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Allometric degree distributions facilitate food-web stability

Nature volume 450, pages 1226–1229 (2007)Cite this article

Abstract

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.

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Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Biology, Darmstadt University of Technology, Schnittspahnstrasse 10, 64287 Darmstadt, Germany,

    Sonja B. Otto, Björn C. Rall & Ulrich Brose

  2. Pacific Ecoinformatics and Computational Ecology Lab, Berkeley, California 94703, USA,

    Ulrich Brose

Authors
  1. Sonja B. Otto
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  2. Björn C. Rall
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  3. Ulrich Brose
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Corresponding author

Correspondence to Sonja B. Otto.

Supplementary information

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). https://doi.org/10.1038/nature06359

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