what type of quantitative research is analysis of food web

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Quantitative analysis of the local structure of food webs

a Departament de Física (Física Estadística), Universitat Autònoma de Barcelona, E-08193 Bellaterra, Catalonia, Spain

b Department of Chemical and Biological Engineering, Northwestern University, Evanston, IL 60208, USA

D.B. Stouffer

L.a.n. amaral.

We analyze the local structure of model and empirical food webs through the statistics of three-node subgraphs. We study analytically and numerically the number of appearances of each subgraph for a simple model of food web topology, the so-called generalized cascade model, and compare them with 17 empirical community food webs from a variety of environments, including aquatic, estuarine, and terrestrial ecosystems. We obtain analytical expressions for the probability of appearances of each subgraph in the model, and also for randomizations of the model that preserve species' numbers of prey and number of predators; their difference allows us to quantify which subgraphs are over- or under-represented in both the model and the empirical food webs. We find agreement between the model predictions and the empirical results. These results indicate that simple models such as the generalized cascade can provide a good description not only of the global topology of food webs, as recently shown, but also of its local structure.

1. Introduction

Food web theory seeks to understand the functioning of ecosystems by studying the trophic relations among its species ( Cohen et al., 1990 ). To this end, in the last years great effort has been devoted to the compilation of comprehensive empirical food webs (see for instance Dunne et al., 2002 ). The statistical treatment of these data has revealed several regularities among food webs belonging to quite diverse habitats, such as deserts, lakes and islands, suggesting that some robust mechanism common to most ecosystems is at work ( Williams and Martinez, 2000 ; Camacho et al., 2002b ; Stouffer et al., 2005 ).

Several models have been proposed to describe the structure of food webs and clarify the origin of these patterns. They differ in the mechanisms underlying them and in the level of description. Some of them describe the dynamics of the network according to evolutionary rules ( Amaral and Meyer, 1999 ; Rossberg et al., 2005 ; Rossberg et al., 2006a , b ), population biology ( Yodzis, 1981 ), or mixtures of both ( Caldarelli et al., 1998 ; Lassig et al., 2001 ). Other so-called static models do not contain the explicit dynamics of the ecosystem, but provide some mechanistic rules aiming to generate food webs with a statistically similar structure to the empirical ones ( Cohen and Newman, 1985 ; Williams and Martinez, 2000 ; Cattin et al., 2004 ; Stouffer et al., 2005 ).

Two of these static models, the niche model ( Williams and Martinez, 2000 ) and the nested-hierarchy model ( Cattin et al., 2004 ), yield good predictions for a wide number of statistical measures of empirical food webs. Indeed, it has been demonstrated analytically that the two models yield the same distributions for the number of prey and number of predators ( Stouffer et al., 2005 ), which imply, for example, the same fractions of top and basal species or the standard deviations of generality and vulnerability, just as observed numerically ( Cattin et al., 2004 ). Remarkably, these distributions are in good agreement with most of the highest quality empirical food webs in the literature, providing a general pattern of food web topology ( Camacho et al., 2002a , b ; Stouffer et al., 2005 ).

It has also been demonstrated that much of the success of these models relies in the fact that they satisfy two basic conditions ( Stouffer et al., 2005 ): (i) the species' niche values form a totally ordered set, and (ii) each species has a specific exponentially decaying probability of preying on a given fraction of the species with lower niche values. Any model which satisfies these conditions will reproduce the distributions of number of prey and number of predators observed empirically. For instance, the generalized cascade model ( Stouffer et al., 2005 )—a generalization of Cohen and Newman's (1985) cascade model to satisfy condition (ii)—exhibits the same distributions. Those two conditions can thus be interpreted as fundamental mechanisms shaping food web structure.

Aside few exceptions ( Melián and Bascompte, 2004 ; Bascompte and Melian, 2005 ), the studies of these models, however, mainly characterize the global structure of food web topology. Here, in contrast, we focus on the analysis of the local structure of food webs through the study of the so-called food web subgraphs or motifs ( Fig. 1 ). This methodology has been applied successfully to a number of empirical networks, including biological, technological and sociological systems, to uncover the underlying structure at a scale in between the entire community and single or pairwise population dynamics ( Milo et al., 2002 , 2004 ). Let us note that some authors have attempted to gain insight into the dynamics and stability of natural ecosystems in terms of small sub-webs containing species strongly connected, the so-called “community modules” ( Holt, 1997 ; Holt and Hochberg, 2001 ). Our perspective is complementary: whereas the latter approach is dynamical and considers only strong links, we focus on structural properties of the food webs; to do so we consider all links, and not only the strong ones. Our perspective is thus similar to the one followed by Bascompte and Melian (2005) , though it differs in several aspects, such as the theoretical approach and our systematic analysis of all three-node subgraphs.

Three-species motifs containing only single links. Notice that each of these motifs has a clear ecological relevance and is additionally related to some community modules. Motif S1 describes the simple food chain, S2 simple omnivorism, S3 a trophic loop involving three species, S4 isolated exploitative competition, and S5 isolated generalist predation.

The purpose of this work is to study the statistics of subgraphs in model and empirical food webs in order to check if the two basic ingredients for food web construction specified above can satisfactorily describe not only the global properties of empirical food webs, such as the distributions of number of prey, of predators and related quantities, but also its local structure. Because it allows for analytical treatment, we will focus here on the generalized cascade model, the simplest model obeying those ingredients. Specifically, we study analytically and numerically the subgraph probabilities for the generalized cascade model and find agreement between the analytical expressions and the empirical results. We conclude that the model is able to capture the basic properties of the local structure of food webs. Therefore, simple static models as the generalized cascade provide a good unifying description of food web structure both at the global and local levels.

The paper is organized as follows. In the second section, we study the statistics of subgraphs for the generalized cascade model. This analysis is twofold: we first evaluate the number of appearances for each subgraph and secondly we study their patterns of over/under-representation. In the third section, we perform the same analysis for the completely random model, as a basis for comparison. Section 4 compares the model predictions with the results obtained for 17 empirical food webs.

2. The generalized cascade model

The original cascade model ( Cohen and Newman, 1985 ; Cohen et al., 1990 ) is based on two rules: (1) species make up an ordered set according to their niche value n drawn uniformly in the interval [0, 1], and (2) any species j with n j < n i becomes a prey of i with fixed probability x 0 = 2 CS /( S − 1); here S is the number of species in the food web, L the number of trophic connections, and C ≡ L / S 2 the directed connectance. Williams and Martinez (2000) demonstrated that this model is not able to reproduce the properties of real food webs.

Stouffer et al. (2005) demonstrated, however, that it can be easily generalized to provide similar agreement to the niche ( Williams and Martinez, 2000 ) or the nested-hierarchy ( Cattin et al., 2004 ) models as compared to many empirical food webs. The generalization consists in that the probability x with which a species i feeds on species j with n j ≤n i is not the same for every predator i , but it is drawn at random from a probability distribution p ( x ) given by

the so-called beta-distribution (see Fig. 2 ). Parameter β is related with the directed connectance of the empirical food web by C = 1/2( β + 1) ( Williams and Martinez, 2000 ).

The generalized cascade model of Stouffer et al. (2005) . In the generalized cascade model species make up an ordered set according to their niche value n , 0< n <1. Each species i then consumes species j with n j ≤n i with a probability x drawn at random from a probability distribution p ( x ) given by the beta-distribution Eq. (1) . In this example the predator (the yellow species) can consume any of the species to its left on the axis, including itself. In this case, x ≈ 0.2 and the yellow predator consumes itself and three other species.

