Discrete-time models for gene frequencies and population densities in plant pathosystems

J. C. Kesinger, L. J.S. Allen, R. E. Strauss

Research output: Contribution to journalConference articlepeer-review

6 Scopus citations


Discrete-time models for the gene frequencies and population densities of plants and pathogens are formulated and analyzed. The gene-frequency models are based on the gene-for-gene hypothesis; a resistant gene in the plant has a corresponding virulent gene in the pathogen. Some basic population genetics models with selection are summarized. Then, gene-frequency models for two populations are formulated. A gene-frequency model for plant pathosystems developed in the 1970's is discussed. For the general model, conditions are derived for local stability of the equilibria. The polymorphic equilibrium EP is shown to be nonhyperbolic but numerical simulations indicate that cycling occurs about EP. In addition, population models for the host and pathogen are formulated, where the genetics of the pathogen are modeled. It is shown that the asymptotic dynamics depend on the basic reproductive number R0, which in turn depends on the fitness values of the host and pathogen.

Original languageEnglish
Pages (from-to)1489-1500
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number3
StatePublished - Aug 2001
Event3rd World Congress of Nonlinear Analysts - Catania, Sicily, Italy
Duration: Jul 19 2000Jul 26 2000


  • Difference equations
  • Gene-frequency
  • Plant pathosystem
  • SIS epidemic


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