Disordered models in community ecology

Disordered models, high-dimensional systems with random parameters, are relevant to community ecology for two main reasons. First, they generate empirical predictions: if these match observations, it suggests that detailed properties are unnecessary to explain community patterns; conversely, discrepancies signal the presence of non-random features or the need for alternative modeling assumptions. Second, disordered systems function as null models upon which specific structure can be imposed and its effects quantified. Motivated by this relevance, in this thesis we review foundational disordered ecological models and extend them to study the impact of ecologically realistic features on community stability, structure, and dynamics. We demonstrate that time-varying interactions can stabilize complexity, promote coexistence, and give rise to abundance distributions that better match experimental data. We also establish that introducing a non-linear saturating response resolves non-physical unbounded population growth. Furthermore, we show that the interplay of memory effects and community heterogeneity can lead to both periodic and aperiodic persistent fluctuations in species abundances. Overall, this thesis adds instruments to the theoretician's toolkit potentially useful for understanding the functioning of ecological communities and complex systems in general.