2.1. Subgraph probabilities

Neglecting cannibalism or self-links, there are two possible unique subgraphs comprising a pair of species: (i) single links, A → B , i.e. species A eats species B but not conversely, and (ii) double links, A ↔ B . With three species, there are 13 unique subgraphs possible. Since predators in the generalized cascade model cannot feed on species having a larger niche value, no trophic loops of any size can exist. As a consequence there is no mutual predation and none of the eight unique motifs which contain double links will be observed in the generalized cascade model. Therefore, our study focusses on the five subgraphs S1–S5 ( Fig. 1 ), while the analysis of the motifs containing double links will be dealt with elsewhere. The present analysis is nonetheless meaningful since single connections account for the vast majority of the links in empirical food webs (see Appendix A ). Notice that these motifs have a clear ecological relevance and are additionally related to some proposed community modules; in particular, motif S1 describes the simple food chain, S2 simple omnivorism, subgraph S3 a trophic loop involving three species, S4 isolated exploitative competition, and S5 isolated generalist predation.

The probability p i of subgraph i is related to the number of appearances of the subgraph N i by

where the denominator is the total number of possible triplets of species. We choose the probability p , instead of the number of appearances N because, as we will later demonstrate, the probability is not a function of S , and instead depends on a single variable, the directed connectance C . This property is a very interesting one because it allows a unified description of food webs of different size.

Recall that no trophic loops are possible within the generalized cascade model. Motif S3 is therefore forbidden and

We next derive expressions for the remaining motifs, S1, S2, S4, and S5. The probability for a given motif to appear is equivalent to the probability for three arbitrary species to be connected in the specified fashion. Let us now consider three arbitrary species, A , B , and C , with n A > n B > n C . We call x i the probability of species i consuming each species with lower niche values. It then follows that

where 〈…〉 indicates the average over the probability distribution p ( x ). In addition, because x A and x B are independent random variables, Eqs. (4) - (6) can be rewritten as

These expressions are valid for arbitrary distributions p ( x ). Substituting the beta-distribution, Eq. (1) (see Appendix B ) becomes

In Fig. 3 , we compare the analytical predictions, Eqs. (10) - (12) , with simulations of the generalized cascade model—in these simulations and throughout the paper, subgraphs have been directly enumerated using dynamic programming, as in the mfinder software for network motif detection. It becomes visually apparent that the expressions we derived compare quite well with the model-generated data. Notice that the probabilities p only depend on the connectance C .

Comparison between analytical expressions, Eqs. (10) - (12) , and simulations of the generalized cascade model for motifs S1, S2, S4, and S5. We exclude motif S3 because, by definition, p S3 = 0. It is visually apparent that the analytical predictions agree with the model-generated data. Filled circles are for food webs with S = 50 and open squares for food webs with S = 100. Each data point represents an average over 1000 model-generated food webs.

2.2. Patterns of over/under-representation of subgraphs

As a second test of the generalized cascade model, we analyze which subgraphs are typically over- or under-represented as compared to the corresponding randomized networks ( Milo etal., 2002 , 2004 ). The randomized networks are obtained by preserving the number of prey k i and of predators m i of each species i as in the generalized cascade model, but rewiring their trophic links randomly using the Markov-chain Monte Carlo switching algorithm ( Maslov and Sneppen, 2002 ; Itzkovitz et al., 2004 ).

By virtue of the randomization a species in the randomized network may feed on a species with a higher niche value than itself, a possibility that is excluded in the model. However, because of the formulation of the Markov-chain Monte Carlo switching algorithm, no double links are produced in the randomization and the resulting networks only contain subgraphs S1–S5 ( Maslov and Sneppen, 2002 ; Itzkovitz et al., 2004 ). Notice, however, that, by construction, the distributions of number of prey or of number of predators are the same ones as in the original network. Then, one must not confuse these randomized networks with completely random networks, whose distributions are different from the original ones. We deal with the latter ones in the next section, as a null model for comparison with the predictions of the generalized cascade model.

Note that, since randomized food webs possess the same degree distributions as the original ones, the occurrence of patterns of over/under-representation of subgraphs in empirical food webs would require an explanation. One can think of two principle arguments for their existence: either they are a consequence of the mechanism generating the network ( Artzy-Randrup et al., 2004 ) or they provide some ecological advantage and have arisen as a result of selection pressure. Here we show that the generalized cascade model yields well-defined patterns of over/under-representation of motifs. If these predictions compare well with empirical food webs, one might conclude that the second hypothesis is not required and all patterns arise as the result of the food web generating mechanisms.

We thus next evaluate the probabilities of subgraphs in randomized networks of the generalized cascade model. Itzkovitz et al. (2003) derived expressions for the mean number of appearances of each subgraph for randomized networks with an arbitrary degree distribution. In Appendix B , we calculate the probabilities for the three-species motifs in the randomizations of the generalized cascade model yielding

Fig. 4 compares the analytical predictions for the randomizations, Eqs. (13) - (17) , with simulations of the generalized cascade model finding good agreement. The small discrepancies observed have their origin in that some of the expressions derived in Itzkovitz et al. (2003) are approximate.

Comparison between analytical expressions, Eqs. (13) - (17) , and randomizations of the generalized cascade model for motifs S1–S5. It is visually apparent that the analytical predictions compare well with the model-generated data. Filled circles are for food webs with S = 50 and open squares for food webs with S = 100 Each data point represents an average over 1000 model-generated food webs.

Finally, we obtain the differences by subtracting the probability of motifs appearing in the model, Eqs. (10) - (12) , and in their randomizations, Eqs. (13) - (17) . Table 1 summarizes these results. We show comparisons between the expressions for p − p rand and simulations of the generalized cascade model in Fig. 5 . Our analytical derivations thus predict that food webs generated by the generalized cascade model have over-expression of motifs S1 (a food chain) and S2 (simple omnivorism) and under-representation of motifs S3 (a trophic loop), S4 (isolated exploitative competition), and S5 (isolated generalist predation). The percentage of under/over-representation is, however, rather small, generally under 10%. These predictions make up our second check of the generalized cascade model.

Comparison between analytical expressions for p − p rand and simulations of the generalized cascade model for motifs S1–S5. The model predicts over-representation of motifs S1 and S2 and under-representation of motifs S3–S5. The analytical predictions compare well with the model-generated data, though they generally overestimate the differences due to the approximate character of the expressions used to evaluate p rand . Filled circles are food webs with S = 50 and open squares food webs with S = 100. Each data point represents an average over 1000 model-generated food webs.

Analytical expressions for appearance probability of motifs S1–S5 in the generalized cascade model

The right column states the prediction of over- or under-representation of each motif according to the model.

3. The completely random model

In the following section, we will compare the analytical expressions derived for the generalized cascade model with empirical data. However, we calculate them now for a different model, a fully random network, in order to determine whether the probability functions for the subgraphs depend significantly on the mechanisms underlying the generation of the network.

In a completely random (Erdos–Renyi) network, each species has the same probability x to be connected to any other species in the network. According to this definition, the average number of prey per species is z ≡ L/S = Sx , and the directed connectance yields C ≡ z/S = x .

Let us consider three arbitrary species in = the network, say A, B, and C. They are connected through subgraph S1 if, for instance, A eats B, and B eats C with no further links among them; this happens with probability x 2 (1 − x ) 4 . Of course, there exist other options to build this subgraph by A, B, and C exchanging their roles, which amounts to a total of six different configurations. As a consequence, we have

Similarly, considering the number of configurations for every subgraph and the probability for each of them, one finds

Finally, since these networks are completely random, their randomization provides equally random networks, so that the probabilities for subgraphs S1–S5 in the randomized networks of this model are exactly the same ones, namely Eqs. (18) - (21) . The differences between them are obviously zero.

4. Subgraphs statistics in empirical food webs

One interesting observation from Figs. ​ Figs.3 3 - ​ -5 5 is that the probabilities generated by model food webs depend on a single variable, the directed connectance C , and very weakly on the size of the food web. This indicates that our representation of the probabilities versus C can be adequate to provide a unified description of empirical data, since it allows us to include in the same plot food webs with different sizes. If empirical food webs behave as model food webs, one expects a common trend for the probabilities as functions of C despite having different S values.

In this section we compute the fraction of appearances for each subgraph S1–S5 for 17 empirical food webs (see Appendix A for details). Figs. ​ Figs.6 6 - ​ -8 8 show the results for the empirical food webs, their randomizations, and the differences, and also the comparison with the generalized cascade and the fully random models. One observes that the analytical expressions obtained for the generalized cascade model provide a reasonable agreement with empirical data for p and p rand with no adjustable parameters; in contrast, the completely random model provides remarkably poorer fits to the empirical values in most cases.

