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Analysis of an integrodifference model for biological invasions with a quasi-local interaction Merchant, Sandra M.

Abstract

The behaviour of a new model for the spatial spread of biological invasions with non-overlapping synchronous generations and well-defined dispersal and sedentary stages is examined. In this integrodifference model, competition between conspecifics takes the form of a quasi-local interaction, where the strength of competition between two individuals depends on their physical distance from each other. Both the deterministic model and a stochastic analogue are examined by numerically simulating the spread of a localized initial population over several generations. By modelling intraspecific competition with a quasi-local interaction, the shape of the travelling waves changed significantly from that of the classical model with only local competition, creating more variable and complex wavefront shapes than are possible with the classical model. The addition of quasi-local competition was also found to alter several aspects of the initial behaviour of this model, including the invasion speed and spatial structure, although in the deterministic case the asymptotic invasion speed and population density behind the front of the wave agreed with those of the classical model. In the stochastic analogue, however, the rate of spread of the invasion was found to be considerably lower than that of the classical model, both initially and asymptotically. Furthermore, the speed achieved by the stochastic invasions was found to depend on the parameters of the quasi-local interaction kernel.

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