Estimation of Recombination Rate and Maternal Linkage Disequilibrium in Half-Sibs

A livestock population can be characterized by different population genetic parameters, such as linkage disequilibrium and recombination rate between pairs of genetic markers. The population structure, which may be caused by family stratification, has an influence on the estimates of these parameters. An expectation maximization algorithm has been proposed for estimating these parameters in half-sibs without phasing the progeny. It, however, overlooks the fact that the underlying likelihood function may have two maxima. The magnitudes of the maxima depend on the maternal allele frequencies at the investigated marker pair. Which maximum the algorithm converges to depends on the chosen start values. We present a stepwise procedure in which the relationship between the two modes is exploited. The expectation maximization algorithm for the parameter estimation is applied twice using different start values, followed by a decision process to assess the most likely estimate. This approach was validated using simulated genotypes of half-sibs. It was also applied to a dairy cattle dataset consisting of multiple half-sib families and 39,780 marker genotypes, leading to estimates for 12,759,713 intrachromosomal marker pairs. Furthermore, the proper order of markers was verified by studying the mean of estimated recombination rates in a window adjacent to the investigated locus as well as in a window at its most distant chromosome end. Putatively misplaced markers or marker clusters were detected by comparing the results with the revised bovine genome assembly UMD 3.1.1. In total, 40 markers were identified as candidates of misplacement. This outcome may help improving the physical order of markers which is also required for refining the bovine genetic map.