Evol Ecol Res 12: 279-305 (2010) Full PDF if your library subscribes.
Spatial competition and the dynamics of rarity in a temporally varying environment
Lauren O’Malley1, G. Korniss1, Sai Satya Praveen Mungara2 and Thomas Caraco3
1Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York, 2Department of Computer Science, University at Albany, Albany, New York and 3Department of Biological Sciences, University at Albany, Albany, New York, USA
Correspondence: T. Caraco, Department of Biological Sciences, University at Albany, Albany, NY 12222, USA.
Questions: How does temporal variation in competitive advantage affect advance from rarity and species abundances in an individual-based ecology? In particular, how does the difference between the timescale of competitive invasion and the timescale of environmental periodicity interact with the spatial clustering underlying invasion to influence global population dynamics?
Features of model: We assume that two species compete preemptively for space in a two-dimensional environment. We categorize invasion of one of them as either the growth of one cluster of the rare species, or as growth of many clusters at the same time. Simulation of a constant environment identifies the characteristic timescale for a competitively superior species to invade and numerically dominate a resident species.
Manipulation of key variables: 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. We set the half-period of the environment much less than, roughly equal to, and much greater than the endogenous timescale. 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.
Conclusions: In the multi-cluster invasion regime, rapid environmental variation produced spatial mixing of the species and non-equilibrium co-existence. 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 a 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 that occurred 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 that occurred much slower than the endogenous dynamics produced symmetric limit cycles, alternations of the constant-environment pattern.
Keywords: ecological invasion, nucleation, population-dynamic timescale, spatial competition, stochastic resonance, temporal variation.
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