The covariance between relatives conditional on genetic markers

Abstract

-The development of molecular genotyping techniques makes it possible to analyze quantitative traits on the basis of individual loci. With marker information, the classical theory of estimating the genetic covariance between relatives can be reformulated to improve the accuracy of estimation. In this study, an algorithm was derived for computing the conditional covariance between relatives given genetic markers. Procedures for calculating the conditional relationship coefficients for additive, dominance, additive by additive, additive by dominance, dominance by additive and dominance by dominance effects were developed. The relationship coefficients were computed based on conditional QTL allelic transmission probabilities, which were inferred from the marker allelic transmission probabilities. An example data set with pedigree and linked markers was used to demonstrate the methods developed. Although this study dealt with two QTLs coupled with linked markers, the same principle can be readily extended to the situation of multiple QTL. The treatment of missing marker information and unknown linkage phase between markers for calculating the covariance between relatives was discussed.covariance between relatives / molecular marker / QTL / transmission probability / relationship matrix

Estimation of Quantitative Trait Loci Parameters for Milk Production Traits in German Holstein Dairy Cattle Population

“…The main advantage of the deterministic approach lies in its speed of computation; however, no method exists at present that is able to use all available marker haplotype and pedigree information. Pong-Wong et al (2001) and Liu et al (2002) proposed methods that can account for a marker bracket. The multiple marker approach was developed by Almasy and Blangero (1998), but it was only applicable to special types of relationships between individuals.…”

“…The mixed inheritance model with random oligogenic (i.e., originating from QTL) and polygenic effects has been regarded as a promising statistical description of genetic variation of quantitative traits (George et al, 2000;Meuwissen and Goddard, 2001;Liu et al, 2002;de Koning et al, 2003;Freyer et al, 2003). The possibility of incorporating information on (co)variances between individuals on average genome level (i.e., polygenic) as well as at a specific position within genome (i.e., QTL) directly into the statistical model is especially suited for data with complex multigenerational pedigrees such as in dairy cattle, whereas statistical models with fixed QTL effects are less realistic approximations of the underlying modes of inheritance for outbred populations.…”

Opportunities for genome-wide selection for pig breeding in developing countries1

“…This ignores the existence of linkage between marker allele and a QTL affecting a trait under selection. With the availability of genomic information, inbreeding can be calculated such that the expectation is adjusted with identity-by-state probabilities at the marker loci to yield actual inbreeding at specific locations across the genome (Pong-Wong et al, 2001;Liu et al, 2002), and if GS can result in shorter generation intervals in swine breeding, then the rate of inbreeding per unit of time might differ from what is expected.…”

Inbreeding in genome‐wide selection

“…When inbreeding is calculated from genotypic data, the expectation is adjusted with identity-bystate probabilities at the marker loci to yield actual inbreeding at specific locations across the genome (Pong-Wong et al 2001;Liu et al 2002;Roughsedge et al 2006). The increasing amount of genotypic data available will lead to new methods for calculating inbreeding which could give an indication of the effect of linkage on the accumulation of localized inbreeding across the genome.…”