Coexistence and diversity in a consumer resource model with a serial dilution setting

The coexistence of species and maintenance of diversity is the most important question in Ecology. Consumer resources models are one of the most interesting settings to model microbial ecosystems. The great majority of theoretical studies have been framed in the chemostat setting, where resources are constantly flowing through the system. On the other hand, both experiments and natural communities, like the gut microbiome, are better described as serial dilution processes, where resources are periodically replenished and consumed. Surprisingly, in this case theoretical results are scarce. The main goal of this thesis is to fill this gap. We study a general multispecies consumer resource model in serial dilution using both numerical tools and analytical techniques borrowed from disordered statistical physics. We find that under general conditions the number of coexisting species is lower than the chemostat setting. Furthermore, both the timescales to reach a stationary state and the shape of the species abundances distribution appear to depend dramatically on the connectivity properties of the consumption matrix: while for a fully connected model the system shows enormous long transients, by introducing a small sparsity such timescales reduces abruptly. We developed a novel algorithm to face this problem of long time scales for the convergence of the process.