Linkage disequilibrium under polysomic inheritance

The influence of genetic drift on linkage disequilibrium in finite populations has been extensively studied in diploids. However, to date the effects of ploidy on LD has not been extensively studied. We here extend the linkage disequilibrium measure D and Burrow’s Δ statistic to include polysomic inheritance, as well as their corresponding squared correlation coefficients r2 and , where the former is for phased genotypes and the latter for unphased genotypes. Weir & Hill’s double non-identity framework is also extended to include polysomic inheritance, and the expressions of double non-identity coefficients are derived under five mating systems. On this basis, the approximated expectations of estimated r2 and at equilibrium state, d2 and δ2, are derived under five mating systems. We assess the behaviors of the estimated r2 and and the influence of the recombination rate on d2 or δ2, simulate the application of estimating effective population size, and evaluate the statistical performance of the method of estimating.

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.