Characterization of phase transitions in a model ecosystem of sessile species

TL;DR

This paper investigates phase transitions in a model ecosystem of sessile species competing for space, analyzing how introduction rates and system size influence the transition between high- and low-diversity states.

Contribution

It extends previous models by exploring finite introduction rates and system sizes, revealing how these factors affect the nature and stability of phase transitions.

Findings

High-diversity state persists for interaction probability above a critical value

Increased introduction rate prolongs the high-diversity state duration

System size influences the probability of remaining in the high-diversity state

Abstract

We consider a model ecosystem of sessile species competing for space. In particular, we consider the system introduced in [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011)] where species compete according to a fixed interaction network with links determined by a Bernoulli process. In the limit of a small introduction rate of new species, the model exhibits a discontinuous transition from a high-diversity state to a low-diversity state as the interaction probability between species, $\gamma$, is increased from zero. Here we explore the effects of finite introduction rates and system-size on the phase transition by utilizing efficient parallel computing. We find that the low state appears for $\gamma>\gamma_c$. As $\gamma$ is increased further, the high state approaches to the low state, suggesting the possibility that the two states merge at a high $\gamma$. We find that the fraction of time spent in the high state becomes longer with higher introduction rates, but the availability of the two states is rather insensitive to the value of the introduction rate. Furthermore we establish a relation between the introduction rate and the system size, which preserves the probability for the system to remain in the high-diversity state.