title: A recursive procedure to compute the gametic relationship matrix and its inverse for marked QTL clusters.
abstract: Recently, a variety of mixed linear models have been proposed for marker-assisted prediction of the effects of quantitative trait loci (QTLs) in outbred populations of animals. One of them addresses the effects of a cluster of linked QTLs, or those of a particular chromosomal segment, marked by DNA marker(s) and requires that the inverse of the corresponding gametic relationship matrix whose elements are the conditional expected values of the identity-by-descent (IBD) proportions between gametes for individuals be evaluated. Here, for a model of this type, utilizing the property of the IBD set and using the information on the joint gametogenesis processes at the flanking marker loci, we present a recursive method to systematically calculate the elements of the gametic relationship matrix and its inverse. A numerical example is given to illustrate the proposed computing procedure.
authors.affiliation: Course of Environmental Management Science, Graduate School of Science and Technology, Niigata, Japan.
authors.forename: Hirokazu
authors.initials: H
authors.lastname: Matsuda
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Iwaisaki
mesh_terms: D000465:Algorithms; D000818:Animals; D000829:Animals, Domestic; D021461:Animals, Outbred Strains; D002874:Chromosome Mapping; D003198:Computer Simulation; D003433:Crosses, Genetic; D005718:Gametogenesis; D008040:Genetic Linkage; D005819:Genetic Markers; D005828:Genetics, Population; D016014:Linear Models; D008957:Models, Genetic; D015233:Models, Statistical; D040641:Quantitative Trait Loci; D019655:Quantitative Trait, Heritable; D013223:Statistics as Topic
chemical_list: D005819:Genetic Markers