Fraction of appearances of motifs for empirical food webs (symbols) compared to the analytical predictions for the generalized cascade model (solid lines) and the random model (dashed lines). Numerical simulations for the generalized cascade model with S = 50 are shown by the dotted line where the error bars are two standard deviations. It is visually apparent that the generalized cascade model fits rather well the empirical data for all the motifs, whereas the random model provides much poorer fits. Note that there are no fitting parameters in model estimates.

Differences between actual appearances of motifs and the corresponding randomized food webs for 17 empirical food webs (symbols) as compared to the analytical predictions for the generalized cascade model (solid line) and the random model (dashed lines). Numerical simulations for the generalized cascade model with S = 50 are shown by the dotted line, where the error bars are two standard deviations. Motifs S1 and S2 are typically over-represented and motifs S3–S5 are under-represented, in agreement with the qualitative predictions of the model. The two noticeable deviations correspond to Bridge Brook ( C = 0:17) and Skipwith Pond ( C = 0:32). Quantitatively, the analytical curves generally overestimate the differences at larger values of C for both the empirical values and the numerical simulations of the generalized cascade model.

In the plots for the differences, the data generally appear more noisy. This is due to the fact that the empirical values for p and p rand are in general quite similar in magnitude; they commonly differ by less than 10%, in agreement with the model predictions. The general trend, however, is that motifs S1 and S2 are typically over-represented and motifs S3–S5 are under-represented, in agreement with the qualitative predictions of the model as expressed in Table 1 . Quantitatively, the theoretical curves generally over-estimate the empirical values, while the numerical simulations of the model provide reasonable estimates.

There exists, however, more noise in the empirical data than exhibited by the model, in particular for motif S2. To explore this issue further, let us note that it is the same two food webs which seem to deviate from the general trend in the plots of Fig. 8 : they are Bridge Brook (with C = 0:17) and Skipwith Pond ( C = 0.32). Why exactly those two food webs behave differently from the others is interesting but unclear. We can note that they are the smallest food webs of the ones studied, each with 25 trophic species (see Table 2 ). Although statistical fluctuations grow with decreasing size, they do not seem enough to explain this behaviour. Note, on the other hand, that they match rather well with the predictions for p and p rand separately (Figs. ​ (Figs.6 6 and ​ and7 7 ).

Fraction of appearances of motifs for randomizations of the empirical food webs (symbols) compared to the analytical predictions for the generalized cascade model (solid line) and the random model (dashed lines). Numerical simulations for the generalized cascade model with S = 50 are shown by the dotted line where the error bars are two standard deviations. It is visually apparent that the generalized cascade model fits rather well the empirical data for all the motifs, whereas the random model provides much poorer fits. Note that there are no fitting parameters in model estimates.

Empirical food webs studied

S is the number of trophic species in the food web and L is the number of trophic predator-prey interactions.

In summary, the behaviour of the two models indicates that the behaviour observed in the empirical data is not a trivial one: not any model would yield a similar behaviour for the quantities analyzed. Furthermore, we observe remarkable agreement between the local structure in the generalized cascade model and the empirical data.

5. Concluding remarks

The predictions of the generalized cascade model for the appearances of subgraphs S1–S5 provide good comparison to the empirical results, in contrast to those for a completely random model. This generalized cascade model was recently shown to fit empirical data for a number of global quantities, including the distributions of the number of prey and predators. Here we show that it also describes the local structure of empirical food webs. This suggests that many features of food web structure could be explained by considering the two principle ingredients inside the model, namely (i) the species' niche values form a totally ordered set, and (ii) each species has a specific exponentially decaying probability of preying on a given fraction of the species with lower niche values. These could then be considered as basic mechanisms actually shaping food webs.

It is an interesting ecological question to determine why these appear to be such important ingredients to explain food web structure. Recently, Rossberg et al. have devised a couple of dynamic models, the speciation model ( Rossberg et al., 2005 , 2006a ) and the matching model ( Rossberg et al., 2006b ) that seem to provide the dynamical explanation. By starting from an ordered set of species, the dynamic evolutionary rules of speciation, extinction, and migration lead to distributions of number of prey and number of predators similar to the ones obtained through the static models. Indeed, the matching model fits remarkably the empirical data, improving in some cases the predictions of the niche model at the expense of a number of adjustable parameters. From the result of an extensive analysis, the authors conclude that the tendency of newly created species to avoid competition with their relatives is indeed the fundamental mechanism responsible of food web structure.

Empirical and model food webs predict over-representation of motifs S1 and S2, and under-representation of motifs S3–S5. Empirical data are rather noisy, and the over-representation of subgraph S2 predicted by the generalized cascade model is unclear in the empirical data. This is also the result found by Bascompte and Melian (2005) , who also analyzed the under/over-representation of a number of ecologically relevant subgraphs, among them, our motifs S1 (food chain) and S2 (simple omnivory). Our methodology, however, differs from theirs in several aspects. On the one hand, we consider trophic species instead of taxonomic ones; on the other hand, we count motifs only once (for instance, we do not count the food chains included in motifs S2 in the evaluation of S1). Despite the different analysis, we still do not find an unambiguous over-representation of omnivorism, in contrast to what one may expect according to its stabilizing role in trophic interactions ( McCann and Hastings, 1997 ).

Finally note that, from the quantitative point of view, the percentage of under/over-representation of motifs is generally small, usually less than a 10%; curiously, this is also the order of magnitude predicted by the generalized cascade model. This high similarity between the number of subgraphs in empirical food webs and in their randomizations indicates that there may be no overwhelming evolutionary trend toward under/over-representation of any motif, and that the small differences observed are more likely a consequence of the mechanisms generating the food web.

Acknowledgements

We thank R. Guimerà and M. Sales-Pardo for stimulating discussions and helpful suggestions. JC thanks the Spanish CICYT (FIS2006-12296-C02-01) and the Direcció General de Recerca (2005 SGR 000 87) for support. DBS acknowledges the NU ChBE Murphy Fellowship and NSF-IGERT “Dynamics of Complex Systems in Science and Engineering” (DGE-9987577). LANA acknowledges a Searle Leadership Fund Award, National Institute of General Medical Sciences/National Institutes of Health K25 Career Award, the J.S. McDonnell Foundation, and the W.M. Keck Foundation.

Appendix A. Empirical food webs

Table 2 provides the list of food webs analyzed as well as some topological parameters characterizing them. They range between 25 and 92 trophic species, and the average connectivity varies from 2.19 to 17.72. It also contains the number of single links, double links, and cannibal links for each empirical food web. One observes that the frequency of double links is generally small, with only one case, Coachella Valley, close to 10%.

Appendix B. Motif probabilities in the generalized cascade model

We calculate here the subgraph probabilities for the randomizations of the generalized cascade model. Itzkovitz et al. (2003) . derived general expressions for the average number of appearances N i of motifs in randomized networks. The fraction of motifs p rand i is obtained dividing N i by the total number of possible triplets of species, S T ≡ S ( S -1)( S -2)/6. For subgraphs S1–S5, these can be cast as

where z ≡ L / S is the average connectivity, k i and m i denote the number of prey and number of predators of species i , respectively, and 〈…〉 is the average over all species in the randomized network. Since these networks have the same distributions of in- and out-links that the original networks, these averages can be calculated directly from the latter ones.

From expressions (23), p rand S 2 and p rand S 3 can be rewritten as

Therefore, p rand i can be evaluated if one knows p 1 , p 4 , and p 5 . In order to calculate these quantities, let us note that they have a direct interpretation. (i) N 1 = Σ i = 1 S k i m i is the number configurations where species A eats B , and B eats C , independently if there is a trophic connection between species A and C (i.e. it is like a generalization of motif S1); therefore, p 1 = N 1 / S T is just the probability for this configuration, namely 〈 x A x B 〉 = 〈 x 〉 2 , since x A and x B are independent random variables. (ii) N 2 = Σ i = 1 S m i ( m i − 1 ) is the number of configurations where species A feeds on C and species B feeds on C , independently if A and B are connected (i.e. like a generalization of motif S4); then, p 4 is the probability 〈 x A x B 〉 = 〈 x 〉 2 . (iii) Similarly, p 5 is the probability of A eating species B and C , independently of the eventual connection of B and C , namely 〈 x A 2 〉 = 〈 x 2 〉 .

