Incorporating Heterogeneous Interactions for Ecological Biodiversity

Abstract

Understanding the behaviors of ecological systems is challenging given their multi-faceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully-connected structure assumed in these previous studies is not realistic as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the well-mixed system, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.

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Cited by in corpus (6)

• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Spectral properties, localization transition and multifractal eigenvectors of the Laplacian on heterogeneous networks
• Exact solution of Dynamical Mean-Field Theory for a linear system with annealed disorder
• Irreversibility in Non-reciprocal Chaotic Systems
• Stabilization of macroscopic dynamics by fine-grained disorder in many-species ecosystems
• Interplay between intraspecific suppression and environment in shaping biodiversity