Coexistence and critical behaviour in a lattice model of competing species

TL;DR

This study investigates a lattice model of two competing species, revealing how resource availability influences coexistence, extinction, and phase transition behaviors across different dimensions, with potential applications to tumor cell dynamics.

Contribution

The paper introduces a lattice model of species competition that captures coexistence and extinction phenomena, analyzing phase transitions and suggesting biological relevance to tumor cell interactions.

Findings

Coexistence occurs when resources are abundant.

Species with slower metabolism go extinct at intermediate resources.

Species with faster metabolism go extinct when resources are scarce.

Abstract

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.