Dispersal and competition models for plants. (English) Zbl 0842.92026
Summary: New models for seed dispersal and competition between plant species are formulated and analyzed. The models are integrodifference equations, discrete in time and continuous in space, and have applications to annual and perennial species. The spread or invasion of a single plant species into a geographic region is investigated by studying the travelling wave solutions of these equations. Travelling wave solutions are shown to exist in the single-species models and are compared numerically. The asymptotic wave speed is calculated for various parameter values. The single-species integrodifference equations are extended to a model for two competing annual plants. Competition in the two-species model is based on a difference equation model developed by A. G. Pakes and R. A. Maller [Mathematical ecology of plant species competition: A class of deterministic models for binary mixtures of plant genotypes. (1990; Zbl 0726.92027)]. The two-species model with competition and dispersal yields a system of integrodifference equations. The effects of competition on the travelling wave solutions of invading plant species are investigated numerically.
MSC:
| 92D40 | Ecology |
| 39A99 | Difference equations |
| 39B99 | Functional equations and inequalities |
| 45M99 | Qualitative behavior of solutions to integral equations |
Keywords:
seed dispersal; plant species; integrodifference equations; travelling wave solutions; single-species models; asymptotic wave speed; competing annual plants; two-species modelCitations:
Zbl 0726.92027References:
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