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 modeling 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 (1958), and compute the stationary S-allele frequency distribution. We find that the stationary distribution proposed by Wright (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.

Methods
Codes and datasets for generating the figures in the main text and the Supplementary Information of the manuscript entitled "Revisiting the number of self-incompatibility alleles: from old models to new results" published in the Journal of Evolutionary Biology (https://doi.org/10.1111/jeb.14061).

Version Update
June 2024: There was a small mistake in the code that has been corrected now. The published figures had to be corrected, which can be found here: doi:10.1093/jeb/voae059/7685015.