Abstract Given a large population with mixed random mating and selfing (one locus-two alleles) different models of frequency-dependent selection were discussed - including a simple biometrical model for considering and analysing the competitive effects between neighbouring individuals in plant populations. For each model there were studied: changes in gene frequencies, population genetic equilibria, times until reaching these equilibria etc. - in dependence of the different parameters used: composition of the initial population, probability of selfing, selection-coefficients, competition-parameters.Apart from only few differing results it follows from the studies performed in these investigations, that the different composition of the initial population is of no particular importance as well for the gene frequencies p̂ at equilibrium as for the time t̂ until reaching these equilibria. This result is especially right for p̂.Different probabilities of selfing and different degrees of dominance in the selection coefficients are indeed of some influence on the existence and location of the population genetic equilibria, but here too we find an disproportionately stronger dependence with the time t̂ until reaching the equilibrium than with the gene frequency p̂ at equilibrium . The special importance of overdominance for the maintenance of genetic polymorphisms, which is well known in the case of non frequency-dependent selection (see: model 1 of the present studies) turn out to be of some other meaning in the models of frequency-dependent selection, which were analysed in the present paper: Depart from only few special situations (model 2 ; complete self-fertilization in models 5 and 6 ; extremely high probabilities of selfing in model 7) nontrivial equilibria are reached for all degrees of dominance. Therefore, the special importance of overdominance mentioned above, not proves right in the case of frequency-dependent selection.The investigations of the present paper have shown, that existence and location of the non trivial population genetic equilibria are determined not so much by degree of dominance and probability of selfing, but the equilibria are mainly determined by the model of the investigation used in the concerning studies.In the case of frequency-dependent selection, therefore, the explicit form of the fitness values as functions of the frequencies plays the decisive role in maintaining genetic polymorphisms.
Martingales and fixation probabilities of evolutionary graphs
