Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction

Polyploids are organisms whose genomes consist of more than two complete sets of chromosomes. Both autopolyploids and allopolyploids may display polysomic inheritance. A peculiarity of polysomic inheritance is multivalent formation during meiosis resulting in double-reduction, which occurs when sister chromatid fragments are segregated into the same gamete. Double-reduction can result in gametes carrying identical-by-descent alleles and slightly increasing homozygosity. This will cause the genotypic frequencies to deviate from expected values and will thus bias the results of standard population genetic analytical methods used in molecular ecology and selective breeding. In this study, we extend existing double-reduction models to account for any even level of ploidy, and derive the symbolic expressions for genotypic frequencies via two methods. Inbreeding coefficients and heterozygosity under double-reduction and inbreeding are also calculated. Numerical solutions obtained by computer simulations are compared with analytical solutions predicted by the model to validate the model.