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Genetic models for plant pathosystems.

Jacob C Kesinger1, Linda J S Allen

  • 1Department of Mathematics and Statistics, Texas Tech University, P.O. Box 41042, Lubbock, TX 79409-1042, USA. kesinger@math.ttu.edu

Mathematical Biosciences
|April 20, 2002
PubMed
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This study develops genetics models for plant-pathogen interactions. While polymorphic equilibrium stability is indeterminate, random selection values promote convergence toward this equilibrium.

Area of Science:

  • Population genetics
  • Plant pathology
  • Mathematical modeling

Background:

  • Leonard's 1977 model analyzed plant-pathogen genetics with haploid pathogens and diploid hosts.
  • The original model focused on a single gene interaction.

Purpose of the Study:

  • To generalize Leonard's model to diploid hosts and pathogens with incomplete dominance.
  • To extend the model to two genes and incorporate stochasticity.
  • To analyze the stability of polymorphic equilibria in these advanced models.

Main Methods:

  • Development of deterministic, discrete-time genetics models.
  • Generalization of a single-gene model to include incomplete dominance.
  • Extension to a two-gene model and formulation of a stochastic model.

Related Experiment Videos

  • Analysis of local stability properties and simulation of the stochastic model.

    • Main Results:

    • The stability of the polymorphic equilibrium was found to be indeterminate (non-hyperbolic) in both the original and generalized models.
    • The stochastic model with random selection values demonstrated a tendency for solutions to converge towards the polymorphic equilibrium.
    • Incomplete dominance in diploid hosts and pathogens was incorporated.

    Conclusions:

    • The generalized models provide a more comprehensive framework for plant-pathogen genetics.
    • While theoretical stability is indeterminate, stochastic factors can drive populations toward a mixed equilibrium.
    • This research contributes to understanding the evolutionary dynamics of host-pathogen systems.