Furthermore, we prove that a maximally coherent network with constant interaction strengths will always be linearly stable. We also propose a simple model that, by correctly capturing the trophic coherence of food webs, accurately reproduces their stability and other basic structural features. Most remarkably, our model shows that stability can increase with size and complexity. This suggests a key to May’s paradox, and a range of opportunities and concerns for biodiversity conservation.

A simple model we propose to capture this feature shows that networks can, in fact, become more stable with size and complexity, suggesting a possible solution to the paradox.

Here we show that food webs (networks describing who eats whom in an ecosystem) exhibit a property we call trophic coherence, a measure of how neatly the species fall into distinct levels.