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

Czuppon, Peter1; Billiard, Sylvain2

Published Aug 11, 2022; Updated Jun 26, 2024 on Dryad. https://doi.org/10.5061/dryad.0zpc86712

Data files

Aug 11, 2022 version files 42.75 MB
Jun 26, 2024 version files 41.67 MB

Abstract

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.