Population genetics of autopolyploids under a mixed mating model and the estimation of selfing rate

Nowadays, the population genetics analysis of autopolyploid species faces many difficulties due to (i) limited development of population genetics tools under polysomic inheritance, (ii) difficulties to assess allelic dosage when genotyping individuals and (iii) a form of inbreeding resulting from the mechanism of 'double reduction'. Consequently, few data analysis computer programs are applicable to autopolyploids. To contribute bridging this gap, this article first derives theoretical expectations for the inbreeding and identity disequilibrium coefficients under polysomic inheritance in a mixed mating model. Moment estimators of these coefficients are proposed when exact genotypes or just markers phenotypes (i.e. allelic dosage unknown) are available. This led to the development of estimators of the selfing rate based on adult genotypes or phenotypes and applicable to any even-ploidy level. Their statistical performances and robustness were assessed by numerical simulations. Contrary to inbreeding-based estimators, the identity disequilibrium-based estimator using phenotypes is robust (absolute bias generally < 0.05), even in the presence of double reduction, null alleles or biparental inbreeding due to isolation by distance. A fairly good precision of the selfing rate estimates (root mean squared error < 0.1) is already achievable using a sample of 30-50 individuals phenotyped at 10 loci bearing 5-10 alleles each, conditions reachable using microsatellite markers. Diallelic markers (e.g. SNP) can also perform satisfactorily in diploids and tetraploids but more polymorphic markers are necessary for higher ploidy levels. The method is implemented in the software SPAGeDi and should contribute to reduce the lack of population genetics tools applicable to autopolyploids.