A model for the estimation of outcrossing rate and gene frequencies using n independent loci

Abstract

A mixed mating model for many unlinked loci is described. A procedure for estimation of the model parameters (outcrossing rate and gene frequencies), based on a multilocus maximum likelihood equation, is discussed and analyzed for bias, variance, and robustness. Genotypic data from families of known or unknown maternal parentage, or data from progenies of known maternal parentage, are used for estimation. The procedure is applicable to dominant or co-dominant Mendelian genes with two or three alleles per locus, and should be particularly useful in studies where the effort in scoring more loci is less than the effort in scoring more progeny. Variances of the multilocus estimates of outcrossing rate and pollen pool gene frequencies decrease when more loci are included in the estimation. Monte Carlo simulations showed the estimates to be unbiased when model assumptions are not violated, but the bias introduced by various violations is reduced when more loci are included in the estimate. Often the variance of a three or four locus estimate closely approaches the minimum variance possible (the variance of an estimate using infinitely many loci), setting a practical limit to the number of loci needed for a nearly minimum variance estimate. An example from some work on Limnanthes is presented to illustrate the use of multilocus model and its fit to data from natural populations.