Department of Terrestrial Ecology, NERI, Vejlsovej 25, 8600 Silkeborg, Denmark

Background and objectives
A positively selected allele is not always fixed in the population. The fixation probability depends on the initial frequency of the allele, the selective advantage of the allele, population size, etc. Here, the fixation probability of a resistance allele is calculated in a finite mixed mating plant host population. The host birth and death processes, as well as the infection process were assumed to have a spatial structure.

The resistance allele is assumed to be dominant and a host with a resistance allele cannot be infected by a pathogen. Susceptible plants could be infected either by a background (or long-distance) type of infection process and/or from diseased neighbouring plants. There were several pathogen generations (infections events) per host generation. Plant mortality was a function of the number of neighbours (density dependent mortality) and diseased plants had a relatively high mortality rate. The female fecundity of diseased plants was relative and depended on the when the plant was initially infected. The host plant had a selfing rate between zero and one, and the seeds were either randomly and/or locally dispersed in the population.

In the case when no spatial structure was assumed, the fixation probability was calculated from the expected mean change in allele frequency in one host generation, using the diffusion approximation [1]. In the case when spatial structure was assumed, the fixation probability was found by MonteCarlo simulation of the model with the host plants arranged in a grid structure.

Results and conclusion
The mating structure had a significant effect on the fixation probability. Depending on the relative female fecundity of diseased plants, the highest fixation probability could be attained by either outcrossing populations, populations with an intermediary selfing rate, or selfing populations. Similarly, the spatial structure of the different processes had a significant effect on the fixation probability. For example, if seeds were locally dispersed the fixation probability increased, especially if not all 'grid points' were filled with plants.

1. Kimura M, 1962. Genetics 47, 713-719.