Phase diagram of the symbiotic two-species contact process.

We study the two-species symbiotic contact process, recently proposed by de Oliveira, Santos, and Dickman [Phys. Rev. E 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 μ<1. Otherwise, the dynamics follows the rules of the basic contact process, with individuals reproducing to vacant neighbor sites at rate λ and dying at a rate of unity. We determine the full phase diagram in the λ-μ 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 μ), 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 λ-μ-D space. Our results raise the possibility that strongly symbiotic associations of mobile species may be vulnerable to sudden extinction under increasingly adverse conditions.