Dispersal and competition models for plants

Edward J. Alien, Linda J.S. Allen, Xiaoning Gilliam

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


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 Pakes and Mailer [26]. 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 is investigated numerically.

Original languageEnglish
Pages (from-to)455-481
Number of pages27
JournalJournal of Mathematical Biology
Issue number4
StatePublished - 1996


  • Integrodifference equation
  • Seed dispersal
  • Travelling wave


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