Genetic models for plant pathosystems

Jacob C. Kesinger, Linda J.S. Allen

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Deterministic, discrete time, genetics models for a resistant plant host and a virulent pathogen are developed and analyzed. The original model was developed by Leonard in 1977 for a single gene with haploid pathogens and diploid hosts [Ann. N.Y. Acad. Sci. 287 (1977) 207]. The original model is generalized to diploid hosts and pathogens with incomplete dominance of the heterozygote. In addition, the single gene model is extended to two genes and a stochastic model with random selection values is formulated and simulated. It is shown using local stability properties that stability of the polymorphic equilibrium is indeterminant; the equilibrium is non-hyperbolic. The original model of Leonard has this same property. However, with random selection values, solutions tend to converge toward the polymorphic equilibrium.

Original languageEnglish
Pages (from-to)247-269
Number of pages23
JournalMathematical Biosciences
StatePublished - 2002


  • Difference equations
  • Gene frequency
  • Gene-for-gene
  • Plant pathosystem


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