Restricted maximum likelihood analysis of linkage between genetic markers and quantitative trait loci for a granddaughter design.

A REML for the estimation of location and variance of a single quantitative trait locus, together with polygenic and residual variance, is described for the analysis of a granddaughter design. The method is based on a mixed linear model that includes the allelic effects of the quantitative trait locus, which are assumed to be normally distributed. Information from four marker loci situated on a single chromosome was available to derive the covariances at the linked quantitative trait locus. A derivative-free algorithm is described that makes use of the specific structure of the granddaughter design. The procedure has been applied to simulated data for a granddaughter design with 50 grandsire families of 40 sires each. Error variance was 60, and total additive genetic variance equaled 40; the quantitative trait locus explained either 10 or 25% of the latter variance. The size of the marker bracket containing the quantitative trait locus was either 10 or 30 cM. The power of detecting the quantitative trait locus ranged from 19 to 99%. Estimates of total genetic variance and variance explained by the quantitative trait locus were found to be empirically unbiased. A small bias was found in location estimates, especially when markers were not fully informative. The accuracy of parameter estimates was greatly improved by the use of information from individual daughters.