By replacing these results in Eqs. (22) - (24) , one finds

Finally, the beta-function (1) yields

The substitution of these expressions into (25) supplies Eqs. (13) - (17) .

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Secondary Production, Quantitative Food Webs, and Trophic Position

Introduction

Secondary production (or the formation of heterotrophic biomass through time) is a topic often considered as a small part of the energy-flow paradigm commonly described in most ecology texts. The energy-flow paradigm begins with energy from the sun being converted into autotrophic biomass by photosynthesis. This formation of biomass (primary production) is ultimately passed on to successive heterotrophic levels via ingestion. Because heterotrophs such as animals do not assimilate all their food and have substantial respiratory demands, only about 10% of what they ingest is converted into their own secondary production according to the paradigm. Energy flow diagrams often depict secondary production as the flow leaving one trophic level and entering (being ingested by) the next. Many ecologists, however, have demonstrated that secondary production, particularly when measured at the population level, has far wider usefulness than solely in describing the flow of energy between trophic levels. Applications extend to questions on single species (habitat-specific microdistributions), communities (e.g., niche overlap and competition), and ecosystems (chemical flows and stoichiometry) (Benke 2010a, Benke & Huryn 2010).

One application of secondary production is in the quantification of food webs. Many food webs described in the ecological literature are "connectivity" webs, in which species are depicted as nodes (dots) and interactions (or linkages) among species are shown as lines connecting the nodes. Such webs have sometimes suggested great complexity in the many linkages between species, but this approach has numerous shortcomings such as not identifying the relative importance of species and not quantifying their interactions (Woodward et al . 2005). As a result there have been attempts to quantify foods webs by measuring various attributes of their interactions (e.g., Berlow et al . 2004, Woodward et al . 2005). One such attempt is determination of taxon-specific secondary production within the assemblage which can lead to measurement of energy or material flows among species (Benke & Wallace 1980, 1997). The key feature of this approach is combining production with diet analyses of those same taxa in order to build detailed quantitative flow webs . Such flow webs represent a significant departure from the early energy flow paradigm described above in terms of complexity and methodology. We might think of flow webs as a type of food web that combines the quantitative aspects of trophic-level energy flow with the species-level detail often observed in connectivity webs (e.g., Closs & Lake 1994, Woodward 2005). The units of such flow webs are typically mass or energy per m 2 per unit time (e.g., grams m -2 y -1 ). Ingestion flows from a single resource (or prey species), for example, may be distributed to many consumers (or predators) and individual flows throughout the community may vary by several orders of magnitude. Such quantitative differences in ingestion flows can thus serve as a measure of bottom-up interaction (or linkage) strength between species and their food resource (Benke & Wallace 1997). That is, the strength of any interaction in the web is measured by the absolute amount of food ingested by each consumer.

Other aspects of food webs may be derived from the basic flow web. The ratio of these same ingestion flows to production of the resource (or prey) from which they came (ingestion/production) may be used as a top-down measure of interaction strength or predation pressure (Benke et al . 2001, Woodward et al . 2005). That is, if a consumer (predator) ingests a large fraction of a resource's (prey's) production (regardless of the absolute amount of that production), it would imply a strong top-down interaction. Finally, the combination of ingestion flows to any species in a flow web can be used to calculate the trophic position of that species (Levine 1980, Hall et al . 2000; Benke et al . 2001). Trophic position, rather than trophic level, shows exactly where a species fits into the trophic hierarchy (e.g., species A has a trophic position of 3.2 rather than being placed within the third trophic level of all secondary consumers). This is exactly the same concept that has been addressed using stable isotopes (e.g., Vander Zanden & Rasmussen 1999; Post 2002; McCutchan et al . 2003).

The general application of secondary production in building flow webs depends heavily on our ability to measure production in the field. Fortunately, production methods have been well established in all environments (freshwater, marine, terrestrial) since at least the 1960s. In recent decades, however, secondary production has been most widely studied for freshwater and marine benthic invertebrates (Benke 1984, Cusson & Bourget 2005, Benke & Huryn 2010), so it is here that we turn for examples of quantitative food webs. In stream ecosystems, numerous investigators have successfully determined taxon-specific production for entire invertebrate assemblages (e.g., Benke et al . 1984, Wallace et al . 1999, Hall et al . 2000). Detailed quantitative gut analyses have sometimes been accomplished in stream assemblages as well (e.g., Wallace et al . 1987, Woodward et al . 2005). Combining assemblage-wide production estimates with gut analyses, and assuming food-specific ecological efficiencies (e.g., 0.40 of algae ingested and 0.70 of animals ingested are assimilated from the digestive tract) allows one to determine the trophic basis of production (Benke & Wallace 1980). This tells us how much each food source is responsible for the production of each species. Subsequently, flow webs can be built using all species, or at least the common species, in the assemblage (e.g., Benke & Wallace 1997, Benke et al . 2001; Hall et al . 2000).

The objectives of this article are to:

• describe a hierarchy of food webs, beginning with a simple connectivity web , by identifying the presence or absence of food items through gut analysis,
• convert the connectivity web into a diet proportion web by quantification of gut analyses,
• convert the diet proportion web into an assimilation web using ecological efficiencies,
• convert the assimilation web into a quantitative flow web using secondary production,
• convert the flow web into an ingestion/production web , and
• determine trophic position for each species in the flow web.

Objectives 3–6 are based on energetic principles involving ecological efficiencies, production analyses, or both. To accomplish these objectives, I use a fictional food web that has been simplified from the more complex web of a riverine invertebrates found on submerged wood (Benke & Wallace 1997; Benke et al . 2001). As each type of food web is constructed, increasing amounts of information are required. It should be emphasized that the food webs shown here are not the only approaches used in attempting to quantify food web interactions.

Types of Food Webs and How to Construct Them

Connectivity webs may be constructed with qualitative gut content information without regard to relative proportions in the gut. Such webs may be built from gut presence/absence data or from literature information. Many investigators have used connectivity webs to calculate various statistics such as the number of interactions per species, maximum food chain length from basal resources to top predator, etc. (Woodward et al . 2005). Although early versions of this approach were criticized for their simplicity and poor quality data, there are now excellent examples of highly detailed webs for streams from gut analyses (e.g., Closs & Lake 1994; Woodward et al . 2005). The major remaining weakness of this approach, no matter how detailed the web, is that it does not account for different linkage strengths between species, however we might measure strength (Benke & Wallace 1997).

Diet proportion webs are based on quantitative gut analyses such as with methods described by Wallace et al . (1987) or Woodward et al . (2005) for stream invertebrates. They represent the simplest type of quantification beyond the connectivity web, and show to what extent a given consumer eats different fractions of its food resources. Tavares-Cromar & Williams (1996) built some very detailed stream webs using this approach. Such webs are more informative than a connectivity web, and line thicknesses from each food resource to a consumer can be used to represent the fraction of each food item ingested. Thus, in a food web diagram, all lines entering a given consumer should sum to 1.00. While line thicknesses reflect dietary preferences for each consumer, differences in line thicknesses between consumer species have little meaning because they do not reflect differences in absolute ingestion.

