First and third authors: Department of Renewable Resources, University of Alberta, Edmonton, AB T6G 2H1, Canada; and second author: Alberta Agriculture, Food and Rural Development, 301, 7000-113 Street, Edmonton, AB T6H 5T6, Canada, and Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, AB T6G 2P5, Canada
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Accepted for publication 25 December 2002.
We have developed a new complementary model of gene interaction between diploid host and haploid pathogen by allowing for arbitrary levels of dominance in the host. This model enables us to assess the effects of overdominance, incomplete dominance, and underdominance on the equilibrium frequencies of resistance and virulence genes and on the stability of equilibria. Our model reduces to a gene-for-gene model when complete dominance of resistance is assumed. Computer simulations show that our model has two new features. First, when there is overdominance or underdominance of resistance, the internal equilibrium points exist even when there is no cost of unnecessary virulence or when there is a cost of necessary virulence at the balance between cost of unnecessary virulence and effectiveness of resistance. Second, the occurrence of stable resistance and virulence polymorphism is strongly dependent on the level of dominance. These two features suggest the need for caution when using the gene-for-gene model, especially in the presence of overdominance or underdominance. Our model is particularly suitable for studying the coevolutionary dynamics between hybrid populations and their pathogens in natural pathosystems.
© 2003 The American Phytopathological Society