Trophic coherence determines food-web stability

The fact that large, complex ecosystems are particularly robust is mysterious in the light of mathematical arguments that suggest they should be unstable; i.e., susceptible to runaway fluctuations in species' abundances. 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. We find that this property makes networks far more linearly stable than if the links (predator-prey interactions) were placed randomly between species, or according to existing structural models. 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.