Assimilation webs add an additional level of quantification beyond the diet proportion web. Assimilation is that portion of ingested food that is assimilated (absorbed) from the digestrive tract for use in metabolism and growth. Assimilation efficiencies (assimilation/ingestion, or "A/I" efficiencies) vary greatly depending on the type of food ingested (e.g., animal food v. detritus). The relative amount of each food type assimilated (and thus contributing to production) can be determined by multiplying the diet proportion of a food type by its assimilation efficiency; that is, you are what you assimilate rather than you are what you ingest. The relative amount assimilated is easily converted into the fractional amount assimilated. Differences between the diet proportion web and the assimilation web are often subtle and only apparent for animals that feed on a diverse diet (i.e., animals ingesting foods having different assimilation efficiencies). Again, line thicknesses only apply to fractional amounts assimilated by a species, all of which sum to 1.00. Although I am unaware of anyone constructing an assimilation web, the information from such a web can be combined with secondary production to determine the trophic basis of production; that is., how much secondary production of a single consumer species is attributed to each food resource (Benke & Wallace (1980). Total production of all species attributable to a single food resource can also be determined. Several studies have now determined the trophic basis of production for groups of similar taxa (e.g., Roeding & Smock 1989; Benke & Jacobi 1994) and entire communities (e.g., Smock & Roeding 1986; Hall et al . 2001).

Flow webs represent a step beyond the assimilation web and trophic basis of production. The absolute ingestion flow between a specific food resource and its consumer species is estimated from the production attributable to the food resource divided by gross production efficiency (Benke & Wallace 1997). Gross production efficiency is assimilation efficiency (A/I) times net production efficiency, the latter being production divided by assimilation (P/A). Thus, GPE = A/I x P/A = P/I. Because GPE is a fraction considerably less than one, ingestion of a food resource will be substantially higher than the production it creates. Once individual ingestion flows (g m -2 y -1 ) are determined for each interaction, a quantitative flow web can be constructed for the entire assemblage/community. Many flow webs have now been built in this manner, primarily in stream systems (e.g., Hall et al . 2000, Benke et al . 2001, Cross et al . 2007, Runck 2007). Flow webs demonstrate major differences in the quantity of materials or energy flow pathways within food webs; these can vary by orders of magnitude within communities or in comparisons among communities. This is the only food web described here that demonstrates absolute differences in ingestion flows among consumers.

Once a quantitative flow web has been constructed, trophic position can be determined for individual species (Levine 1980, Hall et al . 2000, Benke et al . 2001). Although the trophic level of a consumer can be determined by following the longest feeding chain, trophic position for that same consumer can be calculated as 1 plus the sum of the trophic position of each food item times the fraction each food item contributed to the consumer's production (as in the trophic basis of production). For example, TP = 1 + (2 x 0.9) + (2.8 x 0.10) = 3.1, where TP is trophic position of a consumer species, 2 and 2.8 are trophic positions of 2 food types ingested by that species and 0.9 and 0.1 are the fractions these food types contributed to production of the species. If one wants to determine the trophic position for all species, it is necessary to determine the trophic position for those species closest to the basal resources first.

Ingestion/production webs represent an attempt to quantify the top-down effect of a predator on its prey (or food resource). Each interaction is measured as the fraction (I/P) of a prey species' production (P) that is ingested (I) by one of its predators. For example, if production of a prey species is 10 g m -2 y -1 and one of its predators consumes 1 g m -2 y -1 of its production, then the prey's I/P value for this predator is 0.10. Because both I and P have the same units (g m -2 y -1 ), this ratio in unitless. The sum of fractions of a prey species to all its predators represents the total fraction of production that is ingested and the total impact of all predators on this species (Benke et al . 2001, Woodward et al . 2005). Thus, while any one predator may have a weak interaction with a given prey (e.g., 0.10), this approach shows that the sum of, say, 9 similar predators, each with P/I = 0.10, may represent a large impact (i.e., 0.90) on the prey. The sum of all such top-down interactions for a given prey species thus has a range from zero to 1.00.

Comparisons of Food Webs Constructed with the Same Data

The fictional stream food web consists of two basal food resources (algae and detritus) and four species of stream insects: a chironomid midge, an omnivorous trichopteran (caddisfly), a predaceous plecopteran (stonefly), and a predaceous megalopteran (hellgrammite) (Table 1).

The diet proportion web of Figure 1 is based on the feeding fractions from Table 1 rather than just presence-absence data of the connectivity web. The lines from the food sources have different thicknesses corresponding to their fraction in the gut. The total of all lines entering each consumer must sum to 1.00. For example, the diet proportion web shows that 0.50 of the chironomid food is algae and 0.50 is detritus. It shows that 0.70 of trichopteran food is detritus and 0.30 is chironomid.

The assimilation web appears very similar to the diet proportion web except for animals (chironomids and trichopterans) that feed on food types having different assimilation efficiencies (Figure 1, Table 2). All lines entering each consumer again sum to 1.00 but are based on the fraction that each contributes to production (i.e., fraction that is assimilated). While only 0.30 of trichopteran ingestion is chironomids (see diet proportion web), the high assimilation efficiency (0.70) of chironomids results in chironomids being responsible for 0.75 of trichopteran production (i.e., of the food assimilated, 0.75 is from chironomids). Also, while chironomids eat equal amounts of algae and detritus (see diet proportion web), they assimilate much more of the algae (0.80) in the assimilation web.

The flow web shows the actual amount of food ingested after taking production and ecological efficiencies into account (Figure 1, Tables 1, 2). It shows great variation among ingestion flows ranging from 29 to 40000 mg m -2 y -1 (last column of Table 2) as illustrated by line thickness in Figure 1. The wide range in flows is largely explained by great variation in production among species. Because the flow web is highly dependent on production of each consumer, an illustration of the production calculation for Trichoptera is shown in Table 3. The annual production summary of all 4 species is found in Table 1. Ingestion flows are obviously highest for those with highest production (Figure 1, Tables 1, 2). Chironomids ingest the greatest amounts of both algae (40,000 mg m -2 y -1 ) and detritus (40,000 mg m -2 y -1 ) in this assemblage. This equality of ingestion may seem surprising since 0.80 of chironomid production is due to eating algae (see assimilation web), the result of differing assimilation efficiencies. It may also seem surprising that chironomids consume more detritus than is consumed by trichopterans, even though the diet proportion web shows that trichopterans have more detritus in their guts (0.70) than is found in chironomid guts (0.50). Finally, note that the omnivorous trichopteran in the flow web consumes far more animal prey (4286 mg m -2 y -1 ) than either of the species considered as strict predators (286 mg m -2 y -1 for the plecopteran and 1428 mg m -2 y -1 for the megalopteran, last column of Table 2), which is a direct function of differences in production and total ingestion.

The ingestion/production (I/P) web shown on the right side of Figure 1 is constructed from data in Table 4 which summarizes production of each prey species, ingestion flow to each consumer, I/P for each individual flow and total I/P for each food source. Flows for production and ingestion were derived from Tables 1 and 2, respectively. Values also have been added for net primary production of algae and annual inflow of detritus to make the complete I/P web possible (Table 4). In this fictional web, individual impacts (I/P values in parentheses, Table 4) of predator species on prey species (or resources) vary widely from 0.01 to 0.80, but total predatory impacts on a given prey species range from only 0.37 to 0.80 (in parentheses, last column). Clearly the highest impacts for species-species interactions are imposed by chironomids on both algae (0.80) and detritus (0.50), Trichoptera on chironomids (0.43), Megaloptera on Trichoptera (0.36), and Megaloptera on Plecoptera (0.57).

Trophic position is calculated from the flow web (Figure 1) and is shown along with trophic level in Figure 2. There are 5 trophic levels in this simple system if one follows the longest feeding chain from either algae (level 1) or detritus (1) to chironomids (2) to Trichoptera (3) to Plecoptera (4) to Megaloptera (5). Both algae and detritus are basal resources and considered to be at trophic level 1 and trophic position 1. Similarly, chironomids are at trophic level 2 and trophic position 2. Trichopterans, however, obtain their food from more than one trophic position and while they are at trophic level 3, their trophic position is only 2.8. Subsequently, the level-4 plecopterans are at trophic position 3.1 and the level-5 megalopterans are at trophic position 3.4.

The flow web is probably the most informative of all webs considered because it represents actual flows (rather than ratios) which have meaning across species and communities (e.g., ingestion of chironomids primarily passes through the omnivorous trichopteran far more than through the predaceous plecopteran or megalopteran) (Figure 1, Table 2). The flow web, and the individual flows that comprise it, can be considered as one way to quantify interaction (or linkage) strength from a bottom-up perspective throughout the assemblage.

