| Summary: | 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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