Skip to main content
SpringerLink
Log in

Network structure, predator–prey modules, and stability in large food webs

  • Original paper
  • Published:
Theoretical Ecology Aims and scope Submit manuscript

Abstract

Large, complex networks of ecological interactions with random structure tend invariably to instability. This mathematical relationship between complexity and local stability ignited a debate that has populated ecological literature for more than three decades. Here we show that, when species interact as predators and prey, systems as complex as the ones observed in nature can still be stable. Moreover, stability is highly robust to perturbations of interaction strength, and is largely a property of structure driven by predator–prey loops with the stability of these small modules cascading into that of the whole network. These results apply to empirical food webs and models that mimic the structure of natural systems as well. These findings are also robust to the inclusion of other types of ecological links, such as mutualism and interference competition, as long as consumer–resource interactions predominate. These considerations underscore the influence of food web structure on ecological dynamics and challenge the current view of interaction strength and long cycles as main drivers of stability in natural communities.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Arim M, Marquet PA (2004) Intraguild predation: a widespread interaction related to species biology. Ecol Lett 7:557–564

    Article  Google Scholar 

  • Bascompte J, Melian CJ (2005) Simple trophic modules for complex food webs. Ecology 86:2868–2873

    Article  Google Scholar 

  • Bascompte J, Melian CJ, Sala E (2005) Interaction strength combinations and the overfishing of a marine food web. Proc Natl Acad Sci USA 102(15):5443–5447

    Article  PubMed  CAS  Google Scholar 

  • Berlow EL, Neutel AM, Cohen JE, de Ruiter PC, Ebenman B, Emmerson M, Fox JW, Jansen VAA, Jones JI, Kokkoris GD, Logofet DO, McKane AJ, Montoya JM, Petchey O (2004) Interaction strengths in food webs: issues and opportunities. J Anim Ecol 73(3):585–598

    Article  Google Scholar 

  • Bodini A (2000) Reconstructing trophic interactions as a tool for understanding and managing ecosystems: application to a shallow eutrophic lake. Can J Fish Aquat Sci 57:1999–2009

    Article  Google Scholar 

  • Brose U, Williams R, Martinez N (2006) Allometric scaling enhances stability in complex food webs. Ecol Lett 9: 1228–1236

    Article  PubMed  Google Scholar 

  • Cohen J, Briand F, Newman C (1990) Community food webs: data and theory. Springer, Berlin, Germany

    Google Scholar 

  • Dambacher JM, Li HW, Rossignol PA (2002) Relevance of community structure in assessing indeterminacy of ecological predictions. Ecology 83(5):1372–1385

    Article  Google Scholar 

  • Dambacher JM, Luh HK, Li HW, Rossignol PA (2003) Qualitative stability and ambiguity in model ecosystems. Am Nat 161(6):876–888

    Article  PubMed  Google Scholar 

  • Daniels J, MacKay AL (1974) Stability of connected linear-systems. Nature 251(5470):49–50

    Article  Google Scholar 

  • Deangelis DL (1975) Stability and connectance in food web models. Ecology 56(1):238–243

    Article  Google Scholar 

  • Dunne J (2006) Ecological networks: linking structure to dynamics in food webs. Oxford Univ. Press, Chap The network structure of food webs, pp 27–86

  • Emmerson M, Raffaelli D (2004) Predator prey body size, interaction strength and the stability of a real food web. J Anim Ecol 73:399–409

    Article  Google Scholar 

  • Fussmann G, Heber G (2002) Food web complexity and chaotic population dynamics. Ecol Lett 5:394–401

    Article  Google Scholar 

  • Haydon D (1994) Pivotal assumptions determining the relationship between stability and complexity: an analytical synthesis of the stability-complexity debate. Am Nat 144(1):14–29

    Article  Google Scholar 

  • Hutchinson GE (1959) Homage to Santa Rosalia or why are there so many kinds of animals. Am Nat 93:145–159

    Article  Google Scholar 

  • Ives A (1995) Measuring resilience in stochastic systems. Ecol Monogr 65:217–233

    Article  Google Scholar 

  • Jansen VAA, Kokkoris GD (2003) Complexity and stability revisited. Ecol Lett 6(6):498–502

