. The assumptions underlying it are based on the idea that each species is a unique genetic pool of individuals, a product of long-term evolutionary processes, so each species should have a specific structure and functionality (from gene expression to physiological processes). Since the fundamental biological processes (e.g. growth, secondary metabolism, reproduction and storage) have distinct rates in different species, depending on what selection has shaped, the different species have to allocate elements to various traits of tissues and organs differentially. The different use of bio-elements has proved to be even more different in sympatric species as a trait that could avoid direct competition [ 40 ]. Thus, as phosphorus is frequently limiting in tropical rainforests, we should expect that each species tends to have its own P-use strategy (P-metabolome niche) and that this should be underlying the higher species diversity of this high diverse ecosystem. We hypothesized that the tree species would use P in specific ways because each species occupies different functional [ 39 ] and biogeochemical [ 40 ] niches, thus providing species-specific litter that would accordingly modify the 31 P-NMR profile of the underlying soil. Our specific expectations were: (1) species composition would influence the proportions of different P compounds in the underlying soil, and (2) the 31 P NMR profiles would differ amongst and within sites (due to factors such as topography), indicative of differences in P use.

1D 31 P NMR

The spectra of acid-insoluble compounds indicated three main P resonances: monoesters, phospholipids (orthophosphate diester), and DNA. With NMR we were able to determine the family of P-compounds (Fig.  1 ), but we could not determine the exact compounds. Signals from nucleic acids (DNA: −0.37 ppm) and phospholipids were differentiated in the orthophosphate diester region and were readily identified in the soil samples. Inorganic and organic polyphosphates were differentiated by the presence of a signal at − 9 ppm from the α phosphate of organic polyphosphates. Some orthophosphate monoesters, such as mononucleotides derived from RNA and phosphatidyl choline, degraded rapidly to orthophosphate diesters in NaOH-EDTA, although DNA and phospholipids were more stable. The 31 P NMR spectra of NaOH-EDTA extracts from all soil samples generally presented monoesters ( ∼  25%) at 3.4 to 5.4 ppm, unhydrolysed diesters ( ∼  20%) at − 1 to 2.3 ppm, and DNA ( ∼  20%) at − 0.3 ppm. The less abundant forms were polyphosphate ( ∼  10%) at − 5.6 to − 3.8 ppm, inorganic orthophosphate (hereafter ‘phosphate’; ∼ 10%) at 5.7 to 6.5 ppm, and the pyrophosphate inorganic form of P ( ∼  5%) at 0.5 to 0.6 ppm. Glucose-6 phosphates had low resonance intensities, at 5.3 to 5.4 ppm.

31 P NMR chromatogram with the different molecules shown in the chromatogram

Soil P compounds and nutrients

In the PCA of organic P compounds; nutrients N, P, and K; enzymatic activity, and ecophysiological variables PC1 axis correlated best with site whereas PC2 correlates with samples of different topographic positions within each site (PC2) (Fig.  2 ). We examined the PCA results to identify the components that correlated best with site for better understanding the relationships of site with organic P compounds and the concentrations of C, N, P, and K. The PC2 axes correlated with topographic position and separated samples from the top, slope, and bottom positions, in Nourague and those of top and slope with respect to those of bottom in Paracou site.

Principal component analyses of soil organic P compounds (green), nutrients (red), d 13 C, d 15 N, enzymatic activities, and ecophysiological variables (black) indicating significant effects of topographic position and site, with corresponding standard deviations Polyphos (polyphosphate); pyrophos (pyrophosphate) polyphosphos (polyphosphonate); orthophos (orthophosphate), orthophosmono (orthophosphate monosester), orthophosphate-diester (orthophosdiester); glucose6phos (glucose-6phosphates); SPAD—chlorophyll content; C—carbon; N—nitrogen; K—potassium; P—phosphorus. The abbreviations in the legend refer to the site (Paracou and Nouragues) and topographic position: T, top; S, slope; and B, bottom

