2023/06/23 by Sandro Azaele, Amos Maritan, Azaele, Sandro +1
Agricultural and Biological Sciences · Environmental Science · Social Sciences · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Ecosystem dynamics and resilience #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Physical sciences #Plant and animal studies #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2306.13449
openalex publication_date 2023/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the Generalized Lotka-Volterra (GLV) equations, a central model in theoretical ecology, where species interactions are assumed to be fixed over time and heterogeneous (quenched noise). Recent studies have suggested that the stability properties and abundance distributions of large disordered GLV systems depend, in the simplest scenario, solely on the mean and variance of the distribution of species interactions. However, empirical communities deviate from this level of universality. In this article, we present a generalized version of the dynamical mean field theory for non-Gaussian interactions that can be applied to various models, including the GLV equations. Our results show that the generalized mean field equations have solutions which depend on all cumulants of the distribution of species interactions, leading to a breakdown of universality. We leverage on this informative breakdown to extract microscopic interaction details from the macroscopic distribution of densities which are in agreement with empirical data. Specifically, in the case of sparse interactions, which we analytically investigate, we establish a simple relationship between the distribution of interactions and the distribution of species population densities.