S. van der Beek

Covariance between relatives for a marked quantitative trait locus

Summary - Best linear unbiased prediction (BLUP) can be applied to marker-assisted selection. This application requires computation of the inverse of the conditional covariance matrix (Gof additive effects for the quantitative trait locus (QTL) linked to the marker locus (ML), given marker genotypes. This paper presents theory and algorithms to construct G and to obtain its inverse efficiently. These algorithms are suf&ciently general to accommodate situations (1) where paternal or maternal origin of marker alleles cannot be determined and (2) where the marker genotypes of some individuals in the pedigree are unknown. genetic marker / marker-assisted selection / best linear unbiased prediction / covariance between relatives / gametic relationship

Power of two- and three-generation QTL mapping experiments in an outbred population containing full-sib or half-sib families.

QTL mapping experiments involve many animals to be genotyped and performance tested. Consequently, experimental designs need to be optimized to minimize the costs of data collection and genotyping. The present study has analyzed the power and efficiency of experiments with two or three-generation family structures containing full-sib families, half-sib families, or both. The focus was on data from one outbred population because the main interest is to locate genes that can be used for within-line selection. For a two generation experiment more animals had to be typed for marker loci to obtain a certain power than for a three generation experiment. Fewer trait values, however, had to be obtained for a two-generation experiment than for a three-generation experiment. A two or three-generation family structure with full-sib offspring was more efficient than a two or three-generation family structure with half-sib offspring. A family structure with full-sib grand-offspring, however, was less efficient than a family structure with half-sib grand-offspring. For the most efficient family structure each pair of parents had full-sib offspring that were genotyped for the marker. For the most-efficient family structure each full-sib offspring had half-sib grand-offspring for which trait values were obtained. For equal power with a heritability of 0.1 and 100 grand-offspring per full-sib offspring, 30-times less marker typings were required for this most efficient family structure than for a two-generation half-sib structure in which marker genotypes and trait values were obtained for half-sib offspring. The effect of heritability and the type of analysis (single marker or interval analysis) on the efficiency of a family structure is described. The results of this study should help to design QTL mapping experiments in an outbred population.

Use of deterministic sampling for exploring likelihoods in linkage analysis for quantitative traits.

Deterministic sampling was used to numerically evaluate the expected log-likelihood surfaces of QTL-marker linkage models in large pedigrees with simple structures. By calculating the expected values of likelihoods, questions of power of experimental designs, bias in parameter estimates, approximate lower-bound standard errors of estimates and correlations among estimates, and suitability of statistical models were addressed. Examples illustrated that bracket markers around the QTL approximately halved the standard error of the recombination fraction between the QTL and the marker, although they did not affect the standard error of the QTLs effect, that overestimation of the distance between the markers caused overestimation of the distance between the QTL and marker, that more parameters in the model did not affect the accuracy of parameter estimates, that there was a moderate positive correlation between the estimates of the QTL effect and its recombination distance from the marker, and that selective genotyping did not introduce bias into the estimates of the parameters. The method is suggested as a useful tool for exploring the power and accuracy of QTL linkage experiments, and the value of alternative statistical models, whenever the likelihood of the model can be written explictly.

Criteria to optimize designs for detection and estimation of linkage between marker loci from segregating populations containing several families

Construction of a genome map of highly polymorphic markers has become possible in the past decade. Establishing a complete marker map is an enormous task. Therefore, designs to map molecular markers should be optimal. Designs to detect and estimate linkage between markers from segregating populations were studied. Two measures of design quality were used. The expectation of the maximum lod score indicates the possibility of designs to detect linkage. The accuracy of estimating recombination rate was measured as the probability that the true recombination rate is in a specified internal given the estimate. Accurate approximate methods were developed for rapid evaluation of designs. Seven family types (e.g., double backcross) can be distinguished that describe all families in a segregating population. The family type influences the expected maximum lod score and the accuracy of estimation. The frequency of favorable family types increased with increasing marker polymorphism. At a true recombination rate of 0.20,27 observations on offspring when five alleles were segregating, and 55 observations on offspring when two alleles were segregating, were necessary to obtain an expected maximum lod score of 3. The probability that the true recombination rate was between 0.15 and 0.25, given an estimate of 0.20, was about 0.85 for a design with 40 families with ten offspring and two alleles segregating and for a design with ten families with ten offspring and six alleles segregating. For smaller designs, accuracies were less, approximate evaluation of accuracy was not justified and, on average, true recombination rates were much greater than estimated given a specified value for the estimated recombination rate.SummaryConstruction of a genome map of highly polymorphic markers has become possible in the past decade. Establishing a complete marker map is an enormous task. Therefore, designs to map molecular markers should be optimal. Designs to detect and estimate linkage between markers from segregating populations were studied. Two measures of design quality were used. The expectation of the maximum lod score indicates the possibility of designs to detect linkage. The accuracy of estimating recombination rate was measured as the probability that the true recombination rate is in a specified internal given the estimate. Accurate approximate methods were developed for rapid evaluation of designs. Seven family types (e.g., double backcross) can be distinguished that describe all families in a segregating population. The family type influences the expected maximum lod score and the accuracy of estimation. The frequency of favorable family types increased with increasing marker polymorphism. At a true recombination rate of 0.20,27 observations on offspring when five alleles were segregating, and 55 observations on offspring when two alleles were segregating, were necessary to obtain an expected maximum lod score of 3. The probability that the true recombination rate was between 0.15 and 0.25, given an estimate of 0.20, was about 0.85 for a design with 40 families with ten offspring and two alleles segregating and for a design with ten families with ten offspring and six alleles segregating. For smaller designs, accuracies were less, approximate evaluation of accuracy was not justified and, on average, true recombination rates were much greater than estimated given a specified value for the estimated recombination rate.