The PCA results also indicated that soil with higher total P concentrations had higher concentrations of organic P compounds involved in storage (polyphosphates and polyphophos) and of C-free forms of P (orthophosphates and pyrophosphates). In contrast, soils with the lowest total P concentrations had higher concentrations of P compounds involved with genetic information, energy transfer, and protein anabolism such as orthophosphate monosester and orthophosphate-diester. Soils at the upper topographic positions had more total P (Table  1 ), which strongly correlated with the activities of acid and alkaline phosphatase, suggesting a greater “investment” of microbes and plants to allocation in P acquisition from soil when the level of total P is high. Tree characteristics also differed amongst the plots at the three topographic positions with wood density tending to be higher in the top plots whereas growth rate, and tree height tending to be higher in the bottom plots (Margalef et al. 2018). Each species occupied a different position in the 2D-plot of the PCA analysis as reinforced by the results of the PERMANOVAS (Table S3 ). The profiles of organic P compounds in the 31 P NMR did not significantly vary between sites (Paracou vs. Nouragues; pseudo-F = 1.93; R 2  = 0.015, P  = 0.08), nor in function of topographic positions (top, slope, and bottom; pseudo-F = 1.73; R 2  = 0.027, P  = 0.568)) (Table S2 ). The interaction between topographic position and site was neither significant (pseudo-F = 5.68; R 2  = 0.089, P  = 0.195) (Table S2 ). Species had a significant effect on 31 P NMR profile (pseudo-F = 3.09; R 2  = 0.53, P  < 0.001) (Table S3 ).

The concentrations of the most abundant fractions of P (residual P, total P extractable by NaOH-EDTA, organic P, and inorganic P) varied amongst the soil samples, without any clear trends (Fig.  2 ). The total P concentration was 58–299 mg kg − 1 ; 56–88% was extracted by NaOH-EDTA, and the nonextracted fraction represented ‘residual P’. For the P extracted with NaOH-EDTA, 59–74% was organic and 26–41% was inorganic. Thus, most P was present in organic compounds than in inorganic forms suggesting a high biological use of P. Moreover, among these organic forms the highest proportion of P was found in molecules involved in active functions, such as growth, cellular control, or energy transfer. This is the case of the di-ester forms present in nucleic acid chains or storing energy molecules such as ATP.

The ratio of monoester to diester P was near 1, and diester-2 P was more abundant than diester-1 P, except for soils at the upper topographic position (in which the ratios of monoesters to diesters and diester-1 [phospholipids] to diester-2 [DNA and acid-unstable compounds] in the NaOH-EDTA extracts were similar).

Species-specific utilization of phosphorus

Our findings support the hypothesis that soil phosphorus (P) profiles differ among samples collected beneath different tree species. The soil samples associated with each tree species occupy distinct positions in a 2D plot representing the main functional groups of metabolic P molecules and nutrient concentrations in the soils (Fig.  3 ; Table  2 , and table S4 ). Species accounted for over half of the total variance in 31P NMR data. These consistent results indicate a species-specific pattern of P uptake and utilization, as well as species-specific interactions between trees and microbes (including mycorrhiza) and P transformations specific to the microbes associated with each tree species. Additionally, we observed a clear gradient in P compounds from high anabolic energy to storage, with the highest concentrations of P compounds associated with anabolic energy in soils with the lowest total P concentrations.

Principal component analyses of soil organic P compounds (green), nutrients (red), d 13 C, d 15 N, enzymatic activities, and ecophysiological variables (black) with species scores mean position, with corresponding confidence intervals (95%). Polyphos (polyphosphate); pyrophos (pyrophosphate) polyphosphos (polyphosphonate); orthophos (orthophosphate), orthophosmono (orthophosphate monosester), orthophosphate-diester (orthophosdiester); glucose6phos (glucose-6phosphates); SPAD—chlorophyll content; C—carbon; N—nitrogen; K—potassium; P—phosphorus. The abbreviations in the legend refer to the tree species: Aro, Aniba rosaeodora ; Bpr, Bocoa prouacensis ; Car, Chrysophyllum argenteum ; Cde, Capiro decorticans ; Cfr, Catostemma fragrans ; Cgl, Caryocar glabrum ; Csa, Chrysophyllum sanguinolentum ; Csu, Carapa surimensis ; Ctu, Chimarrhis turbita ; Dgu, Dicorynia guianensis ; Dod, Dipteryx odorata ; Dva, Drypetes variabilis ; Eco, Eschweilera coriacea ; Ede, Eschweilera decolorans ; Efa, Eperua falcata ; Egr, Eperua grandiflora ; Emy, Eugenia ; Hbi, Hirtella bicornis ; hco, Hymanea courbaril ; Lal, Licania alba ; Mco, Moronobea coccinea ; Mve, Micropholis venulosa ; Oas, Oxandra asbeckii ; Peu, Pouteria eugeniifolia ; Pgu, Paloue guianensis ; Pop, Protium opacum ; Ppt, Pradosia ptychandra ; Sel, Sloanea ; Sgr, Sapotaceae grandiflora ; Spr, Sterculia pruriens ; Ssp, Sterculia speciose ; TCl, Tovomita clusiaceae ; Tmy, Tetragastris ; Tpr, Talisia praealta ; Vam Vouacapoua america ; and Vsa, Vochysia sabatieri

