Gametic disequilibria between virulence genes in barley powdery mildew populations in relation to selection and recombination. I. Models

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Two‐ and three‐locus models were developed to study the dynamics of gametic disequilibria (linkage disequilibria) between virulence genes in an aerial population of a haploid, biotrophic pathogen, illustrated by the fungus Erysiphe graminis f.sp. hordei. The models predicted that selection induced by two or three resistance genes in host varieties would generate gametic disequilibria between the corresponding virulence genes and that recombination taking place during sexual reproduction in most cases would reduce the amount of gametic disequilibrium attained by selection. The reduction of gametic disequilibrium during sexual reproduction depended on the recombination frequency multiplied by the proportion of spores produced by sexual reproduction and by the relative acreage of varieties on which the virulence genes considered were‘unnecessary'. The dynamics of gametic disequilibria in the aerial population were shown to be different depending on the use of resistance genes in host varieties. Two resistance genes present mainly in different varieties would generate negative gametic disequilibrium between the corresponding virulence genes, whereas two resistance genes present mainly in the same variety would generate positive gametic disequilibrium between the corresponding virulence genes. In both cases, the signs would be maintained as predicted until the virulence genes became fixed. However, if the disequilibrium initially was non‐zero with a sign opposite to that predicted from the distribution of the varieties, then the sign of the disequilibrium would not change instantaneously. These general results were valid for sexual as well as asexual reproduction. The predictions of the models were largely in accordance with those observed in Danish barley powdery mildew populations (Hovmøller & østergard, 1991). The results of the models were complemented by numerical studies to illustrate the dynamics of gametic disequilibria in specific cases, and to demonstrate the different evolutionary patterns of the virulence gene and genotype frequencies under different selection regimes.