If one interprets interaction strength from a top-down perspective (as many do), however, this can be accomplished with the I/P web (e.g., Woodward et al . 2005). For example, the trichopteran ingestion of 0.43 chironomid production suggests a relatively strong linkage (Figure 1). This is not the entire impact on chironomids because two other predators consume them as well, increasing their total I/P to 0.52. In the case of the chironomid-Trichoptera linkage both the flow web and I/P web indicate a strong interaction. Comparisons between other flow web and I/P web links indicate exactly the opposite relationship. Thus, there is no predictable pattern between the flow web and I/P web, as has been pointed out by Paine (1980) and others. For real stream food webs, however, total ingestion by predators has sometimes been shown to be >90% of prey production (e.g., Smith & Smock 1992, Wallace et al . 1997, Huryn 1998). Such high total I/P suggests a strong top-down influence, but it may be distributed among several predators with individual linkage strengths well below 1.00 (diffuse predation).

Trophic position is an interesting concept because it recognizes that many consumer species do not easily fall into trophic levels but rather occur in a staggered hierarchy. For example, the megalopteran could be identified at the fifth trophic level but is actually only at trophic position 3.4 because some of its prey are at trophic positions <3 (Figure 2). Results using this flow web approach should be very similar to trophic positions identified by stable isotope (SI) methods. But both methods depend on the accuracy of certain assumptions. For example, the SI approach assumes a constant fractionation from one trophic level to the next of 3.4. The flow web approach assumes that the selected assimilation efficiencies are reasonable approximations of reality. A major advantage of SI methods for estimating trophic position is that measurement is much less time-consuming than the flow web and it can be done for individual species of interest. On the other hand, the SI approach cannot itself define a true food web because linkages between species are not identified. It would be enlightening to compare these approaches for calculating trophic position in a single system, but I am unaware of any attempts to do so.

In summary, among the many ways in which secondary production has been used in addressing ecological questions (Benke & Huryn 2010) is its application to food web analysis. The same assemblage-level production information enables the quantification of at least three food-web approaches in contemporary community ecology: bottom-up linkages with flow webs, top-down linkages with ingestion/production webs, and assessment of trophic positions.

References and Recommended Reading

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———. Concepts and patterns of invertebrate production in running waters. Verhandlungen der internationale Vereinigung für theoretische und angewandte Limnologie 25 , 15–38 (1993).

———. Secondary production as part of bioenergetic theory - contributions from freshwater benthic science. River Research and Applications 26 , 36–44 (2010a).

———. Secondary Production. Nature Education Knowledge 1 , 5 (2010b).

Benke, A. C. & Huryn, A. D. "Secondary production of macroinvertebrates," In Methods in Stream Ecology, 2nd ed ., eds. F. R. Hauer & G. A. Lamberti (Burlington, MA: Academic Press, 2006): 691–710.

———. Benthic invertebrate production: facilitating answers to ecological riddles in freshwater ecosystems. Journal of the North American Benthological Society 29 , 264–285 (2010).

Benke, A. C. & Jacobi, D. I. Production dynamics and resource utilization of snag-dwelling mayflies in a blackwater river. Ecology 75 , 1219–1232 (1994).

Benke, A. C. & Wallace, J. B. Trophic basis of production among net-spinning caddisflies in a southern Appalachian stream. Ecology 61 , 108–118 (1980).

———. Trophic basis of production among riverine caddisflies: implications for food web analysis. Ecology 78, 1132–1145 (1997).

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Energetic Food Webs: An analysis of real and model ecosystems

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This book bridges the gap between the energetic and species approaches to studying food webs, addressing many important topics in ecology. Species, matter, and energy are common features of all ecological systems. Through the lens of complex adaptive systems thinking, the authors explore how the inextricable relationship between species, matter, and energy can explain how systems are structured, and how they persist in real and model systems. Food webs are viewed as open and dynamic systems. The central theme of the book is that the basis of ecosystem persistence and stability rests on the interplay between the rates of input of energy into the system from living and dead sources, and the patterns in utilization of energy which result from the trophic interactions among species within the system. To develop this theme, the authors integrate the latest work on community dynamics, ecosystem energetics, and stability. In so doing, they present a unified ecology that dispels the categorization of the field into the separate subdisciplines of population, community, and ecosystem ecology.

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Empirical methods of identifying and quantifying trophic interactions for constructing soil food-web models

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• Mathematical and Statistical Methods - Biometris

Research output : Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

Introduction Food-web models, which depict the trophic relationships between organisms within a community, form a powerful and versatile approach to study the relationships between community structure and ecosystem functioning. Although food-web models have recently been applied to a wide range of ecological studies (Memmott, 2009; Sanders et al., 2014), such approaches can be greatly improved by introducing high-resolution trophic information from empirical studies and experiments that realistically describe topological structure and energy flows (de Ruiter et al., 2005). Over the last decades major technological advances have been made in empirically characterizing trophic networks by describing, in detail, the connectedness and flows in food webs. Existing empirical techniques, such as stable isotope probing (SIP) (Layman et al., 2012), have been refined and new approaches have been created by combining methods, e.g., combining Raman spectroscopy or fatty acid analysis with SIP (Ruess et al., 2005a; Li et al., 2013). These empirical methods can provide insight into different aspects of food webs and together form an extensive toolbox to investigate trophic interactions. It is crucial to recognize the potential and limitations of a range of empirical approaches in order to choose the right method in the design of empirically based food-web studies. Empirically based food webs are generally classified according to the type of input information that is required. In the following lines we will provide an overview of four types of food-web model: connectedness webs, semi-quantitative webs, energy-flow webs, and functional webs. Paine (1980) introduced three of those webs, which are widely accepted and applied in food-web studies across ecosystems. We propose to add a fourth type of empirically based food web, the semi-quantitative web. All of these food webs have the same basic structure, but the conceptual webs differ in the type of trophic information they describe and represent (Figure 16.1). Connectedness webs (Figure 16.1a) define the basic structure of a food web by describing the food-web connections per se.

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• 10.1017/9781316871867.018

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• Identifying Earth and Planetary Sciences 100%
• Soil Food Web Earth and Planetary Sciences 100%
• Trophic Interaction Earth and Planetary Sciences 100%
• Information Economics, Econometrics and Finance 100%
• Connectedness Psychology 100%
• Spider Web Agricultural and Biological Sciences 66%
• Investigation Earth and Planetary Sciences 41%
• Designation of Origin Economics, Econometrics and Finance 33%

T1 - Empirical methods of identifying and quantifying trophic interactions for constructing soil food-web models

AU - Heijboer, Amber

AU - Ruess, Liliane

AU - Traugott, Michael

AU - Jousset, Alexandre

AU - de Ruiter, Peter C.

PY - 2017/12

Y1 - 2017/12

N2 - Introduction Food-web models, which depict the trophic relationships between organisms within a community, form a powerful and versatile approach to study the relationships between community structure and ecosystem functioning. Although food-web models have recently been applied to a wide range of ecological studies (Memmott, 2009; Sanders et al., 2014), such approaches can be greatly improved by introducing high-resolution trophic information from empirical studies and experiments that realistically describe topological structure and energy flows (de Ruiter et al., 2005). Over the last decades major technological advances have been made in empirically characterizing trophic networks by describing, in detail, the connectedness and flows in food webs. Existing empirical techniques, such as stable isotope probing (SIP) (Layman et al., 2012), have been refined and new approaches have been created by combining methods, e.g., combining Raman spectroscopy or fatty acid analysis with SIP (Ruess et al., 2005a; Li et al., 2013). These empirical methods can provide insight into different aspects of food webs and together form an extensive toolbox to investigate trophic interactions. It is crucial to recognize the potential and limitations of a range of empirical approaches in order to choose the right method in the design of empirically based food-web studies. Empirically based food webs are generally classified according to the type of input information that is required. In the following lines we will provide an overview of four types of food-web model: connectedness webs, semi-quantitative webs, energy-flow webs, and functional webs. Paine (1980) introduced three of those webs, which are widely accepted and applied in food-web studies across ecosystems. We propose to add a fourth type of empirically based food web, the semi-quantitative web. All of these food webs have the same basic structure, but the conceptual webs differ in the type of trophic information they describe and represent (Figure 16.1). Connectedness webs (Figure 16.1a) define the basic structure of a food web by describing the food-web connections per se.