Polyphosphates and polyphosphonates are chains of orthophosphates that serve as stored phosphate compounds. Our results revealed higher concentrations of orthophosphate, pyrophosphates, polyphosphonates, and polyphosphates in soils with higher total P concentrations and lower P availability at our study sites. Proportionally, more P was allocated to active metabolic molecules (e.g., DNA) and energy transfer (poly P, pyro P) in soils with lower total P concentrations and higher P availability. Higher concentrations of P storage compounds in the soil can be associated with low P availability, ensuring a controlled source of P for microbes when accessing soil P is challenging [ 44 ]. Moreover, the investment of microbes in building phosphatases was significantly lower in conditions of low carbon (C) and high poly P concentrations. This suggests that high polyphosphate concentrations may be associated with C conservation, particularly in sites where the soil has a high capacity to retain P. In these cases, higher polyphosphate reserves can serve as a P conservation trait, preserving C and providing a biological mechanism for accessing P from P reserves in microbial cells when necessary. Similarly, under conditions of very low C availability, higher PolyP levels may act as a compound for storing energy to conserve C [ 42 ].

Another study in the same ecosystem reported clear species-specific signatures in general foliar metabolomics profiles, indicating functional niches for dominant tree species in the region [ 43 , 44 ]. Our results align with our initial hypothesis that the quantities of different P compounds would differ among soil samples due to interspecific differences in P utilization strategies and cycling. This finding is consistent with previous observations [ 45 , 46 ]. For example, in a Panama rainforest, Condit et al. (2013) found that dry-season intensity and soil phosphorus were the strongest predictors, affecting the distribution of over half of a set of 550 tree species.

Our findings are also in line with previous studies that have identified associations between sets of species and specific habitats in tropical rainforests. The distribution of tree species is influenced by spatial variability in soil properties, such as nutrient availability and topography [ 47 , 48 , 49 , 50 ]. An extension of classical ecological niche theory, known as the “biogeochemical niche hypothesis“ [ 45 ], suggests that each species tends to reach an optimal chemical composition linked to a specific function that allows it to survive in its niche [ 39 , 51 , 52 ]. Our study provides evidence that organic P measurements can be used to characterize soil niches. The measurement and identification of different organic P molecules can serve as a powerful tool for characterizing most P-limited rainforests [ 23 , 53 ]. In these cases, “P-metabolome niches” arise due to soil niche differentiation along natural spatial gradients of biotic and abiotic factors that influence P availability, total concentrations, and chemical forms of P, which, in turn, are associated with P utilization and cycling. Tropical trees may exhibit finely subdivided niches [ 54 ], although direct evidence for measurable variables of overall functional differences among sympatric species and geological processes is currently limited. However, our results clearly indicate that soil beneath each tree species possesses a specific soil P-metabolome. The distinct strategies of individual tree species for P uptake, litter quality, retranslocation, allocation, soil exudates, and biotic interactions with soil microorganisms and other tree species contribute to a micro-scale soil space with a unique P-metabolome profile.

Topography and regional factors

In addition to the differences in P-metabolome profiles in soils associated with different tree species, we also observed relationships between P-metabolome profiles and other factors such as site and topographic position (Fig.  2 ). These relationships suggest that microsite variations in P-metabolome profiles are influenced by biotic conditions and associated with distinct soil traits, including texture, that vary across different topographic situations. Topography creates diverse soil P conditions, with higher total P concentrations and lower P availability at higher elevations, and vice versa at lower elevations. This finding is consistent with more conservative resource-use traits observed at higher elevations, such as the higher wood density of trees, and the opposite pattern at lower elevations. Furthermore, the spread of species along the 2D space generated by the two principal component axes was also associated with these findings. Thus, each species has developed a specific niche for highly efficient P utilization along the gradient, resulting in a distinctive distribution profile of P compounds that maximizes their use efficiency. These results also suggest that a “niche” of P profiles is associated with a physical gradient, primarily determined by topographic positions, and reflects species-specific strategies for mineralizing, mobilizing, utilizing, and acquiring soil P.

The abundance of organic P compounds, such as diesters and phosphonates, varied according to site and topographic position. Specifically, DNA and polyphosphate concentrations increased from the bottom to the top. DNA, polyphosphate, and phosphonates are abundant in soils with high microbial activity [ 31 ]. Site and topographic position explained some of the variance in the P profiles, likely due to clay content, which can form organomineral complexes and better retain organic material, including organic P. Variations in P profiles may also be influenced by metal oxides, as they can strongly occlude P, including organic P molecules. The occasional flooding of the bottom plots may have influenced the redox states of metal oxides (specifically iron and manganese oxides; aluminum oxides are less affected), which, in turn, could have affected the adsorption/desorption dynamics of P fractions in the soil.

