Rank abundance relations in evolutionary dynamics of random replicators

TL;DR

This paper develops a non-equilibrium statistical mechanics framework to analyze rank abundance relations in ecological communities modeled by random replicator systems, extending previous equilibrium models to include various interaction symmetries.

Contribution

It introduces an analytical approach for non-equilibrium ecological models with diverse interaction structures, expanding understanding of species abundance distributions beyond symmetric interactions.

Findings

Species abundance distributions are truncated normal or transformed distributions.

Distribution shapes resemble observed ecological skewness.

Interaction structures influence community stability and food-web configurations.

Abstract

We present a non-equilibrium statistical mechanics description of rank abundance relations (RAR) in random community models of ecology. Specifically, we study a multi-species replicator system with quenched random interaction matrices. We here consider symmetric interactions as well as asymmetric and anti-symmetric cases. RARs are obtained analytically via a generating functional analysis, describing fixed-point states of the system in terms of a small set of order parameters, and in dependence on the symmetry or otherwise of interactions and on the productivity of the community. Our work is an extension of Tokita [Phys. Rev. Lett. {\bf 93} 178102 (2004)], where the case of symmetric interactions was considered within an equilibrium setup. The species abundance distribution in our model come out as truncated normal distributions or transformations thereof and, in some case, are similar to left-skewed distributions observed in ecology. We also discuss the interaction structure of the resulting food-web of stable species at stationarity, cases of heterogeneous co-operation pressures as well as effects of finite system size and of higher-order interactions.