Stability criteria for complex ecosystems
Abstract
Forty years ago, May proved that sufficiently large or complex ecological networks have a probability of persisting that is close to zero, contrary to previous expectations. May analysed large networks in which species interact at random. However, in natural systems pairs of species have welldefined interactions (for example predatorprey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predatorprey interactions, which are stabilizing, and mutualistic and competitive interactions, which are destabilizing. We provide analytic stability criteria for all cases. We use the criteria to prove that, counterintuitively, the probability of stability for predatorprey networks decreases when a realistic food web structure is imposed or if there is a large preponderance of weak interactions. Similarly, stability is negatively affected by nestedness in bipartite mutualistic networks. These results are found by separating the contribution of network structure and interaction strengths to stability. Stable predatorprey networks can be arbitrarily large and complex, provided that predatorprey pairs are tightly coupled. The stability criteria are widely applicable, because they hold for any system of differential equations.
 Publication:

Nature
 Pub Date:
 March 2012
 DOI:
 10.1038/nature10832
 arXiv:
 arXiv:1105.2071
 Bibcode:
 2012Natur.483..205A
 Keywords:

 Quantitative Biology  Populations and Evolution
 EPrint:
 12 pages 7 figures 1 table