Eco-evolutionary feedback can stabilize diverse predator-prey communities

Ecological models with random interactions have provided insight into the problem of diversity, particularly showing that high variance in the distribution of interaction rates can lead to instability, chaos and extinction. However, these models have traditionally neglected evolution, which is central to the generation of biological variation and can act on timescales comparable to ecological change. We demonstrate that when a stochastic predator-prey system is coupled to high-dimensional evolutionary dynamics, high variance interactions counter-intuitively stabilize the population, delaying extinction and increasing the total population size. Using both stochastic and deterministic simulations and theory based on the statistical physics of disordered systems, this stabilizing effect is shown to be driven by an eco-evolutionary feedback loop which causes the population size to grow as a power law of the variance of the interactions. We show that the stable regime corresponds with the clonal interference regime of population genetics. We conjecture that qualitative aspects of our results generalize to other evolving complex systems.