Coexistence in large ecosystems: from structure to function

Biological systems are composed of many interacting components - in ecological communities, populations of different species. Though the first models for interacting populations date to almost a century ago, the role of species interactions in regulating the response to perturbations, and in shaping community composition, is yet not well understood. Models for ecological communities have so far concentrated on small systems. Here I show that, on the other hand, large ecological communities display simple and consistent patterns that can be understood as the result of elementary stochastic processes. Using random matrix techniques, I study how the properties of the interaction networks influence the stability of ecological communities and the persistence of the populations. I conclude with a list of challenges that need to be overcome to have a more complete understanding of statical and dynamical properties of large ecosystems.