Unveiling complexity: Statistical physics approaches to ecological communities

Species-rich ecosystems, notably microbial communities, display regular patterns in diversity, abundance distribution, and function, independently of their specific composition. The effort to understand how such regularities are achieved and maintained has driven the development of theoretical approaches inspired by complex systems and statistical physics. We introduce three classical frameworks for modelling biological communities —neutral models, the Generalized Lotka-Volterra equations, and a Consumer-Resource model— and discuss their hypotheses and empirical support. We further discuss a few theoretical challenges for future research, emphasizing the pivotal role of interfacing theory with ecological data.