Mapping linked quantitative trait loci via residual maximum likelihood

A residual maximum likelihood method is presented for estimation of the positions and variance contributions of two linked QTLs. The method also provides tests for zero versus one QTL linked to a group of markers and for one versus two QTLs linked. A deterministic, derivative-free algorithm is employed. The variance-covariance matrix of the allelic effects at each QTL and its inverse is computed conditional on incomplete information from multiple linked markers. Covariances between effects at different QTLs and between QTLs and polygenic effects are assumed to be zero. A simulation study was performed to investigate parameter estimation and likelihood ratio tests. The design was a granddaughter design with 2 000 sons, 20 sires of sons and nine ancestors of sires. Data were simulated under a normal-effects and a biallelic model for variation at each QTL. Genotypes at five or nine equally spaced markers were generated for all sons and their ancestors. Two linked QTLs accounted jointly for 50 or 25% of the additive genetic variance, and distance between QTLs varied from 20 to 40 cM. Power of detecting a second QTL exceeded 0.5 all the time for the 50% QTLs and when the distance was (at least 30 cM for the 25% QTLs. An intersection-union test is preferred over a likelihood ratio test, which was found to be rather conservative. Parameters were estimated quite accurately except for a slight overestimation of the distance between two close QTLs.