    Article  Google Scholar 

  • Jeffries C (1974) Qualitative stability and digraphs in model ecosystems. Ecology 55(6):1415–1419

    Article  Google Scholar 

  • Lafferty K, Dobson A, Kuris A (2006) Parasite dominates food web links. Proc Natl Acad Sci U S A 103:11, 211–11, 216

    Article  CAS  Google Scholar 

  • Lawlor LR (1978) Comment on randomly constructed model ecosystems. Am Nat 112(984):445–447

    Article  Google Scholar 

  • Levins R (1975) Ecology and evolution of communities, Harvard Univ. Press, Cambridge, Chap Evolution in communities near equilibrium, pp 16–50

  • Logofet DO, Ulianov NB (1982) Sign stability in model-ecosystems – a complete class of sign-stable patterns. Ecol Model 16(2-4):173–189

    Article  Google Scholar 

  • Martinez N, Williams R, Dunne J (2006) Ecological networks. Linking structure to dynamics in food webs. Oxford Univ. Press, Chap Diversity, complexity, and persistence in large model ecosystems, pp 163–186

  • May RM (1972) Will a large complex system be stable? Nature 238(5364):413–414

    Article  PubMed  CAS  Google Scholar 

  • May RM (1973) Qualitative stability in model ecosystems. Ecology 54(3):638–641

    Article  Google Scholar 

  • May R (1974) Stability and complexity in model ecosystems. Princeton Univ. Press

  • May R (2006) Network structure and the biology of populations. Trends Ecol Evol 21:394–399

    Article  Google Scholar 

  • McCann K, Hastings A, Huxel GR (1998) Weak trophic interactions and the balance of nature. Nature 395(6704):794–798

    Article  CAS  Google Scholar 

  • McCann KS (2000) The diversity–stability debate. Nature 405(6783):228–233

    Article  PubMed  CAS  Google Scholar 

  • Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298(5594):824–827

    Article  PubMed  CAS  Google Scholar 

  • Montoya J, Pimm S, Sole R (2006) Ecological networks and their fragility. Nature 442(7100):259–264

    Article  PubMed  CAS  Google Scholar 

  • Neutel AM, Heesterbeek JAP, de Ruiter PC (2002) Stability in real food webs: weak links in long loops. Science 296(5570):1120–1123

    Article  PubMed  CAS  Google Scholar 

  • Pascual M, Dunne J (eds) (2006) Ecological networks. Linking structure to dynamics in food webs. Oxford Univ. Press

  • Pimm S (1982) Food webs. Chapman & Hall, New York

    Google Scholar 

  • Prill RJ, Iglesias PA, Levchenko A (2005) Dynamic properties of network motifs contribute to biological network organization. PLoS Biol 3(11):1881–1892

    Article  CAS  Google Scholar 

  • Puccia C, Levins R (1985) Qualitative modeling of complex systems: an introduction to loop analysis and time averaging. Harvard Univ. Press, Cambridge

    Google Scholar 

  • Rooney N, McCann K, Gellner G, Moore J (2006) Structural asymmetry and the stability of diverse food webs. Nature 442:265–269

    Article  PubMed  CAS  Google Scholar 

  • Sole R, Alonso D, McKane A (2002) Self-organized instability in complex ecosystems. Phil Trans Roy Soc Lond B 357: 667–681

    Article  Google Scholar 

  • Tilman D (1999) The ecological consequences of changes in biodiversity: a search for general principles. Ecology 80:231–251

    Google Scholar 

  • Williams RJ, Martinez ND (2000) Simple rules yield complex food webs. Nature 404:180–183

    Article  PubMed  CAS  Google Scholar 

  • Willmer C, Sinha S, Brede M (2002) Examining the effects of species richness on community stability: an assembly model approach. Oikos 99:363–367

    Article  Google Scholar 

  • Yodzis P (1981) The stability of real ecosystems. Nature 289(5799):674–676

    Article  Google Scholar 

Download references

Acknowledgements

We thank D. Alonso, A. Bodini, J.M. Dambacher and A. P. Dobson for stimulating discussions. This work was supported by a Centennial Fellowship by the J. S. McDonnell Foundation to M.P.

Author information

Authors and Affiliations

  1. Department of Ecology and Evolutionary Biology, University of Michigan, Natural Science Building, 830 North University, Ann Arbor, MI, 48109, USA

    Stefano Allesina & Mercedes Pascual

Authors
  1. Stefano Allesina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mercedes Pascual
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefano Allesina.

