Dynamical persistence in high-diversity resource-consumer communities

We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. These fluctuations appear, robustly and predictably, in certain regimes of parameter space. Their origin is closely tied to the ratio of realized species diversity to the number of resources. This ratio is set by competition, through the balance between species being pushed out and invading. When this ratio is smaller than one, dynamics will reach stable equilibria. When this ratio is larger than one, the competitive exclusion principle dictates that fixed-points are either unstable or marginally stable. If they are unstable, the system is repelled from fixed points, and abundances forever fluctuate. While marginally-stable fixed points are in principle allowed and predicted by some models, they become structurally unstable at high diversity. This means that even small changes to the model, such as non-linearities in how resources combine to generate species’ growth, will result in persistent abundance fluctuations.Author summary: Competition over resources is one of the main mechanisms by which species interact. In recent years, considerable interest has been directed towards species-rich communities that compete over resources. An important and basic question concerns the dynamics of such communities: do abundances reach stable equilibria, or continue to fluctuate even without environmental fluctuations? Much of the work on high-diversity resource-competition models starts from the highly-influential MacArthur model or similar models, known to always relax to equilibria at long times, seemingly precluding any long-time non-equilibrium phenomena. And so while long-lived chaos has been demonstrated in few-species models, the question of persistent dynamics at high-diversity remains open. We show that high-diversity resource-competition models generically have a regime of parameters in which abundances do not reach equilibria. The MacArthur model and related models, which always relax to equilibrium, are in fact structurally unstable in that regime: when small changes are made to the model, non-equilibrium dynamics appear. We present a theoretical framework: we identify the relevant model parameters, and explain when long-time abundance fluctuations appear in a predictable and reproducible way. We show that diversity may significantly exceed the bound set by competitive exclusion.