Estimation of linkage disequilibrium for loci with multiple alleles: basic approach and an application using data from bighorn sheep.

The great expansion of population genetic data using molecular techniques now allows examination of the extent of linkage disequilibrium for many pairs of loci, each locus often with multiple alleles. The expectation-maximization (EM) algorithm for generating maximum likelihood estimates of gametic frequencies from multiallelic genotypic data is described and applied. The EM algorithm is used in desert bighorn sheep where the population size, and consequently the sample size, is often small. We calculated haplotype frequencies for all pairwise combinations of five major histocompatibility loci and three microsatellite loci in 14 populations; the performance of the algorithm is discussed. Disequilibrium values are calculated and tested for statistical significance. High levels of disequilibrium are found between all pairs of major histocompatibility complex (MHC) loci and between MHC and a linked microsatellite locus.