Statistical Physics of Invasion in Microbial Ecosystems

Ecological communities are complex interacting systems whose collective behaviour emerges from many heterogeneous components. A suitable model system, because of experimental accessibility and relevance to problems in public health, are microbial ecosystems. In this context, a central problem is understanding when a new species can successfully invade an established community. Recent experiments on the human gut microbiome have shown that the ability of a community to resist invasion from a pathogen species depends strongly on its ecological structure, with higher diversity associated with increased resistance (Foster et al., Science, 2023). In this thesis, the invasion problem will be studied within the framework of consumer-resource dynamics using methods from dynamical systems and statistical physics. Combining analytical approaches and numerical simulations, the goal is to relate the invasibility of a community to statistical properties of the interaction matrix between different species, offering a solid theoretical interpretation of the experimental results.