AB - Introduction Food-web models, which depict the trophic relationships between organisms within a community, form a powerful and versatile approach to study the relationships between community structure and ecosystem functioning. Although food-web models have recently been applied to a wide range of ecological studies (Memmott, 2009; Sanders et al., 2014), such approaches can be greatly improved by introducing high-resolution trophic information from empirical studies and experiments that realistically describe topological structure and energy flows (de Ruiter et al., 2005). Over the last decades major technological advances have been made in empirically characterizing trophic networks by describing, in detail, the connectedness and flows in food webs. Existing empirical techniques, such as stable isotope probing (SIP) (Layman et al., 2012), have been refined and new approaches have been created by combining methods, e.g., combining Raman spectroscopy or fatty acid analysis with SIP (Ruess et al., 2005a; Li et al., 2013). These empirical methods can provide insight into different aspects of food webs and together form an extensive toolbox to investigate trophic interactions. It is crucial to recognize the potential and limitations of a range of empirical approaches in order to choose the right method in the design of empirically based food-web studies. Empirically based food webs are generally classified according to the type of input information that is required. In the following lines we will provide an overview of four types of food-web model: connectedness webs, semi-quantitative webs, energy-flow webs, and functional webs. Paine (1980) introduced three of those webs, which are widely accepted and applied in food-web studies across ecosystems. We propose to add a fourth type of empirically based food web, the semi-quantitative web. All of these food webs have the same basic structure, but the conceptual webs differ in the type of trophic information they describe and represent (Figure 16.1). Connectedness webs (Figure 16.1a) define the basic structure of a food web by describing the food-web connections per se.

U2 - 10.1017/9781316871867.018

DO - 10.1017/9781316871867.018

M3 - Chapter

AN - SCOPUS:85048681284

SN - 9781107182110

BT - Adaptive Food Webs

PB - Cambridge University Press

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Home » Quantitative Research – Methods, Types and Analysis

Quantitative Research – Methods, Types and Analysis

Table of Contents

Quantitative Research

Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions . This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected. It often involves the use of surveys, experiments, or other structured data collection methods to gather quantitative data.

Quantitative Research Methods

Quantitative Research Methods are as follows:

Descriptive Research Design

Descriptive research design is used to describe the characteristics of a population or phenomenon being studied. This research method is used to answer the questions of what, where, when, and how. Descriptive research designs use a variety of methods such as observation, case studies, and surveys to collect data. The data is then analyzed using statistical tools to identify patterns and relationships.

Correlational Research Design

Correlational research design is used to investigate the relationship between two or more variables. Researchers use correlational research to determine whether a relationship exists between variables and to what extent they are related. This research method involves collecting data from a sample and analyzing it using statistical tools such as correlation coefficients.

Quasi-experimental Research Design

Quasi-experimental research design is used to investigate cause-and-effect relationships between variables. This research method is similar to experimental research design, but it lacks full control over the independent variable. Researchers use quasi-experimental research designs when it is not feasible or ethical to manipulate the independent variable.

Experimental Research Design

Experimental research design is used to investigate cause-and-effect relationships between variables. This research method involves manipulating the independent variable and observing the effects on the dependent variable. Researchers use experimental research designs to test hypotheses and establish cause-and-effect relationships.

Survey Research

Survey research involves collecting data from a sample of individuals using a standardized questionnaire. This research method is used to gather information on attitudes, beliefs, and behaviors of individuals. Researchers use survey research to collect data quickly and efficiently from a large sample size. Survey research can be conducted through various methods such as online, phone, mail, or in-person interviews.

Quantitative Research Analysis Methods

Here are some commonly used quantitative research analysis methods:

Statistical Analysis

Statistical analysis is the most common quantitative research analysis method. It involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis can be used to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.

Regression Analysis

Regression analysis is a statistical technique used to analyze the relationship between one dependent variable and one or more independent variables. Researchers use regression analysis to identify and quantify the impact of independent variables on the dependent variable.

Factor Analysis

Factor analysis is a statistical technique used to identify underlying factors that explain the correlations among a set of variables. Researchers use factor analysis to reduce a large number of variables to a smaller set of factors that capture the most important information.

Structural Equation Modeling

Structural equation modeling is a statistical technique used to test complex relationships between variables. It involves specifying a model that includes both observed and unobserved variables, and then using statistical methods to test the fit of the model to the data.

Time Series Analysis

Time series analysis is a statistical technique used to analyze data that is collected over time. It involves identifying patterns and trends in the data, as well as any seasonal or cyclical variations.

Multilevel Modeling

Multilevel modeling is a statistical technique used to analyze data that is nested within multiple levels. For example, researchers might use multilevel modeling to analyze data that is collected from individuals who are nested within groups, such as students nested within schools.

Applications of Quantitative Research

Quantitative research has many applications across a wide range of fields. Here are some common examples:

• Market Research : Quantitative research is used extensively in market research to understand consumer behavior, preferences, and trends. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform marketing strategies, product development, and pricing decisions.
• Health Research: Quantitative research is used in health research to study the effectiveness of medical treatments, identify risk factors for diseases, and track health outcomes over time. Researchers use statistical methods to analyze data from clinical trials, surveys, and other sources to inform medical practice and policy.
• Social Science Research: Quantitative research is used in social science research to study human behavior, attitudes, and social structures. Researchers use surveys, experiments, and other quantitative methods to collect data that can inform social policies, educational programs, and community interventions.
• Education Research: Quantitative research is used in education research to study the effectiveness of teaching methods, assess student learning outcomes, and identify factors that influence student success. Researchers use experimental and quasi-experimental designs, as well as surveys and other quantitative methods, to collect and analyze data.
• Environmental Research: Quantitative research is used in environmental research to study the impact of human activities on the environment, assess the effectiveness of conservation strategies, and identify ways to reduce environmental risks. Researchers use statistical methods to analyze data from field studies, experiments, and other sources.

Characteristics of Quantitative Research

Here are some key characteristics of quantitative research:

• Numerical data : Quantitative research involves collecting numerical data through standardized methods such as surveys, experiments, and observational studies. This data is analyzed using statistical methods to identify patterns and relationships.
• Large sample size: Quantitative research often involves collecting data from a large sample of individuals or groups in order to increase the reliability and generalizability of the findings.
• Objective approach: Quantitative research aims to be objective and impartial in its approach, focusing on the collection and analysis of data rather than personal beliefs, opinions, or experiences.
• Control over variables: Quantitative research often involves manipulating variables to test hypotheses and establish cause-and-effect relationships. Researchers aim to control for extraneous variables that may impact the results.
• Replicable : Quantitative research aims to be replicable, meaning that other researchers should be able to conduct similar studies and obtain similar results using the same methods.
• Statistical analysis: Quantitative research involves using statistical tools and techniques to analyze the numerical data collected during the research process. Statistical analysis allows researchers to identify patterns, trends, and relationships between variables, and to test hypotheses and theories.
• Generalizability: Quantitative research aims to produce findings that can be generalized to larger populations beyond the specific sample studied. This is achieved through the use of random sampling methods and statistical inference.

