Generalised Lotka-Volterra model with hierarchical interactions

TL;DR

This paper introduces a hierarchical generalization of the Lotka-Volterra model using the cascade interaction framework, revealing how hierarchy influences stability, species survival, and community structure in complex ecosystems.

Contribution

It incorporates the cascade model into Lotka-Volterra dynamics, demonstrating the stabilizing effect of hierarchy and its impact on species abundance and community composition.

Findings

Hierarchical interactions stabilize the community.

Hierarchy reduces the number of surviving species.

Heterogeneity in interaction variances destabilizes the community.

Abstract

In the analysis of complex ecosystems it is common to use random interaction coefficients, often assumed to be such that all species are statistically equivalent. In this work we relax this assumption by choosing interactions according to the cascade model, which we incorporate into a generalised Lotka-Volterra dynamical system. These interactions impose a hierarchy in the community. Species benefit more, on average, from interactions with species further below them in the hierarchy than from interactions with those above. Using dynamic mean-field theory, we demonstrate that a strong hierarchical structure is stabilising, but that it reduces the number of species in the surviving community, as well as their abundances. Additionally, we show that increased heterogeneity in the variances of the interaction coefficients across positions in the hierarchy is destabilising. We also comment on the structure of the surviving community and demonstrate that the abundance and probability of survival of a species is dependent on its position in the hierarchy.