Linkage disequilibrium under polysomic inheritance

Abstract

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 Burrows {Delta} statistic to include polysomic inheritance, as well as their corresponding squared correlation coefficients r2 and [Formula], where the former is for phased genotypes and the latter for unphased genotypes. Weir & Hills 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 [Formula] at equilibrium state, d2 and{delta} 2, are derived under five mating systems. We assess the behaviors of the estimated r2 and [Formula] and the influence of the recombination rate on d2 or{delta} 2, simulate the application of estimating effective population size, and evaluate the statistical performance of the method of estimating.