MAPPING LINKED QUANTITATIVE TRAIT LOCI VIA RESIDUAL MAXIMUM-LIKELIHOOD

A residual maximum likelihood method is presented for estimation of th e positions and variance contributions of two linked QTLs. The method also provides tests for zero versus one QTL linked to a group of marke rs and for one versus two QTLs linked. A deterministic, derivative-fre e algorithm is employed. The variance-covariance matrix of the allelic effects at each QTL and its inverse is computed conditional on incomp lete information from multiple linked markers. Covariances between eff ects at different QTLs and between QTLs and polygenic effects are assu med to be zero. A simulation study was performed to investigate parame ter estimation and likelihood ratio tests. The design was a granddaugh ter design with 2 000 sons, 20 sires of sons and nine ancestors of sir es. Data were simulated under a normal-effects and a biallelic model f or variation at each QTL. Genotypes at five or nine equally spaced mar kers 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 se cond QTL exceeded 0.5 all the time for the 50% QTLs and when the dista nce was (at least 30 cM for the 25% QTLs. An intersection-union test i s 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.