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Short communication

Identifying important species: Linking structure andfunction in ecological networks

Ferenc Jordana,b,∗, Thomas A. Okeyc,d, Barbara Bauere, Simone Libralato f

a Collegium Budapest, Institute for Advanced Study, Szentharomsag u. 2., H-1014, Hungaryb Animal Ecology Research Group of HAS, Hungarian Natural History Museum, Ludovika ter 2., H-1083, Budapest, Hungaryc Bamfield Marine Sciences Centre, Bamfield, BC, V0R 1B0, Canadad University of Victoria, School of Environmental Studies, Victoria, BC V8W 2Y2, Canadae Szent Istvan University, Institute of Biology, Budapest, Hungaryf Department Oceanography, Italian National Institute of Oceanography and Experimental Geophysics, OGS,Sgonico-Zgonik (Trieste), Italy

a r t i c l e i n f o

Article history:

Received 17 December 2007

Received in revised form

2 April 2008

Accepted 11 April 2008

Published on line 2 June 2008

Keywords:

Food web

Community importance

Keystone species

Indirect effects

Ecopath with Ecosim

Prince William Sound

Functional indices

Structural indices

Network analysis

a b s t r a c t

At least two different approaches have been used to quantitatively assess the importance of

species in communities. One approach is to derive relatively simple, structural importance

indices from network analysis. This assumes that well-connected species are more impor-

tant. Another approach is to derive functional importance indices using dynamical simula-

tions. We performed both kinds of analysis, and we ranked the species of the Prince William

Sound food web based on 13 structural and 5 functional importance indices. We then com-

pared the rank correlation between structural and functional indices. Our results show that

different approaches to quantifying importance give different results; unweighted structural

indices never correlate significantly with functional ones, but certain weighted structural

indices correlate reasonably well with simulated function. This line of research could help in

improving our understanding of the usefulness of structural approaches in quantifying the

importance of species and understanding biological communities in general. The results

strongly indicate the fundamental importance of indirect effects in governing ecosystem

dynamics and the need to account for them in structural approaches. Conversely, it generally

verifies the usefulness of functional approaches to the investigation of biological communi-

ties that account for indirect effects, whether they are modelling or direct empirical studies.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

There is an increasing need for quantitatively evaluating theimportance of species and predicting the most important tar-

∗ Corresponding author at: Animal Ecology Research Group of HAS, Hungarian Natural History Museum, Ludovika ter 2., H-1083, Budapest,Hungary. Tel.: +36 1 22 48 300; fax: +36 1 22 48 310.

E-mail addresses: jordan.ferenc@gmail.com (F. Jordan), tokey@bms.bc.ca (T.A. Okey), b baver@yahoo.de (B. Bauer),slibralato@ogs.trieste.it (S. Libralato).

gets for conservation practice (e.g. keystone species, Paine,1966; Power et al., 1996). Since species are involved in com-plex interaction networks in natural communities, one majoraspect of importance is how the effects starting from a focal

0304-3800/$ – see front matter © 2008 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2008.04.009

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76 e c o l o g i c a l m o d e l l i n g 2 1 6 ( 2 0 0 8 ) 75–80

species reach the others, both directly and indirectly (Menge,1995). Technically this means that functionally importantspecies could be the ones in central positions in the interactionnetwork. We might expect more central species to play rela-tively more important roles in the community either throughmany direct links or indirectly—mediated by only a few neigh-bours (Allesina and Bodini, 2004). There are several networkindices for quantifying centrality and they estimate quite var-ied importance ranks for different species (Jordan et al., 2007).It is difficult to test the predictions of these network ana-lytical techniques because experiments, time series analysesand microcosm studies are all problematic. Simulations usingwhole food web trophodynamic models might represent auseful basis for evaluating these network structural indices.These models include quantitative estimates of biomasses,flows, trophic and non-trophic mediation and functionaldynamic relationships in addition to structural informationabout networks of interactions, and they are among the mostuseful and frequently applied models of ecosystems ecology(Christensen, 1998; Christensen and Walters, 2004). Moreover,indices for ranking relative functional importance based onthese mass-balance modelling simulations are also emerging(Mills et al., 1993; Okey, 2004; Libralato et al., 2006). Despite thedifferent meaning carried by each functional importance mea-sure, their comparison with structural indices may providefruitful insights. Until now, the comparison of structural andfunctional indices mainly regarded “ecosystem level” indica-tors (Finn, 1976; Christensen, 1995). Findings showed highereffects of food web representation (trophic aggregation) onstructural indices than on functional ones (see for exam-ple, the comparison between the Connectance Index and theSystem Omnivory Index; Libralato, 2008). In this paper we cal-culate 13 structural and 5 functional importance indices forthe trophic components of an ecosystem model and exam-ine their relationships. If statistically significant correlations

