Revisiting the number of self‐incompatibility alleles in finite populations: From old models to new results

Under gametophytic self‐incompatibility (GSI), plants are heterozygous at the self‐incompatibility locus (S‐locus) and can only be fertilized by pollen with a different allele at that locus. The last century has seen a heated debate about the correct way of modelling the allele diversity in a GSI population that was never formally resolved. Starting from an individual‐based model, we derive the deterministic dynamics as proposed by Fisher (The genetical theory of natural selection ‐ A complete, Variorum edition, Oxford University Press, 1958) and compute the stationary S‐allele frequency distribution. We find that the stationary distribution proposed by Wright (Evolution, 18, 609, 1964) is close to our theoretical prediction, in line with earlier numerical confirmation. Additionally, we approximate the invasion probability of a new S‐allele, which scales inversely with the number of resident S‐alleles. Lastly, we use the stationary allele frequency distribution to estimate the population size of a plant population from an empirically obtained allele frequency spectrum, which complements the existing estimator of the number of S‐alleles. Our expression of the stationary distribution resolves the long‐standing debate about the correct approximation of the number of S‐alleles and paves the way for new statistical developments for the estimation of the plant population size based on S‐allele frequencies. Gametophytic self‐incompatibility, a prevalent mating system in plants, has been the subject of a long debate among theoretical population geneticists during the last century. At the core of this debate was an argument between Wright, Fisher, Moran and others about the correct way of modelling the allele frequency dynamics of this particular system. We explicitly compute the stationary allele frequency distribution to formally resolve this dispute. Additionally, we derive expressions for the invasion probability of a novel self‐incompatibility allele, the diversification rate of the self‐incompatibility locus and develop a new estimator for the effective population size of a sampled population.