Species exclusion and coexistence in a noisy voter model with a competition-colonization tradeoff

TL;DR

This paper introduces an asymmetric noisy voter model with a competition-colonization tradeoff to explore species coexistence and exclusion, revealing complex phase transitions and irreversible species loss driven by immigration and dispersal strategies.

Contribution

It presents a novel asymmetric noisy voter model incorporating immigration and a competition-dispersal tradeoff, uncovering diverse coexistence regimes and phase transitions in species competition dynamics.

Findings

Identification of mono-stable and bi-stable coexistence regimes.

Discovery of a discontinuous transition leading to species loss.

Revealing a cusp catastrophe in species competition dynamics.

Abstract

We introduce an asymmetric noisy voter model to study the joint effect of immigration and a competition-dispersal tradeoff in the dynamics of two species competing for space in regular lattices. Individuals of one species can invade a nearest-neighbor site in the lattice, while individuals of the other species are able to invade sites at any distance but are less competitive locally, i.e., they establish with a probability $g \le 1$. The model also accounts for immigration, modeled as an external noise that may spontaneously replace an individual at a lattice site by another individual of the other species. This combination of mechanisms gives rise to a rich variety of outcomes for species competition, including exclusion of either species, mono-stable coexistence of both species at different population proportions, and bi-stable coexistence with proportions of populations that depend on the initial condition. Remarkably, in the bi-stable phase, the system undergoes a discontinuous transition as the intensity of immigration overcomes a threshold, leading to a half loop dynamics associated to a cusp catastrophe, which causes the irreversible loss of the species with the shortest dispersal range.