emerge, we may be able to find the most efficient approachesfor ranking the relative importance of species or functionalgroups in a system, or at least gain insight into the specificusefulness of each index.

2. Materials and methods

2.1. Data

We further analyse a previously well studied ecosystem modelof Prince William Sound, Alaska (Okey and Pauly, 1999; Okey,2004; Okey and Wright, 2004). The trophic network contains51 components, including 3 nonliving groups (Appendix A).Trophic links are weighted: flows are in tonnes wet weightkm−2 year−1 (Figure 1 and Appendix B).

2.2. Quantifying importance

Mass-balance trophic models (Ecopath with Ecosim,Christensen and Walters, 2004) have been used to esti-mate functional importance either by simulating the removalof components from the interaction web (Okey, 2004; Okeyet al., 2004; Libralato et al., 2006) or by examining networkattributes such as mixed trophic impact matrices (Hannon,1973; Ulanowicz and Puccia, 1990; Libralato et al., 2006).

We calculated five functional importance indices (Table 1):community importance (CI – Mills et al., 1993; Okey, 2004),community longevity support (CLS), interaction strengthindex (ISI), and keystoneness index (KI) (Okey, 2004) andanother keystoneness index (KS), derived from the biomass-scaled measure of overall effect (Libralato et al., 2006). All ofthese indices quantify the importance of species in commu-nities. Still, there are important differences between them:besides the original index of CI (community impact related

Table 1 – The functional and structural indices of community importance that are evaluated here

Index Code Citation

FunctionalCommunity importance CI Mills et al., 1993; Okey, 2004Interaction strength index (trophic) ISI Okey, 2004Keystoneness index (dynamic) KICommunity longevity support CLSKeystoneness index (network) KS Libralato et al., 2006

StructuralDegree (undirected, unweighted) D Wassermann and Faust, 1994Weighted degree (undirected) wDBetweenness centrality (directed, unweighted) BCUndirected betweenness centrality (unweighted) uBCCloseness centrality (undirected, unweighted) CCTopological importance, max step number = 1 TI Jordan et al., 2003Topological importance, max step number = 2 T2Topological importance, max step number = 3 T3Topological importance, max step number = 8 T8Weighted topological importance, max step number = 1 W1Weighted topological importance, max step number = 2 W2Weighted topological importance, max step number = 3 W3Weighted topological importance, max step number = 8 W8Trophic level (fractional) TL Odum and Heald, 1975

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Table 2 – Spearman rank correlation coefficients between 13 structural and 5 functional importance indices

D BC wD uBC CC TI1 WI1 TI2 WI2 TI3 WI3 TI8 WI8 Mean

CI 0.17 0.16 0.28 0.22 0.17 0.24 0.28 0.21 0.29 0.21 0.30 0.18 0.30 0.23CLS 0.02 −0.01 0.16 0.06 0.06 0.04 0.20 0.05 0.20 0.06 0.19 0.06 0.18 0.10ISI 0.00 −0.08 0.44 0.08 0.01 0.07 0.55 0.04 0.54 0.03 0.53 0.00 0.49 0.22KI −0.11 −0.18 −0.75 −0.09 −0.06 −0.15 −0.54 −0.13 −0.63 −0.12 −0.66 −0.09 −0.71 0.32KS 0.08 0.05 0.21 0.21 0.08 0.16 0.52 0.13 0.49 0.12 0.47 0.10 0.42 0.23Mean 0.08 0.09 0.37 0.13 0.08 0.13 0.42 0.11 0.43 0.11 0.43 0.09 0.42

Bold is significant (>0.29 and <−0.29). “Mean” is average of absolute values.

to biomass), CLS is the only one considering productivity, ISIdoes not depend on the biomass of the focal species, KI isa biomass-related form of ISI, and KS is the biomass-basedscaling of overall effects of species.

