Phase diagram of the symbiotic two-species contact process

TL;DR

This paper investigates the phase diagram of a two-species symbiotic contact process, revealing how symbiosis and mobility influence phase transitions and extinction risks in lattice models.

Contribution

It provides the first comprehensive phase diagram of the 2SCP, including effects of asymmetry and diffusion, and identifies conditions for discontinuous transitions and potential extinction.

Findings

Discontinuous phase transitions occur at strong symbiosis and high diffusion.

The phase diagram in the λ-μ-D space shows complex critical surfaces.

Strong symbiosis can lead to sudden extinction under adverse conditions.

Abstract

We study the two-species symbiotic contact process (2SCP), recently proposed in [de Oliveira, Santos and Dickman, Phys. Rev. E {\bf 86}, 011121 (2012)] . In this model, each site of a lattice may be vacant or host single individuals of species A and/or B. Individuals at sites with both species present interact in a symbiotic manner, having a reduced death rate, $\mu < 1$. Otherwise, the dynamics follows the rules of the basic CP, with individuals reproducing to vacant neighbor sites at rate $\lambda$ and dying at a rate of unity. We determine the full phase diagram in the $\lambda-\mu$ plane in one and two dimensions by means of exact numerical quasistationary distributions, cluster approximations, and Monte Carlo simulations. We also study the effects of asymmetric creation rates and diffusion of individuals. In two dimensions, for sufficiently strong symbiosis (i.e., small $\mu$), the absorbing-state phase transition becomes discontinuous for diffusion rates $D$ within a certain range. We report preliminary results on the critical surface and tricritical line in the $\lambda-\mu-D$ space. Our results raise the possibility that strongly symbiotic associations of mobile species may be vulnerable to sudden extinction under increasingly adverse conditions.