Stability Criteria for Complex Ecosystems

TL;DR

This paper extends May's stability analysis to real ecological interactions, revealing that predator-prey relationships tend to stabilize ecosystems, while mutualistic and competitive interactions often destabilize them, with implications for ecological network design.

Contribution

The study provides analytic stability criteria for ecological networks with realistic interactions, differentiating effects of predator-prey, mutualistic, and competitive relationships on stability.

Findings

Predator-prey interactions increase ecosystem stability.

Mutualistic and competitive interactions tend to destabilize ecosystems.

Realistic food web structures and weak interactions decrease stability.

Abstract

Forty years ago, Robert May questioned a central belief in ecology by proving that sufficiently large or complex ecological networks have probability of persisting close to zero. To prove this point, he analyzed large networks in which species interact at random. However, in natural systems pairs of species have well-defined interactions (e.g., predator-prey, mutualistic or competitive). Here we extend May's results to these relationships and find remarkable differences between predator-prey interactions, which increase stability, and mutualistic and competitive, which are destabilizing. We provide analytic stability criteria for all cases. These results have broad applicability in ecology. For example, we show that, surprisingly, the probability of stability for predator-prey networks is decreased when we impose realistic food web structure or we introduce a large preponderance of weak interactions. Similarly, stability is negatively impacted by nestedness in bipartite mutualistic networks.