Genetic models for plant pathosystems.
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.
Kesinger
Jacob C
JC
Department of Mathematics and Statistics, Texas Tech University, P.O. Box 41042, Lubbock, TX 79409-1042, USA. kesinger@math.ttu.edu
Allen
Linda J S
LJ
D008957:Models, Genetic; D010935:Plant Diseases / Q000235:genetics*; D010944:Plants / Q000235:genetics*; D013269:Stochastic Processes