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According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which mechanisms confer an advantage to a given species against the other(s)? In general, it is expected that the species with the higher reproductive/death ratio will win the competition, but other mechanisms, such as asymmetry in interspecific competition or unequal diffusion rates, have been found to change this scenario dramatically. In this work, we examine competitive advantage in the context of quasi-neutral population models, including stochastic models with spatial structure as well as macroscopic (mean-field) descriptions. We employ a two-species contact process in which the "biological clock" of one species is a factor of $\alpha$ slower than that of the other species. Our results provide new insights into how stochasticity and competition interact to determine extinction in finite spatial systems. We find that a species with a slower biological clock has an advantage if resources are limited, winning the competition against a species with a faster clock, in relatively small systems. Periodic or stochastic environmental variations also favor the slower species, even in much larger systems., Comment: Reviewed extended version

We study a contact process (CP) with two species that interact in a symbiotic manner. In our model, each site of a lattice may be vacant or host individuals of species A and/or B; multiple occupancy by the same species is prohibited. Symbiosis is represented by a reduced death rate, mu < 1, for individuals at sites with both species present. Otherwise, the dynamics is that of the basic CP, with creation (at vacant neighbor sites) at rate lambda and death of (isolated) individuals at a rate of unity. Mean-field theory and Monte Carlo simulation show that the critical creation rate, lambda_c (mu), is a decreasing function of mu, even though a single-species population must go extinct for lambda < lambda_c(1), the critical point of the basic CP. Extensive simulations yield results for critical behavior that are compatible with the directed percolation (DP) universality class, but with unusually strong corrections to scaling. A field-theoretical argument supports the conclusion of DP critical behavior. We obtain similar results for a CP with creation at second-neighbor sites and enhanced survival at first neighbors, in the form of an annihilation rate that decreases with the number of occupied first neighbors., Comment: 27 pages, 12 figures

We study a contact process with creation at first- and second-neighbor sites and inhibition at first neighbors, in the form of an annihilation rate that increases with the number of occupied first neighbors. Mean-field theory predicts three phases: inactive (absorbing), active symmetric, and active asymmetric, the latter exhibiting distinct sublattice densities on a bipartite lattice. These phases are separated by continuous transitions; the phase diagram is reentrant. Monte Carlo simulations in two dimensions verify these predictions qualitatively, except for a first-neighbor creation rate of zero. (In the latter case one of the phase transitions is discontinuous.) Our numerical results confirm that the symmetric-asymmetric transition belongs to the Ising universality class, and that the active-absorbing transition belongs to the directed percolation class, as expected from symmetry considerations.

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate of the critical exponent nu_|| with a precision of 0.5%.

We review a recently devised Monte Carlo simulation method for the direct study of quasi-stationary properties of stochastic processes with an absorbing state. The method is used to determine the static correlation function and the interparticle gap-length distribution in the critical one-dimensional contact process. We also find evidence for power-law decay of the interparticle distance distribution in the two-particle subspace., Comment: 9 pages, 4 figures

For a large class of processes with an absorbing state, statistical properties of the surviving sample attain time-independent values in the quasi-stationary (QS) regime. We propose a practical simulation method for studying quasi-stationary properties, based on the equation of motion governing the QS distribution. The method is tested in applications to the contact process. At the critical point, our method is about an order of magnitude more efficient than conventional simulation., Comment: 9 pages, 4 figures