Abstract
The inverse of the gametic covariance matrix between relatives, G-1, for a marked quantitative trait locus (QTL) is required in best linear unbiased prediction (BLUP) of breeding values if marker data are available on a QTL. A rapid method for computing the inverse of a gametic relationship matrix for a marked QTL without building G itself is presented. The algorithm is particularly useful due to the approach taken in computing inbreeding coefficients by having to compute only few elements of G. Numerical techniques for determining, storing, and computing the required elements of G and the nonzero elements of the inverse are discussed. We show that the subset of G required for computing the inbreeding coefficients and hence the inverse is a tiny proportion of the whole matrix and can be easily stored in computer memory using sparse matrix storage techniques. We also introduce an algorithm to determine the maximum set of nonzero elements that can be found in G-1 and a strategy to efficiently store and access them. Finally, we demonstrate that the inverse can be efficiently built using the present techniques for very large and inbred populations.
Highlights
The utilization of marker quantitative trait loci associations in genetic evaluation is possible and likely to be used more extensively in the future
Marked quantitative trait locus (QTL) alleles were considered random in the context of the mixed model terminology, and algorithms to construct and invert the covariance matrix pertaining to QTL additive effects were developed
An algorithm to directly build the inverse of a conditional gametic relationship matrix, from given marker data, was developed
Summary
The utilization of marker quantitative trait loci associations in genetic evaluation is possible and likely to be used more extensively in the future. Many authors have estimated gain through marker-assisted selection, e.g. Marker information will not replace phenotypic records because a full prediction of phenotype from DNA sequence is still far from achievable [3]. Joint utilization of marker and phenotype information in current genetic prediction models is, progressing at a rapid pace. Fernando and Grossman [2]. Marked QTL alleles were considered random in the context of the mixed model terminology, and algorithms to construct and invert the covariance matrix pertaining to QTL additive effects were developed
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