Furthermore, the higher presence of mono- and diesters observed in bottom soils with higher sand content aligns with previous findings. A greater presence of monoester phosphorous compounds has been linked to the decomposition of organic matter rich in P metabolites, such as phosphatidylcholine and phospholipids [ 31 , 55 ]. Similarly, higher soil concentrations of diester phosphates have been positively associated with higher concentrations of sand-sized fractions compared to silt and clay fractions [ 56 , 57 ].

Significant variations were observed in the ratios of monoesters to diesters and the ratios of different diesters (diester-1 and diester-2; Table  1 ) across different parts of the 31P NMR spectra. Gressel et al. (1996) suggested that the correlation between monoester P and alkyl C in the organic horizons of a tropical forest soil indicates that the mineralization of monoester P fractions is linked to the decomposition of plant structural components, and that a significant portion of the monoester P in NaOH extracts may originate from hydrolyzed phospholipids derived from plants. The alkaline hydrolysis of phosphatidylcholine to monoesters is well-documented [ 31 , 55 , 58 ]. Soils in semi-arid northern Tanzania [ 59 ], enriched with diesters in sand-sized fractions relative to silt and clay fractions, likely derive these diesters from plants. Labile organic P compounds (e.g., phosphonates and diesters) and phosphate diesters (e.g., DNA and other diesters) often exhibit inverse relationships. For instance, diester P may increase while phosphonates decrease when comparing soils from a native savanna to Oxisol soil of an improved pasture in Colombia [ 36 , 53 ]. Similarly, in a Spodosol soil of a spruce-fir forest, diester P (0 ppm) increased while unidentified diester compounds (1.5 to 2.5 ppm) decreased with increasing decomposition levels [ 46 ].

The top plots had higher concentrations of total P but lower levels of available P due to adsorption onto fine-grained particles, particularly highly reactive P oxides. This occlusion mechanism of P requires greater investments in microbial and root activities to acquire P, which is consistent with the higher activities of acid and alkaline phosphatases observed. However, the higher presence of molecules associated with P storage (orthophosphate, pyrophosphates, and polyphosphate inorganic chains) in these top soils is consistent with a more conservative strategy [ 47 , 48 , 49 , 50 , 51 ], where more P is stored within cells to support biological functions that require P, independent of P uptake from the soil. Furthermore, in top soils, the limited availability of soil P was associated with tree species characterized by higher wood density, typically exhibiting more conservative traits. These findings provide further evidence of the links between soil P status, species distribution, and their life strategies in this tropical rainforest [ 52 , 53 , 54 ].

In conclusion, our study reveals that variations in P-metabolome profiles in soils are not only influenced by different tree species but also by other factors such as site and topographic position. Topography creates distinct soil P conditions, which, combined with the spread of species along the gradient, leads to species-specific strategies for P utilization and uptake. Additionally, the abundance of organic P compounds varies with site and topographic position, influenced by factors such as clay content and metal oxides. The presence of mono- and diesters in soils correlates with organic matter decomposition and sand content. The ratios of different P compounds further highlight the complex dynamics of P cycling in the soil. Our findings contribute to a better understanding of the interactions between vegetation, soil, and P dynamics in tropical rainforest ecosystems.

The P metabolomic profiles of soil samples collected at different sites under trees in French Guianese rainforests differed greatly, with very significant differences amongst soils collected beneath different tree species. This result is consistent with the ecological niche theory and the biogeochemical niche hypothesis (a correspondence of species with specific environmental conditions) in this highly diverse tropical ecosystem. Using 31 P-metabolomic profiles to analyse the functions of different plant species in a community thus allowed us to identify different soil 31 P NMR profiles associated with each tree species.

Our multivariate analyses of the soil 31 P NMR metabolomics data notably indicated a trend to find higher soil concentrations of P biomolecules associated with low P use and high P storage under higher total P concentrations at the top sites, coinciding with tree species with more conservative strategies associated with denser wood and with a soil texture and mineral composition providing high P immobilization capacity. The bottom sites tended, instead, to have higher soil concentrations of P biomolecules associated with biological activity under lower total P concentrations, but higher P-availability, coinciding with tree species with less dense wood and a soil coarser texture.

Our combined analysis of soil elemental composition and P metabolomics provides an improved understanding of environmentally linked shifts in soil P concentrations and availability with different allocations of P for growth and other functions, such as storage, defense, reproduction, or resistance that stress the key role of this element in tropical rainforest functioning. As more P is available, more P is invested in active metabolism and functional activity and less in storage.