We also calculated a range of 13 structural importanceindices in order to represent unweighted vs weighted, undi-rected vs directed and local vs mesoscale indices (Table 1).These include degree (D), weighted degree (wD), between-ness centrality (BC), undirected betweenness centrality (uBC),closeness centrality (CC) (Wassermann and Faust, 1994), aswell as the measure of topological importance (TIn), andweighted importance (WIn), based on indirect effects up to nsteps (n = 1,2,3,8, Jordan et al., 2003). We also present the frac-tional trophic level (TL) for each species—a standard networkparameter (Odum and Heald, 1975, Table 1).

The relationships between structural and functionalindices were evaluated using Spearman rank correlation. Therelationships among structural indices have been studiedelsewhere (Jordan et al., 2007). We ranked only the livingcomponents of the network (though the three nonlivingcomponents were included in simulations and calculations).Structural and functional indices were evaluated individuallyby calculating their overall score (mean of absolute values ofcorrelation coefficients).

3. Results

Different importance indices, whether structural or func-tional, give different ranks of importance for the species ofthe same food web (Fig. 1). Note, for example, that the impor-tance rank of Porpoises (#7) ranges from 37 (BC) to 24 (CLS) to 3(D and KI). Beyond following the ranks of a particular species,we were interested in the relationships between the studiedstructural and functional indices (Table 2). The overall scoreof each structural index (bottom row in Table 2) is the averageof the absolute value of the Spearman correlation coefficientsbetween the importance ranks of the given structural indexand each of the functional ones. Conversely, the overall scoreof each functional index (right column in Table 2) is the averageof the absolute value of the Spearman correlation coefficientsbetween the importance ranks of the given functional indexand each of the structural ones. By calculating the average val-ues of the correlation coefficients, we have considered all theindices of the opposite type as equally important in each case.

Table 2 shows that no significant correlation was revealedbetween binary network indices (D, BC, uBC, CC, TIn) andany of the functional indices. Direction of links is even less

important; our directed index (BC) correlates with none ofthe functional indices. The direct index (D) is also a veryweak predictor of species importance if our functional mea-sures are realistic, indicating that consideration of indirecteffects is essential. Indeed, indirect indices correlated withfunctional indices best out of all the structural indices; shortindirect effects (TI1) are the best correlates in the unweightedcase, while interaction chain length matters little in theweighted case (WIn). Weighted structural indices were mostcorrelated with the functional attributes. KI was the best cor-relating functional index in terms of significant correlationswith structural attributes; its correlations were significant(−0.75, −0.54) with weighted direct and short indirect mea-sures of structure, but also particularly with weighted longindirect measures (−0.63, −0.66, −0.71). KS correlated sig-nificantly with indirect weighted structural measures (0.52,0.49, 0.47, 0.42). CI correlated significantly with the longer,weighted structural indices (WIn>1). ISI was significantly cor-related with all the weighted direct and indirect structuralmeasures, though it was most closely correlated with theindirect measures. Significant correlations were not detectedbetween CLS and any of the structural indices. According toTable 2, the best correlating functional and structural indicesare KI and WIn (0.32, 0.42), respectively. If we consider onlyunweighted indices of community structure, overall corre-lation for uBC and TI1 (0.13 for both) are the highest. Thestrongest correlation is between KI and wD (−0.75). Table 3shows that the structural indices used show significant (andalways negative) rank correlation with fractional trophic levelif and only if they are weighted (wD, WIn). Functional indicesmay show positive (KI), negative (CLS) or no significant (CI, ISI,KS) correlation.

