Quantitative trait locus analysis of hybrid pedigrees: variance-components model, inbreeding parameter, and power

Abstract

Background: For the last years reliable mapping of quantitative trait loci (QTLs) has become feasible through linkage analysis based on the variance-components method. There are now many approaches to the QTL analysis of various types of crosses within one population (breed) as well as crosses between divergent populations (breeds). However, to analyse a complex pedigree with dominance and inbreeding, when the pedigree's founders have an inter-population (hybrid) origin, it is necessary to develop a high-powered method taking into account these features of the pedigree.

Results: We offer a universal approach to QTL analysis of complex pedigrees descended from crosses between outbred parental lines with different QTL allele frequencies. This approach improves the established variance-components method due to the consideration of the genetic effect conditioned by inter-population origin and inbreeding of individuals. To estimate model parameters, namely additive and dominant effects, and the allelic frequencies of the QTL analysed, and also to define the QTL positions on a chromosome with respect to genotyped markers, we used the maximum-likelihood method. To detect linkage between the QTL and the markers we propose statistics with a non-central chi2-distribution that provides the possibility to deduce analytical expressions for the power of the method and therefore, to estimate the pedigree's size required for 80% power. The method works for arbitrarily structured pedigrees with dominance and inbreeding.

Conclusion: Our method uses the phenotypic values and the marker information for each individual of the pedigree under observation as initial data and can be valuable for fine mapping purposes. The power of the method is increased if the QTL effects conditioned by inter-population origin and inbreeding are enhanced. Several improvements can be developed to take into account fixed factors affecting trait formation, such as age and sex.

Figure 1

Pedigrees including the shortest inbred loop with a single and two common ancestors and pedigrees without the loop. a, b) Pedigrees with and without the loop formed as a result of inbred cross between parent and offspring, respectively. c, d) Pedigrees with and without the loop formed as a result of inbred cross between sibs, respectively.

Figure 2

Bar graphs for W₁ and W₂ statistical characteristics depending on the sample size at the QTL position 5 cM. Bar graphs hatched by bold lines correspond to characteristic W₁; bar graphs hatched by thin lines correspond to characteristic W₂; vertical lines are intended for the method realized by software Qxpak; horizontal lines are intended for the method proposed in this study.

Figure 3

Bar graphs for W₁ and W₂ statistical characteristics depending on the sample size at the QTL position 10 cM. Bar graphs hatched by bold lines correspond to characteristic W₁; bar graphs hatched by thin lines correspond to characteristic W₂; vertical lines are intended for the method realized by software Qxpak; horizontal lines are intended for the method proposed in this study.