French Guiana is on the northeastern coast of South America between 2°10′ and 5°45′N and 51°40′ and 54°30′W. 97% of the region is covered by lowland wet tropical forest [ 55 ]. A pronounced dry season, characterised by < 100 mm precipitation per month, extends from September to November and is associated with the displacement of the intertropical convergence zone. Mean daily temperature is 25.8 °C and varies by only 2 °C throughout the year; daily temperatures vary by 7 °C during the rainy season and by 10 °C in the dry season [ 56 , 57 ].

Field work was conducted at two sites of mature lowland tropical rainforest: the Paracou Research Station (5°18′N, 52°53′W) and the Nouragues Research Station (4°05′N, 52°40′W). Mean annual rainfall is 2990 mm at Nouragues and 3160 mm at Paracou [ 58 ], although the dry season is more severe at Paracou [ 58 ]. Three topographical locations were selected at each site: top of hills (top), middle of slopes at an intermediate elevation (slope), and bottom of slopes at a low elevation, immediately above a creek [ 59 ].

Study plots

We established 12 plots of 0.25 ha at each site stratified by three topographic positions to account for the heterogeneous soil texture: top of the hills, slope and bottom of the valleys, thus with 4 plots in each topographic position. In each plot, we delimited a central 20 × 20 m quadrat where we marked five evenly spaced sampling points around which we focused all our measurements. This design thus contained a total of 120 sampling points (2 sites × 3 topographic positions × 4 replicate plots per topographic position × 5 sampling points in each plot). In each sampling point we annotated the nearest tree in function of the linear distance to the trunk base. The bottom plots at both sites had higher sand contents and lower clay contents than the top and slope plots [ 57 ]. All trees (diameter at breast height ≥ 10 cm) within the 0.25-ha plots were mapped, tagged, and identified to species or genus using herbarium vouchers for determining the richness of the tree species for each plot.

Sample collection

Thus, we collected five soil samples per plot to a depth of 15 cm (Topsoil) in June (wet season) 2015. Each sample was collected using an auger/corer and was a composite of three borings near (< 2 m apart) each other. All voucher specimens were deposited in the Herbarium of International Center for Tropical Botany in Miami, FL 33,199 USA. A total of 120 samples were collected around the trees. We aliquoted 5 g of each sample for 31 P NMR analyses that were immediately placed into a paper bag and frozen in liquid nitrogen before transporting the samples to the laboratory. The rest of soil sample was transported to the lab and stored in plastic zip bags at 4ºC until all the other analyses (within 4 weeks). Soil storage at 4ºC has been shown to keep enzymatic activity of tropical soils better than frozen samples. Fresh soil was sieved to 2 mm; for each sample one part was used for enzymatic activity analyses and the other part was dried 24 h at 105ºC for gravimetric water content. The other soil variables were analyzed from the same soil samples as those used in the 31 P NMR analyses to determine the effect of the tree species.

Environmental biotic and abiotic data

We compiled data for 28 variables describing the pools of soil nutrients, activities of extracellular enzymes, and aboveground tree-community data for each site to characterise the potential micro-environmental and biotic drivers. Nutrient concentrations and ratios, d 13 C, d 15 N, enzymatic activities, and ecophysiological variables are abbreviated as: C, N, P, C:N, C:P, N:P, K, d 13 C, d 15 N, leu (enzymes leucine), gly (enzymes glycine aminopeptidases), alkp (enzymes alkaline phosphatases), acidp (enzymes acid phosphatases), bgluc (enzymes β- glucosidase), p_olsen (amount of soil phosphorus available by Olsen test), p_bray (amount of soil phosphorus available by Bray test), scw_lab (laboratory surface water content), swc_field (field surface water content), surf_temp (soil surface temperature), EC (soil electric conductivity, mS/cm), MBP (microbial biomass P, µg P / g soil DW), MBP_Ke-P (microbial biomass P, µg P / g soil DW with factor KeP = 0.40), MBP_P recov (microbial biomass P, µg P / g soil DW with P-recovery factor), MBP_Ke-P + P recov (microbial biomass P, ug P / g soil DW with P-recovery factor and KeP), TEP (Total extractable P, µg P / g soil DW), TEP_recov P (Total extractable P, µg P / g soil DW with recovery factor P applied ), OEP (Organic extractable P, µg P / g soil DW), and PmgkgLOQ (P concentration in soil, mg/kg Limit of Quantification). All the acronyms used throughout the text are described in Table S1 .