Examples of Quantitative Research

Here are some examples of quantitative research in different fields:

• Market Research: A company conducts a survey of 1000 consumers to determine their brand awareness and preferences. The data is analyzed using statistical methods to identify trends and patterns that can inform marketing strategies.
• Health Research : A researcher conducts a randomized controlled trial to test the effectiveness of a new drug for treating a particular medical condition. The study involves collecting data from a large sample of patients and analyzing the results using statistical methods.
• Social Science Research : A sociologist conducts a survey of 500 people to study attitudes toward immigration in a particular country. The data is analyzed using statistical methods to identify factors that influence these attitudes.
• Education Research: A researcher conducts an experiment to compare the effectiveness of two different teaching methods for improving student learning outcomes. The study involves randomly assigning students to different groups and collecting data on their performance on standardized tests.
• Environmental Research : A team of researchers conduct a study to investigate the impact of climate change on the distribution and abundance of a particular species of plant or animal. The study involves collecting data on environmental factors and population sizes over time and analyzing the results using statistical methods.
• Psychology : A researcher conducts a survey of 500 college students to investigate the relationship between social media use and mental health. The data is analyzed using statistical methods to identify correlations and potential causal relationships.
• Political Science: A team of researchers conducts a study to investigate voter behavior during an election. They use survey methods to collect data on voting patterns, demographics, and political attitudes, and analyze the results using statistical methods.

How to Conduct Quantitative Research

Here is a general overview of how to conduct quantitative research:

• Develop a research question: The first step in conducting quantitative research is to develop a clear and specific research question. This question should be based on a gap in existing knowledge, and should be answerable using quantitative methods.
• Develop a research design: Once you have a research question, you will need to develop a research design. This involves deciding on the appropriate methods to collect data, such as surveys, experiments, or observational studies. You will also need to determine the appropriate sample size, data collection instruments, and data analysis techniques.
• Collect data: The next step is to collect data. This may involve administering surveys or questionnaires, conducting experiments, or gathering data from existing sources. It is important to use standardized methods to ensure that the data is reliable and valid.
• Analyze data : Once the data has been collected, it is time to analyze it. This involves using statistical methods to identify patterns, trends, and relationships between variables. Common statistical techniques include correlation analysis, regression analysis, and hypothesis testing.
• Interpret results: After analyzing the data, you will need to interpret the results. This involves identifying the key findings, determining their significance, and drawing conclusions based on the data.
• Communicate findings: Finally, you will need to communicate your findings. This may involve writing a research report, presenting at a conference, or publishing in a peer-reviewed journal. It is important to clearly communicate the research question, methods, results, and conclusions to ensure that others can understand and replicate your research.

When to use Quantitative Research

Here are some situations when quantitative research can be appropriate:

• To test a hypothesis: Quantitative research is often used to test a hypothesis or a theory. It involves collecting numerical data and using statistical analysis to determine if the data supports or refutes the hypothesis.
• To generalize findings: If you want to generalize the findings of your study to a larger population, quantitative research can be useful. This is because it allows you to collect numerical data from a representative sample of the population and use statistical analysis to make inferences about the population as a whole.
• To measure relationships between variables: If you want to measure the relationship between two or more variables, such as the relationship between age and income, or between education level and job satisfaction, quantitative research can be useful. It allows you to collect numerical data on both variables and use statistical analysis to determine the strength and direction of the relationship.
• To identify patterns or trends: Quantitative research can be useful for identifying patterns or trends in data. For example, you can use quantitative research to identify trends in consumer behavior or to identify patterns in stock market data.
• To quantify attitudes or opinions : If you want to measure attitudes or opinions on a particular topic, quantitative research can be useful. It allows you to collect numerical data using surveys or questionnaires and analyze the data using statistical methods to determine the prevalence of certain attitudes or opinions.

Purpose of Quantitative Research

The purpose of quantitative research is to systematically investigate and measure the relationships between variables or phenomena using numerical data and statistical analysis. The main objectives of quantitative research include:

• Description : To provide a detailed and accurate description of a particular phenomenon or population.
• Explanation : To explain the reasons for the occurrence of a particular phenomenon, such as identifying the factors that influence a behavior or attitude.
• Prediction : To predict future trends or behaviors based on past patterns and relationships between variables.
• Control : To identify the best strategies for controlling or influencing a particular outcome or behavior.

Quantitative research is used in many different fields, including social sciences, business, engineering, and health sciences. It can be used to investigate a wide range of phenomena, from human behavior and attitudes to physical and biological processes. The purpose of quantitative research is to provide reliable and valid data that can be used to inform decision-making and improve understanding of the world around us.

Advantages of Quantitative Research

There are several advantages of quantitative research, including:

• Objectivity : Quantitative research is based on objective data and statistical analysis, which reduces the potential for bias or subjectivity in the research process.
• Reproducibility : Because quantitative research involves standardized methods and measurements, it is more likely to be reproducible and reliable.
• Generalizability : Quantitative research allows for generalizations to be made about a population based on a representative sample, which can inform decision-making and policy development.
• Precision : Quantitative research allows for precise measurement and analysis of data, which can provide a more accurate understanding of phenomena and relationships between variables.
• Efficiency : Quantitative research can be conducted relatively quickly and efficiently, especially when compared to qualitative research, which may involve lengthy data collection and analysis.
• Large sample sizes : Quantitative research can accommodate large sample sizes, which can increase the representativeness and generalizability of the results.

Limitations of Quantitative Research

There are several limitations of quantitative research, including:

• Limited understanding of context: Quantitative research typically focuses on numerical data and statistical analysis, which may not provide a comprehensive understanding of the context or underlying factors that influence a phenomenon.
• Simplification of complex phenomena: Quantitative research often involves simplifying complex phenomena into measurable variables, which may not capture the full complexity of the phenomenon being studied.
• Potential for researcher bias: Although quantitative research aims to be objective, there is still the potential for researcher bias in areas such as sampling, data collection, and data analysis.
• Limited ability to explore new ideas: Quantitative research is often based on pre-determined research questions and hypotheses, which may limit the ability to explore new ideas or unexpected findings.
• Limited ability to capture subjective experiences : Quantitative research is typically focused on objective data and may not capture the subjective experiences of individuals or groups being studied.
• Ethical concerns : Quantitative research may raise ethical concerns, such as invasion of privacy or the potential for harm to participants.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Cave Ecology pp 309–328 Cite as

Food Webs in Caves

• Michael P. Venarsky 12 , 13 &
• Brock M. Huntsman 14  
• First Online: 05 January 2019

1365 Accesses

8 Citations

Part of the book series: Ecological Studies ((ECOLSTUD,volume 235))

Energy (carbon) availability is considered the primary mechanism influencing both evolutionary and ecological processes in cave ecosystems, and both experimental and observational studies broadly support this hypothesis. However, we suggest that this conceptual model overlooks several factors that also influence cave community dynamics. In this chapter we explore these additional factors in two types of cave food webs, those supported by energy from detritus (dead animal or plant matter) and chemolithoautotrophic bacteria. We begin by examining the origin of each energy source and then explore what factors influence the input and/or productivity rates of each energy source, including the strength of surface connectivity, the productivity of surface habitats, and the compounds available for oxidation. We then explore how several factors are influencing cave community dynamics, including resource quantity and quality, size of resource surpluses, spatial distribution of resources, consumer-resource stoichiometry, top-down forces, and the relative harshness of certain cave environments. We hope this discussion both provides a broad overview of how food web dynamics influence cave community structure and highlights areas of future research.

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Venarsky, M.P., Huntsman, B.M. (2018). Food Webs in Caves. In: Moldovan, O., Kováč, Ľ., Halse, S. (eds) Cave Ecology. Ecological Studies, vol 235. Springer, Cham. https://doi.org/10.1007/978-3-319-98852-8_14

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Quantitative Data Analysis 101

The lingo, methods and techniques, explained simply.

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Quantitative data analysis is one of those things that often strikes fear in students. It’s totally understandable – quantitative analysis is a complex topic, full of daunting lingo , like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a little more attention in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t that hard , even for those of us who avoid numbers and math . In this post, we’ll break quantitative analysis down into simple , bite-sized chunks so you can approach your research with confidence.

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Don’t be a sucker – give your descriptive statistics the love and attention they deserve!

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the composition of your sample is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post .

What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are just a handful of inferential techniques – there are many, many more. Importantly, each statistical method has its own assumptions and limitations.

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why descriptive statistics are so important – they’re the first step to knowing which inferential techniques you can and can’t use.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Why does this matter?

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why descriptive statistics are so important – they tell you all about the shape of your data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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74 Comments

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