Feasibility and stability in large Lotka Volterra systems with interaction structure

TL;DR

This paper explores how the structure of interactions in large Lotka-Volterra systems influences their feasibility and stability, revealing that different interaction types have contrasting effects on system robustness.

Contribution

It analytically and numerically demonstrates the complementary roles of RMT and feasibility in assessing large ecological systems with structured interactions.

Findings

Feasibility increases with predator-prey interactions.

Competition and mutualism decrease feasibility.

Interaction structure critically impacts stability.

Abstract

Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalised Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.