Phase diagram of the symbiotic two-species contact process

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.

arXiv commentto appear in Physical Review E

References in corpus (15)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Universality classes in nonequilibrium lattice systems
• Paths to Self-Organized Criticality
• Directed percolation criticality in turbulent liquid crystals
• Driving, conservation and absorbing states in sandpiles
• Quasi-stationary distributions for stochastic processes with an absorbing state
• Moment ratios for absorbing-state phase transitions
• Competition and cooperation in one-dimensional stepping stone models
• Environmental vs. demographic variability in two-species predator-prey models
• Growth, competition and cooperation in spatial population genetics
• Quasi-stationary simulation of the contact process
• Asymmetric Mutualism in Two- and Three-Dimensional Range Expansions
• What ecological factors shape species-area curves in neutral models?
• On the absorbing-state phase transition in the one-dimensional triplet creation model
• Parasites on parasites: coupled fluctuations in stacked contact processes

Cited by in corpus (12)

• Generic finite size scaling for discontinuous nonequilibrium phase transitions into absorbing states
• Fundamental ingredients for the emergence of discontinuous phase transitions in the majority vote model
• Partial inertia induces additional phase transition in the explosive majority vote model
• Finite-size scaling for discontinuous nonequilibrium phase transitions
• The symbiotic contact process: phase transitions, hysteresis cycles, and bistability
• Comparing the influence of distinct kinds of temporal disorder in a low dimensional absorbing transition model
• The advantage of being slow: the quasi-neutral contact process
• Heterogeneous mean-field theory for two-species symbiotic processes on networks
• Dynamical correlations and pairwise theory for the symbiotic contact process on networks
• Effects of diffusion in competitive contact processes on bipartite lattices
• Visibility graphs of critical and off-critical time series for absorbing state phase transitions
• Influence of competition in minimal systems with discontinuous absorbing phase transitions