"Patterns and coexistence in large ecosystems driven by non-Gaussian interactions"Azaele, SandroIn the exploration of theoretical ecology, the Generalized Lotka-Volterra (GLV) equations stand as a pivotal model, traditionally characterized by static and diverse species interactions. Current approaches postulate that for large, disordered GLV systems, stability and species abundance are dictated by the mean and variance of interaction distributions. Yet, this assumption does not hold up against the backdrop of empirical ecological communities, where deviations from such universality are observed. We will introduce a generalized dynamical mean field theory tailored for non-Gaussian interactions, with applicability extending well beyond the GLV model. We find that the solutions to the new equations are influenced by the full spectrum of cumulants in the interaction distribution, signaling a departure from the expected universality. We will delve into the implications of this significant shift, demonstrating how this enables us to deduce the statistical properties of microscopic interactions from the observable macroscopic distribution of species densities. Our findings are also able to elucidate the effects of sparse interactions, where our analytical tools reveal a straightforward connection between the interaction distribution and species population densities in several regions of the parameter space. Our results not only resonate with empirical data, but also pave the way for a deeper understanding of the complex dynamics governing ecological systems. |
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