4. Discussion

The initial motivation of this exercise was to evaluate howstructural indices might correlate with the importance rankof species estimated using some functional indices of speciesimportance. Structural features of a system influence itsdynamical behaviour, so the correlation of structure and func-tion is not surprising: the real question was exactly whichstructural properties of a given network node make it func-tionally important in the system. The converse question alsoemerged during this exercise; which of the functional indiceswere most useful indicators of structural properties. Our pri-mary finding is that unweighted indices of the interaction webstructure of a community show no correlation with any of the

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Fig. 1 – The Prince William Sound food web of 48 living components (#1–#48) and 3 nonliving components (#49–#51). Namesof components are given in Appendix A. Link width is proportional to interaction strength. Radius of nodes is proportionalto particular importance indices (larger nodes represent more important species): (a) degree (D); (b) weighted topologicalimportance index for two steps (WI2); (c) community longevity support (CLS); (d) keystone index (KI). In (e) radius isproportional to trophic level (TL): smallest nodes are producers, largest nodes are top predators. Drawn using UCINET(Borgatti et al., 2002).

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Table 3 – Spearman rank correlation coefficientsbetween 18 importance indices (topological andfunctional) and trophic level (trophic height)

D 0.21BC 0.16wD −0.85uBC 0.15CC 0.21TI1 0.12WI1 −0.41TI2 0.15WI2 −0.52TI3 0.16WI3 −0.56TI8 0.20WI8 −0.63CI −0.26CLS −0.32ISI −0.15KI 0.66KS 0.09

Bold is significant.

functional indices. This is especially true of degree (D), whichis the most local (i.e. direct) unweighted index. This is animportant message for network analysts focusing on degreein searching for key nodes in many kinds of networks (Albertet al., 2000), and is especially important for ecologists whowould otherwise underestimate the importance of weightinglinks in food webs. As for the weighted structural indices,we found that indices that include indirect interactions cor-relate better with functional indices than those that includeonly direct ones. Empirical tests (Wootton, 1994; Menge, 1995)and theoretical studies (Higashi and Patten, 1989; Fath andPatten, 1999; Schramski et al., 2007) already highlighted theimportance of indirect effects in communities, and our con-tribution agrees with their findings. This result is valuablefor field and theoretical researchers, but also for resourcemanagers and conservation professionals involved in debatesabout the role of indirect effects of human activities andmanagement actions. No correlation was revealed betweenD and ISI (but see Bascompte et al., 2006). The negative cor-relation between KI and the weighted structural indices maybe related to top-down effects emphasised by Ecosim mod-els (Watters et al., 2003; Maury and Lehodey, 2005): speciesof high WI-values are more frequent at lower trophic levelsand expected to have mostly bottom-up effects. The rela-tively strong positive correlation between KI and TL supportsthe traditional notion that keystone species tend to be hightrophic level species. This manifests because the KI reflectsthat keystone species, by definition (sensu Power et al., 1996),have low biomasses (or abundances) and because speciesat the top of food webs usually have low biomasses (dueto constraints of trophic transfer efficiencies, see Lindeman,1942).

Community longevity support is more of a measure of thecontribution of a species or functional group toward the sup-port of community stability or resilience, directly or indirectly,rather than a measure of interaction strength or keystone-ness. It is therefore not surprising that significant correlations

were not detected between the CLS and any of the structuralindices.

The present contribution highlights the role of networkanalysis in understanding how to link species to communi-ties and how to quantify their relative importance. Structuraland functional indices are more understandable and appli-cable if we can clarify their relationships and assess theirstrengths and weaknesses. This line of research is use-ful to better understand large networks where the use ofdynamical analyses is sometimes limited. From a struc-tural point of view, results of structural network analysisare useful only if they can be tested and verified as reli-able in the context of functional approaches. Perhaps thecombination of the two approaches reveals the most impor-tant mechanisms driving dynamics. Indirect effects, forexample, play a large role in governing ecosystem dynam-ics. Observing only structure without taking into accountthe magnitude of flows was less informative. The presentexercise provides a simple framework for evaluating theseindices.

Acknowledgements

Construction of the Prince William Sound model was sup-ported by the Exxon Valdez Oil Spill Trustee CouncilRestoration Program (Project 99330), a broad collaboration ofexperts on Prince William Sound, and D. Pauly. TAO’s currentcontributions are supported in part by a Pew Marine Conserva-tion Fellowship through the Pew Institute for Ocean Science.FJ is grateful to Vera Vasas and Marco Scotti for technical helpand Society in Science: The Branco Weiss Fellowship, ETHZurich for total support.

Appendix A. Supplementary data

Supplementary data associated with this article can be found,in the online version, at doi:10.1016/j.ecolmodel.2008.04.009.

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