Microbial communities harbor hundreds or thousands of species, whose ecological dynamics are classically modeled by generalized Lotka-Volterra equations.

First, I will consider regimes where interactions are chosen randomly, according to a distribution of set the mean and variance, and are strong (they do not scale with the number of species). If complete competitive exclusion is prevented by a small amount of immigration, species largely coexist in out-of-equilibrium, chaotic oscillations. At any time, only a handful of species dominate the community and coexist with a majority of rare species, whose abundance decreases as a power law of exponent larger than 1 – as observed in plankton communities. Over time, such a low-dimensional dominant community is regularly superseded by a subset of rare species, in a continuous turnover akin to observed fluctuations of plankton strains. The deterministic behavior of every species in the community is well approximated by a single-species stochastic model that can be parametrized on the time series of one species. Beyond such ‘typical’ dynamics, species differences are reflected in the frequency of the booms and busts that bring every species to intermittently partake in the dominant community.

I will then briefly discuss the role of random interactions when they are superposed to community structure, given for instance by functional groups or shared resources. In this case, a mesoscopic description dictated by the structure allows us to generalize some results obtained for fully disordered communities, and to explore the role of unknown sources of interaction variation on the emergent regimes of community dynamics.