Do ecosystems prefer equilibria with more biomass?

When the species composition in a given environment is strongly perturbed by extinctions and invasions, the system may have multiple possible equilibria with different persistent sets of species. This talk presents recent research with James O'Dwyer, Akshit Goyal and Nitesh Patro that explores the probability of reaching different stable states in such ecological systems. For a variety of simple competitive Lotka-Volterra models, we demonstrate that equilibria with greater biomass generally have larger basins of attraction. For simple competitive discrete niche models of S species, we find exponentially many equilibria, with a range of niche separations that provide new perspective on the idea of limiting similarity. In an idealized large S limit, we prove that basin size grows exponentially with biomass. For random matrix interactions, qualitative results are similar. These results may have implications for understanding the fate of ecosystems perturbed by human activity, as well as for ecological restoration.