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Given an endogenous timescale set by invasion in a constant environment, weintroduced periodic temporal variation in competitive superiority byalternating the species' propagation rates. By manipulating habitat size andintroduction rate, we simulated environments where successful invasion proceedsthrough growth of many spatial clusters, and where invasion can occur only as asingle-cluster process. In the multi-cluster invasion regime, rapidenvironmental variation produced spatial mixing of the species andnon-equilibrium coexistence. The dynamics' dominant response effectivelyaveraged environmental fluctuation, so that each species could avoidcompetitive exclusion. Increasing the environment's half-period to match thepopulation-dynamic timescale let the (initially) more abundant residentrepeatedly repel the invader. Periodic transition in propagation-rate advantagerarely interrupted the exclusion process when the more abundant species hadcompetitive advantage. However, at infrequent and randomly occurring times, therare species could invade and reverse the density pattern by rapidly erodingthe resident's preemption of space. In the single-cluster invasion regime,environmental variation occurring faster than the population-dynamic timescaleprohibited successful invasion; the first species to reach its stationarydensity (calculated for a constant environment) continued to repel the otherduring long simulations. When the endogenous and exogenous timescales matched,the species randomly reversed roles of resident and invader; the waiting timesfor reversal of abundances indicate stochastic resonance. For both invasionregimes, environmental fluctuation occurring much slower than the endogenousdynamics produced symmetric limit cycles, alternations of theconstant-environment pattern.

Spatial competition and the dynamics of rarity in a temporally varying environment