Computing the condensed conditional gametic QTL relationship matrix and its inverse

C.f Baes ,Norbert Reinsch

doi:10.5194/aab-50-294-2007

Abstract

Abstract. The inverse of the conditional gametic relationship matrix (G-1) for a marked quantitative trait locus (MQTL) is required for estimation of gametic effects in best linear unbiased prediction (BLUP) of breeding values if marker data are available. Calculation of the "condensed" gametic relationship matrix G* – a version of G where linear dependencies have been removed – and its inverse G*-1 is described using a series of simplified equations following a known algorithm. The software program COBRA (covariance between relatives for a marked QTL) is introduced, and techniques for storing and computing the condensed gametic relationship matrix G* and the non-zero elements of its inverse are discussed. The program operates with both simple pedigrees and those augmented by transmission probabilities derived from marker data. Using sparse matrix storage techniques, G* and its inverse can be efficiently stored in computer memory. COBRA is written in FORTRAN 90/95 and runs on a variety of computers. Pedigree data and information for a single MQTL in the German Holstein population are used to test the efficiency of the program.

Highlights

The joint utilization of marker and phenotype information in current genetic prediction models is evolving rapidly. FERNANDO and GROSSMAN (1989) incorporated marked quantitative trait loci (MQTL) information into the existing best linear unbiased prediction (BLUP) breeding value estimation model by splitting the ‘genetic’portion of the model into the additive effects of the unique QTL gametes and the polygenic effects
TUCHSCHERER et al (2004) showed that the calculation of G depends on the mode of gamete identification, the final MA BLUP breeding value of each animal is identical irrespective of the gamete identification method employed
The generalisation developed by TUCHSCHERER et al (2004) showed that under certain circumstances identical rows and columns in G may occur if parents pass identical copies of their gametes to their offspring (i.e. G may be rank deficient); in such cases, the inverse matrix G−1 is not defined

Summary

Introduction

The joint utilization of marker and phenotype information in current genetic prediction models is evolving rapidly. FERNANDO and GROSSMAN (1989) incorporated marked quantitative trait loci (MQTL) information into the existing best linear unbiased prediction (BLUP) breeding value estimation model by splitting the ‘genetic’. TUCHSCHERER et al (2004) showed that the calculation of G depends on the mode of gamete identification (gametes identified by markers vs gametes identified by parental origin), the final MA BLUP breeding value of each animal is identical irrespective of the gamete identification method employed. They suggested that gamete identification by parental origin may have practical advantages compared to that by markers; for example, fewer values are required to denote marker related transmission probabilities. Two values (paternal and maternal) represent all four possible probabilities

Method

Findings

Discussion