Nutrient pools

We collected soil cores from the topsoil of each sampling point using a soil auger (4 cm in diameter and 15 cm in length; Van Walt, Haslemere, UK) to analyse the nutrient status. The samples were sieved to 2 mm and then freeze-dried (Alpha 1–2 LDplus, Martin Chirst Freeze Dryers, Osterode, Germany). Subsamples were pulverised in a ball mill (MM400, Retsch, Haan, Germany) for the analysis of elemental composition. We weighed 0.15–0.2 g of soil using an MX5 microbalance (Mettler Toledo, Columbus, USA) for determining the concentrations of total carbon (C) and nitrogen (N) by combustion coupled to an isotopic ratio mass spectrometer at the Stable Isotopes Facility (UC Davis, USA). Concentrations of total P and potassium (K) were determined by diluting 0.25 g of soil with an acid mixture of HNO 3 (60%) and H 2 O 2 (30% w/v) and digested in a MARS Xpress microwave oven (CEM Corporation, Matthews, USA). The digested solutions were then diluted to final volumes of 50 mL with ultrapure water and 1% HNO 3 . Blank solutions (5 mL of HNO 3 with 2 mL of H 2 O 2 but no sample biomass) were regularly analysed. The content of each element was determined using inductively coupled plasma/optical emission spectrometry (ICP-OES Optima 4300DV, PerkinElmer, Wellesley, USA). We used the standard certified biomass NIST 1573a to assess the accuracy of the biomass digestion and analytical procedures.

Determination of activities of extracellular enzymes

We determined the activities of the extracellular enzymes β-glucosidase, leucine and glycine aminopeptidases, and acid and alkaline phosphatases (βgluc, leu, gly, acidP, and alkP, respectively) in all the 120 topsoil samples. The activities of these enzymes can serve as proximal variables of microbial nutritional metabolism and depend mostly on the interaction of the relationship between supply and demand with environmental kinetics [ 60 ]. Fresh subsamples of 2-mm sieved soil were stored in ziplock plastic bags and stored at 4 °C until analysis. We quantified the maximum potential activities of each enzyme by colorimetric assays using p -nitrophenylphosphate and p -nitroaniline derivative chromogenic substances. These enzymes are involved in the mineralization of C, N and P (Sinsabaugh and Shah, 2012). β -glucosidase participates in the decomposition of plant tissues, catalyzing the hydrolysis of 1–4 glucosidic bonds of labile cellulose (cellobiose and cellodextrins) to yield glucose. Leucine and glycine amino-peptidases cleave N-terminal residues from proteins and peptides. Acid and alkaline phosphatases release orthophosphate from organic P compounds like labile nucleic acids, phospholipids and inositol phosphates by the hydrolyzation of oxygen-P bonds.

Soil microbial biomass P and soil extractable P

Phosphorus in the microbial biomass (MBP) was measured using the chloroform fumigation extraction method according to Brookes et al. (1982) and Brookes et al. (1985). Two subsamples (10 g fresh weight) of sieved soil were taken for each topsoil sample. One subsample was fumigated for 24 h with chloroform and extracted with 0.5 M of NaHCO 3 (10:1 v:w) after 30 min shaking. The other subsample was directly extracted following the same protocol. The extracts were then filtered with Whatman 42 equivalent paper. Total P content in the extracts was determined after digestion of 2.5 g of aliquot with HNO 3 in a microwave oven (MARS Xpress, CEM Corporation, Matthews, USA). The digested solutions were then diluted to a final volume of 50 mL with ultrapure water and 1% HNO 3 . Blank solutions were regularly analysed in parallel. P concentration in the digested samples and blanks was determined using inductively coupled plasma/optical emission spectrometry (ICP-OES Optima 4300DV, Perkin-Elmer, Wellesley, USA). The microbial biomass P content was calculated from the difference between fumigated and non-fumigated samples and expressed per unit of soil dry mass. Given that inorganic P molecules can absorb onto soil surfaces (organic matter and minerals) it is necessary to account for this effect during the extraction of P from soil, this is done through the application of an empirically determined “P-recovery factor”. Thus, a known amount of inorganic P (12.5 µg of inorganic P added as KH 2 PO 4 ) was added to some of the controls to calculate the P-recovery factor in our soils. Microbial biomass was then calculated using the fumigated and non-fumigated samples corrected with the P-recovery coefficient (MBP_P.recov). Microbial biomass P was also corrected to take into account the efficiency of the fumigation (MBP_Ke.P), using the conversion factor KeP = 0.40 (Jenkinson et al. 2004). The factor KeP is an empirical coefficient used to relate the quantity of material solubilized by chloroform to the size of the original biomass, in this case it indicates that with fumigation 40% of the biomass-P is extracted as inorganic P. We have used all the microbial biomass P variables with and without corrections (MBP, MBP_P.recov, MBP_Ke.P and MBP_Ke.P…P.recov) in the analyses to give an overview of the methodological issues related to the quantification of extractable P in soils and microbes and to provide additional information for those readers with a background in soil biogeochemistry.