Electronic Supplementary Material

Below is the link to the electronic supplementary material

Supplementary Fig. 1

Number of right-signed terms in the characteristic polynomial of the system represented in Figure 3. (a) percentage of terms with the right sign for each coefficient of the characteristic polynomial. (b) Sign difference: number of terms with the right sign - number of terms with the wrong sign (EPS 5.85 kb)

Supplementary Fig. 2a

Percentage of food webs, built with the “cascade model” (left) and the “niche” model (right), that are stable given C and S (EPS 29.6 kb)

Supplementary Fig. 2b

(EPS 26.2 kb)

Supplementary Fig. 3

Comparison between random matrices (left) and random predator-prey matrices (right) when interaction strengths are drawn from a lognormal (μ = 0, σ = 1) distribution. (a-b) Percentage of stable systems for each pair (C, S). (c-d) Average percentage of eigenvalues with negative real part. (e-f) Percentage of stable matrices produced by randomizing 100 times the coefficients of each stable matrix in (a-b). The number of matrices concurring to form this average is not fixed, as in the previous graphs, depending on the number of stable matrices (a-b). The dots represent the values of 10 empirical food webs (EPS 111 kb)

Supplementary Fig. 4

Comparison between random matrices (left) and random predator-prey matrices (right) when interaction strengths are drawn from an uniform (U[0,1]) distribution. (a-b) Percentage of stable systems for each pair (C, S). (c-d) Average percentage of eigenvalues with negative real part. (e-f) Percentage of stable matrices produced by randomizing 100 times the coefficients of each stable matrix in (a-b). The number of matrices concurring to form this average is not fixed, as in the previous graphs, depending on the number of stable matrices (a-b). The dots represent the values of 10 empirical food webs (EPS 117 kb)

Supplementary Fig. 5

Percentage of stable systems when 10% of the connectance is represented by double (mutualism or interference) connections (top). In the bottom graph we see the effects on stability of increasing the percentage of double interactions. The solid line represents the effects on predator-prey systems and the dashed line the effects on random networks (EPS 38.4 kb)

Supplementary Fig. 6

Effects on stability of increasing the percentage of null (left) or positive (right) coefficients on the diagonal. The solid line represents the effects on predator-prey systems and the dashed line the effects on random networks. In the right part of the graph, red dashed and solid lines represent the fraction of systems with negative trace (EPS 6.76 kb)

Supplementary Fig. 7

Comparison between random matrices (left) and random predator-prey matrices (right) when diagonal elements are positive with 5% probability and null with 5% probability. The other diagonal coefficients are negative. (a-b) Percentage of stable systems for each pair (C, S). (c-d) Average percentage of eigenvalues with negative real part. (e-f) Percentage of stable matrices produced by randomizing 100 times the coefficients of each stable matrix in (a-b). The number of matrices concurring to form this average is not fixed, as in the previous graphs, depending on the number of stable matrices (a-b). The dots represent the values of 10 empirical food webs (EPS 110 kb)

Supplementary Fig. 8

Effects of the distribution range on the probability of stability illustrating that the fraction of weak interactions has no effect on the probability of stability. We built 500 networks of the random (red) and predator-prey (blue) type. Each network contains 25 species and has connectance 0.1. The coefficient strengths are taken from a χ 2 distribution with k degrees of freedom. The coefficient signs are chosen as in the main text. Changing the degree of freedom reduces the fraction of weak interactions and moves the mean of the distribution toward higher values (EPS 8.71 kb)

Supplementary Table 1

Transformation of food webs into community matrices (PDF 39.5 kb)

Supplementary Table 2

Numerical computation of the number of terms with the right sign in a predator-prey matrix that is completely connected (PDF 33.6 kb)

12080_2007_7_MOESM11_ESM.pdf

Network structure, predator-prey modules, and stability in large food webs: Electronic Supplementary Material (ESM) (PDF 116 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Allesina, S., Pascual, M. Network structure, predator–prey modules, and stability in large food webs. Theor Ecol 1, 55–64 (2008). https://doi.org/10.1007/s12080-007-0007-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12080-007-0007-8

Keywords

Search

Navigation