Spatial competition and the dynamics of rarity in a temporally varying   environment
  Given an endogenous timescale set by invasion in a constant environment, we introduced periodic temporal variation in competitive superiority by alternating the species' propagation rates. By manipulating habitat size and introduction rate, we simulated environments where successful invasion proceeds through growth of many spatial clusters, and where invasion can occur only as a single-cluster process. In the multi-cluster invasion regime, rapid environmental variation produced spatial mixing of the species and non-equilibrium coexistence. The dynamics' dominant response effectively averaged environmental fluctuation, so that each species could avoid competitive exclusion. Increasing the environment's half-period to match the population-dynamic timescale let the (initially) more abundant resident repeatedly repel the invader. Periodic transition in propagation-rate advantage rarely interrupted the exclusion process when the more abundant species had competitive advantage. However, at infrequent and randomly occurring times, the rare species could invade and reverse the density pattern by rapidly eroding the resident's preemption of space. In the single-cluster invasion regime, environmental variation occurring faster than the population-dynamic timescale prohibited successful invasion; the first species to reach its stationary density (calculated for a constant environment) continued to repel the other during long simulations. When the endogenous and exogenous timescales matched, the species randomly reversed roles of resident and invader; the waiting times for reversal of abundances indicate stochastic resonance. For both invasion regimes, environmental fluctuation occurring much slower than the endogenous dynamics produced symmetric limit cycles, alternations of the constant-environment pattern. 
Lauren O'Malley, G. Korniss, Sai Satya Praveen Mungara, and Thomas   Caraco
q-bio.PE cond-mat.stat-mech