The total P concentration measured in non-fumigated bicarbonate-extracts was referred as the total extractable P (TEP) fraction. One aliquot of the non-fumigated extracts was used to determine the inorganic extractable P (P_Olsen) by Olsen’s method (Watanabe and Olsen, 1965). The organic extractable P (OEP) in the non-fumigated extracts was calculated as the difference between TEP and P_Olsen. All bicarbonate-extractable P fractions were expressed as µg of P per gram dry soil. Soil extractable P was also determined with Bray-P (P_Bray) acid fluoride extraction (Bray and Kurtz 1945) in oven-dried soil subsamples.

Sample processing for 31 P NMR analysis

The soils were frozen in liquid nitrogen, lyophilised, and stored in paper bags at -80 °C. The samples were ground with a ball mill at 1500 rpm for 3 min, and the fine powder was stored at -80 °C until extraction of the metabolites.

One-dimensional 31 P NMR

Conventional one-dimensional (1D) 31 P NMR (Box 1) was used to quantify the main organic and inorganic forms of extractable P using NaOH-EDTA, including DNA, total diesters and monoesters, phosphonates, pyrophosphate, and polyphosphate. All the identification of the target P classes was based on chemical shifts and previous reported data (Turner et al. 2003; Vestergren et al. 2012). P was extracted by shaking 1.5 g of dry ground soil from each composite sample for 4 h in 30 mL of a solution containing 250 mM NaOH and 50 mM Na 2 EDTA (Cade-Menun and Preston 1996). The extracts were centrifuged at 14 000 g for 30 min, and the supernatant (23 mL) was frozen at − 80 °C overnight and then lyophilised. Lyophilisation yielded 750 ± 50 mg of material, 80 mg of which was redissolved in 640 µL (1:8 w/v) of a solution containing 530 µL of D 2 O, 10 µL of 14.2 M NaOD, and 50 µL of 16 mM methylene diphosphonic acid trisodium salt (MDPA, Sigma-Aldrich product number M1886). The MDPA served as a P reference for quantifying individual compounds, and each 50-µL spike contained 50 µg of P. The redissolved solution was vortexed for 2 min and centrifuged at 10 000 g for 5 min, and 560 µL was then transferred to a 5-mm NMR tube for 1D 31 P NMR.

NMR spectra for 31 P were obtained using an Avance III 600 MHz spectrometer (Bruker, Ettlingen, Germany) operating at 161.76 MHz. NaOH-EDTA extracts were analysed using a 3.9-µs pulse (90°), a relaxation delay time of 2.0 s, an acquisition time of 0.9 s, and broadband proton decoupling. We recorded 15 000 scans per sample, and the experimental time was 12.5 h. Spectra were processed with a line broadening of 2 Hz, and chemical shifts of signals were determined in parts per million (ppm) relative to an external standard (85% orthophosphoric acid, H 3 PO 4 ). The main chemical types of P compounds were identified based on previously reported chemical shifts [ 32 , 61 ]. Peaks were first identified using an automatic procedure for fitting peaks; peaks that were clearly visible were manually selected using TopSpin 2.0 NMR software (Bruker, Germany). Signal areas were calculated by the deconvolution and integration of individual peaks. Concentrations of P compounds (mg P kg –1 soil) were calculated using the known P concentration of MDPA spiked in the sample, and concentrations per weight of air-dried soil were given. All NMR spectra were processed using TopSpin 2.0.

Signal intensity in the 31 P spectra was assigned to the different types of P by first integrating across the following regions of broad chemical shifts: -21.5 to -18.5 ppm for nonterminal polyphosphate (poly P), -5.3 to -4.8 ppm for pyrophosphate (pyro P), -4.8 to -4.0 for terminal poly P, -1.5 to 2.5 for diester-P, and 2.5 to 7 ppm for orthophosphate (ortho-P and monoester-P). Deconvolution was then used to determine the intensity of up to 16 resonances in the ortho-P and monoester-P regions. Deconvolution analysis began by manually identifying chemical shifts of peaks and shoulders. Peak chemical shifts varied only slightly amongst the samples. The orthophosphate signal shifted the most (range: 5.56–5.74 ppm), which shifted amongst soil samples, sites, species, and topographic positions. This variation was most likely due to slight differences in pH amongst the samples, because the orthophosphate peak is highly sensitive to variation in pH [ 62 ]. Thus, 31 P NMR allows the determination of the family of P-compounds (Fig.  3 ), but not of the exact compounds.

