Linkage disequilibrium under polysomic inheritance.

Linkage disequilibrium (LD) is the non-random association of alleles at different loci. Squared LD coefficients r 2 (for phased genotypes) and [Formula: see text] (for unphased genotypes) will converge to constants that are determined by the sample size, the recombination frequency, the effective population size and the mating system. LD can therefore be used for gene mapping and the estimation of effective population size. However, current methods work only with diploids. To resolve this problem, we here extend the linkage disequilibrium measures to include polysomic inheritance. We derive the values of r 2 and [Formula: see text] at equilibrium state for various mating systems and different ploidy levels. For unlinked loci, [Formula: see text] for monoecious and dioecious (with random pairing) mating systems or [Formula: see text] for dioecious mating systems (with lifetime pairing), where f is the number of females in a half-sib family and η is a constant related to the ploidy level. We simulate the application of estimating N e using unphased genotypes. We find that estimating N e in polyploids requires similar sample sizes and numbers of loci as in diploids, with the main source of bias due to using 0.5 as the recombination frequency.