Estimation of Allele Frequencies at Isoloci

In some polyploid animals and plants, pairs of duplicated loci occur that share alleles encoding proteins with identical electrophoretic mobilities. Except in cases where these ``isoloci' are known to be inherited tetrasomically, individual genotypes cannot be determined unambiguously, and there is no direct way to assign observed variation to a particular locus of the pair. For a pair of diallelic isoloci, nine genotypes are possible but only five phenotypes can be identified, corresponding to individuals with 0-4 doses of the variant allele. A maximum likelihood (ML) approach is used here to identify the set of allele frequencies (p, q) at the individual gene loci with the highest probability of producing the observed phenotypic distribution. A likelihood ratio test is used to generate the asymmetrical confidence intervals around ML estimates. Simulations indicate that the standard error of p is typically about twice the binomial sampling error associated with single locus allele frequency estimates. ML estimates can be used in standard indices of genetic diversity and differentiation and in goodness-of-fit tests of genetic hypotheses. The noncentral χ(2) distribution is used to evaluate the power of a test of apparent heterozygote deficiency that results from attributing all variation to one locus when both loci are polymorphic.