31 P nuclear magnetic resonance ( 31 P-NMR) is an analytical NMR technique that allows the detection of both the concentration and the chemical form of the most abundant phosphorus isotope, 31 P, in the analytical sample. In the concrete case of 31 P this analytical tool allows to separately detect the intensity of the signal (proportional to concentration in the analyzed sample) of each molecular structure where the 31 P is located. In this way, we can detect the most abundant types of compounds containing 31 P in biological samples. We explored different aqueous/organic solvent methods to extract as many groups of compounds as possible and the preliminary results showed that using an aqueous solution allowed extracting most of groups compounds. Standard 1D 31 P NMR was used to quantify concentrations of the main organic and inorganic P classes, including DNA, total orthophosphate diesters and monoesters, phosphonates, pyrophosphate and polyphosphate. Phosphorus was extracted by shaking 1.5 g of dry and ground soil from each composite soil sample in 30 mL of a solution containing 250 mM NaOH and 50 mM Na2EDTA (ethylenediaminetetraacetate) for 4 h (Cade-Menun and Preston 1996). Identification of the target P classes was based on chemical shifts and previous reported data [ 32 , 63 ].

Statistical analyses

The relationships of the P compounds with species, site and topographic position were identified by a PERMANOVA [ 64 ] of the NMR data for each soil sample. Euclidean distance, species identity, site, and topographic position were the fixed factors, and plot was a random effect, with 2000 permutations. Differences amongst species, site, and topographic position and amongst the P compounds most responsible for these differences were determined by comparing the areas of the different metabolite peaks normalized relatively to internal standards. Principal component analyses (PCAs) were used for processing the “omic” data sets together with the other potential influencing soil parameters, to detect the part of the variance explained by species [ 65 ]. Pearson’s correlation was used to identify the relationships of the 1D NMR measurements and the relationships between the concentrations of nutrients and organic P compounds. Error estimates are standard errors of the mean unless otherwise stated.

All statistical procedures were performed using R v 3.5 ( www.r-project.org ) with the SEQKNN, VEGAN, FACTOEXTRA, FACTOMINER, DPLYR, RANDOMFOREST, and MIXOMICS packages.

Data availability

All data generated or analysed during this study are included in this published article [and its supplementary information files].

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Acknowledgements

We appreciate the cooperation of all the people that help in anything related with this research.

This research was supported by the European Research Council Synergy grant ERC-2013-SyG-610028 IMBALANCE-P, the European FP7 S-Clima project PIEF-GA-2013-626234, the Spanish Government grant PID2019-110521GB-I00, the Fundacion Ramon Areces grant ELEMENTAL-CLIMATE, and the Catalan Government grant SGR 2017 − 1005. We thank the staff of the Nouragues station managed by USR mixte LEEISA (CNRS; Cayenne) and the Paracou station managed by UMR Ecofog (CIRAD, INRA; Kourou). Both research stations benefit from “Investissement d’Avenir” grants managed by Agence Nationale de la Recherche (CEBA: ANR-10-LABX-25-01; ANAEE-France: ANR-11-INBS-0001). A.G.G. was supported by the Ministry of Education, Youth and Sports of CR within the project Mobility CzechGlobe, CZ.02.2.69/0.0/0.0/16_027/0008137. A.G.G. and O.U. were also supported by the project SustES (CZ.02.1.01/0.0/0.0/16_019/0000797).

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Albert Gargallo-Garriga

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Albert Gargallo-Garriga & Marta Ayala-Roque

Global Ecology Unit, CSIC, CREAF-CSIC-UAB, Bellaterra, 08193, Catalonia, Spain

Jordi Sardans, Joan Llusià, Guille Peguero, Otmar Urban, Karel Klem & Josep Peñuelas

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Jordi Sardans, Joan Llusià, Guille Peguero & Josep Peñuelas

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Elodie A. Courtois

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Clément Stahl

Servei de Ressonància Magnètica Nuclear, Universitat Autònoma de Barcelona, Bellaterra, 08193, Spain

Pau Nolis, Miriam Pérez-Trujillo & Teodor Parella

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A.G.G., J.S. and J.P. designed the study with the help of all co-authors. A.G.G., J.L., G.P., M.A.R, E.C., C.S., O.U., K.K., P.N., M.P., T.P., A.R., I.J., J.S. and J.P. authors participated in the field measurements or chemical and statistical analyses. All authors contributed to the writing of the manuscript and the drafting of the figures. All authors read and approved the final version of the manuscript.

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Gargallo-Garriga, A., Sardans, J., Llusià, J. et al. Different profiles of soil phosphorous compounds depending on tree species and availability of soil phosphorus in a tropical rainforest in French Guiana. BMC Plant Biol 24 , 278 (2024). https://doi.org/10.1186/s12870-024-04907-x

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Received : 20 January 2023

Accepted : 13 March 2024

Published : 12 April 2024

DOI : https://doi.org/10.1186/s12870-024-04907-x

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