Well-mixed Lotka-Volterra model with random strongly competitive interactions

TL;DR

This paper analyzes a symmetric, strongly competitive random Lotka-Volterra model, revealing phase behaviors and abundance distributions, and extends understanding of ecological community dynamics under different interaction regimes.

Contribution

It provides a detailed analysis of the strongly competitive case with symmetric interactions, bridging previous weak interaction results and exploring phase diagrams and abundance distributions.

Findings

At zero temperature, multiple equilibria exist even with strong competition.

At finite temperature, only a single stable equilibrium is present.

The study identifies two distinct behaviors for mean abundance depending on temperature.

Abstract

The random Lotka-Volterra model is widely used to describe the dynamical and thermodynamic features of ecological communities. In this work, we consider random symmetric interactions between species and analyze the strongly competitive interaction case. We investigate different scalings for the distribution of the interactions with the number of species and try to bridge the gap with previous works. Our results show two different behaviors for the mean abundance at zero and finite temperature respectively, with a continuous crossover between the two. We confirm and extend previous results obtained for weak interactions: at zero temperature, even in the strong competitive interaction limit, the system is in a multiple-equilibria phase, whereas at finite temperature only a unique stable equilibrium can exist. Finally, we establish the qualitative phase diagrams in both cases and compare the two species abundance distributions.