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Allometric degree distributions facilitate food-web stability


In natural ecosystems, species are linked by feeding interactions that determine energy fluxes and create complex food webs. The stability of these food webs1,2 enables many species to coexist and to form diverse ecosystems. Recent theory finds predator–prey body-mass ratios to be critically important for food-web stability3,4,5. However, the mechanisms responsible for this stability are unclear. Here we use a bioenergetic consumer–resource model6 to explore how and why only particular predator–prey body-mass ratios promote stability in tri-trophic (three-species) food chains. We find that this ‘persistence domain’ of ratios is constrained by bottom-up energy availability when predators are much smaller than their prey and by enrichment-driven dynamics when predators are much larger. We also find that 97% of the tri-trophic food chains across five natural food webs7 exhibit body-mass ratios within the predicted persistence domain. Further analyses of randomly rewired food webs show that body mass and allometric degree distributions in natural food webs mediate this consistency. The allometric degree distributions hold that the diversity of species’ predators and prey decreases and increases, respectively, with increasing species’ body masses. Our results demonstrate how simple relationships between species’ body masses and feeding interactions may promote the stability of complex food webs.

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Figure 1: Population dynamics in tri-trophic food chains.
Figure 2: Population persistence in tri-trophic food chains depending on Rti and Rib.


  1. De Ruiter, P. C., Wolters, V., Moore, J. C. & Winemiller, K. O. Food web ecology: Playing Jenga and beyond. Science 309, 68–70 (2005)

    Article  CAS  Google Scholar 

  2. Montoya, J. M., Pimm, S. L. & Solé, R. V. Ecological networks and their fragility. Nature 442, 259–264 (2006)

    Article  ADS  CAS  Google Scholar 

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

    Article  Google Scholar 

  4. Loeuille, N. & Loreau, M. Evolutionary emergence of size-structured food webs. Proc. Natl Acad. Sci. USA 102, 5761–5766 (2005)

    Article  ADS  CAS  Google Scholar 

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

    Article  Google Scholar 

  6. Yodzis, P. & Innes, S. Body size and consumer–resource dynamics. Am. Nat. 139, 1151–1175 (1992)

    Article  Google Scholar 

  7. Brose, U. et al. Body sizes of consumers and their resources. Ecology 86, 2545 (2005)

    Article  Google Scholar 

  8. Williams, R. J. & Martinez, N. D. Simple rules yield complex food webs. Nature 404, 180–183 (2000)

    Article  ADS  CAS  Google Scholar 

  9. Bascompte, J. & Melian, C. J. Simple trophic modules for complex food webs. Ecology 86, 2868–2873 (2005)

    Article  Google Scholar 

  10. Milo, R. et al. Network motifs: Simple building blocks of complex networks. Science 298, 824–827 (2002)

    Article  ADS  CAS  Google Scholar 

  11. Hastings, A. & Powell, T. Chaos in a three-species food chain. Ecology 72, 896–903 (1991)

    Article  Google Scholar 

  12. Jonsson, T. & Ebenman, B. Effects of predator–prey body size ratios on the stability of food chains. J. Theor. Biol. 193, 407–417 (1998)

    Article  CAS  Google Scholar 

  13. McCann, K., Hastings, A. & Huxel, G. R. Weak trophic interactions and the balance of nature. Nature 395, 794–798 (1998)

    Article  ADS  CAS  Google Scholar 

  14. Muratori, S. & Rinaldi, S. Low- and high frequency oscillations in three-dimensional food chain systems. SIAM J. Appl. Math. 52, 1688–1706 (1992)

    Article  MathSciNet  Google Scholar 

  15. Gard, T. C. Persistence in food webs: Holling type II food chains. Math. Biosci. 49, 61–67 (1980)

    Article  MathSciNet  Google Scholar 

  16. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. Toward a metabolic theory of ecology. Ecology 85, 1771–1789 (2004)

    Article  Google Scholar 

  17. Savage, V. M., Gillooly, J. F., Brown, J. H., West, G. B. & Charnov, E. L. Effects of body size and temperature on population growth. Am. Nat. 163, E429–E441 (2004)

    Article  Google Scholar 

  18. Rosenzweig, M. L. Paradox of enrichment: destabilization of exploitation of ecosystems in ecological time. Science 171, 385–387 (1971)

    Article  ADS  CAS  Google Scholar 

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

    Article  Google Scholar 

  20. Koelle, K. & Vandermeer, J. Dispersal-induced desynchronization: from metapopulations to metacommunities. Ecol. Lett. 8, 167–175 (2005)

    Article  Google Scholar 

  21. McCann, K. S., Rasmussen, J. B. & Umbanhowar, J. The dynamics of spatially coupled food webs. Ecol. Lett. 8, 513–523 (2005)

    Article  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  23. Woodward, G. et al. Body size in ecological networks. Trends Ecol. Evol. 20, 402–409 (2005)

    Article  Google Scholar 

  24. Brose, U. et al. Consumer–resource body-size relationships in natural food webs. Ecology 87, 2411–2417 (2006)

    Article  Google Scholar 

  25. Beckerman, A. P., Petchey, O. L. & Warren, P. H. Foraging biology predicts food web complexity. Proc. Natl Acad. Sci. USA 103, 13745–13749 (2006)

    Article  ADS  CAS  Google Scholar 

  26. Jonsson, T., Cohen, J. E. & Carpenter, S. R. Food webs, body size, and species abundance in ecological community description. Adv. Ecol. Res 36, 1–84 (2005)

    Article  Google Scholar 

  27. Montoya, J. M. & Solé, R. V. Topological properties of food webs: from real data to community assembly models. Oikos 102, 614–622 (2003)

    Article  Google Scholar 

  28. Stouffer, D. B., Camacho, J., Guimera, R., Ng, C. A. & Amaral, L. A. N. Quantitative patterns in the structure of model and empirical food webs. Ecology 86, 1301–1311 (2005)

    Article  Google Scholar 

  29. Cattin, M. F., Bersier, L. F., Banasek-Richter, C., Baltensperger, R. & Gabriel, J. P. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Jeschke, J. M., Kopp, M. & Tollrian, R. Predator functional responses: Discriminating between handling and digesting prey. Ecol. Monogr. 72, 95–112 (2002)

    Article  Google Scholar 

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We thank U. Jacob for providing the Weddell Sea data; A. de Roos, E. Berlow, S. Scheu and M. Visser for comments; R. Williams for simulation programs; and N. Martinez for editorial assistance. Financial support was provided by the German Research Foundation.

Author Contributions S.B.O., B.C.R. and U.B. contributed equally to this work. All authors discussed the results and commented on the manuscript.

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Correspondence to Sonja B. Otto.

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Supplementary Information

The file contains Supplementary Notes, Supplementary Methods, Supplementary Figures 1-3 with Legends and additional references. The SI (1) evaluates the sensitivity of our results to variation in two model parameters (carrying capacity, K and maximum consumption, y), and contains (2) methods and (3) analyses on complex food web stability. SI-Fig. 1 (eight panels) displays the size of the 'persistence domain' in dependence on K and y. SI-Fig. 2 displays the percentage of persistent food chains (empirical and re-wired) as functions of K and y. SI-Fig. 3 (two panels) displays the fraction and maximum trophic level of dynamically persistent populations in complex food webs. (PDF 229 kb)

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Otto, S., Rall, B. & Brose, U. Allometric degree distributions facilitate food-web stability. Nature 450, 1226–1229 (2007).

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