Linkage disequilibrium in two-stage marker-assisted selection

Introduction DNA markers on genetic linkage maps can be used to search for quantitative trait loci (QTL) which affect economically important traits in breeding populations. Several such QTL have already been found in cattle ( Cowan et al. 1990 ; Ron et al. 1994 ; Georges et al. 1995 ; Blattman et al. 1996 ). One way of utilizing this information is marker‐assisted selection (MAS) ( Soller 1978; Soller & Beckmann 1983; Lande & Thompson 1990) to increase the accuracy of selection and improve genetic merit of livestock. Dairy cattle provide a particular opportunity for markers to be used to distinguish between full sibs prior to entry into progeny testing. Pre‐sorting based on markers within animals of identical pedigree should provide an additional selection round and improve the merits of animals entering progeny test ( Kashi et al. 1990 ; Ruane & ; Colleau 1995) . Bulmer (1971) has shown that directional selection induces negative gametic disequilibrium. The use of MAS may lower the total genetic response compared with traditional selection schemes because of this disequilibrium ( Gibson et al. 1990 ; Gomez‐Raya & Gibson 1993; Spelman & Garrick 1997). In this paper preselection based on marker genotypes within full sibs selected on pedigree merit as a strategy to improve the genetic merit of progeny‐tested sires is investigated. In particular, the disequilibrium induced by this scheme is compared with that expected from the traditional pedigree selection of candidates. Methods Genetic model A single sex‐limited trait (phenotype P) with a polygenic component (PG), a non‐genetic component (NG), and two QTL physically unlinked to the polygenes or to each other (QTL1, QTL2) was modelled. The phenotypic data and estimated breeding values (EBV) were a linear combination of these terms. Polygenic effects in the base population were generated from a normal distribution. Polygenic variance was derived assuming a polygenic heritability () of 0.3, defined as the ratio of the polygenic variance to the sum of the polygenic and non‐genetic variance. The non‐genetic component was generated from an independent normal distribution. The variance of the non‐genetic component was derived without inclusion of QTL effects and was thus not dependent on changes of genetic variance due to QTL allele frequencies. The two QTL were modelled as additive, diallelic and physically unlinked. QTL alleles were assumed to be completely identified by the use of close flanking markers and to