Linear models for joint association and linkage QTL mapping

<p>Abstract</p> <p>Background</p> <p>Populational linkage disequilibrium and within-family linkage are commonly used for QTL mapping and marker assisted selection. The combination of both results in more robust and accurate locations of the QTL, but models proposed so far have been either single marker, complex in practice or well fit to a particular family structure.</p> <p>Results</p> <p>We herein present linear model theory to come up with additive effects of the QTL alleles in any member of a general pedigree, conditional to observed markers and pedigree, accounting for possible linkage disequilibrium among QTLs and markers. The model is based on association analysis in the founders; further, the additive effect of the QTLs transmitted to the descendants is a weighted (by the probabilities of transmission) average of the substitution effects of founders' haplotypes. The model allows for non-complete linkage disequilibrium QTL-markers in the founders. Two submodels are presented: a simple and easy to implement Haley-Knott type regression for half-sib families, and a general mixed (variance component) model for general pedigrees. The model can use information from all markers. The performance of the regression method is compared by simulation with a more complex IBD method by Meuwissen and Goddard. Numerical examples are provided.</p> <p>Conclusion</p> <p>The linear model theory provides a useful framework for QTL mapping with dense marker maps. Results show similar accuracies but a bias of the IBD method towards the center of the region. Computations for the linear regression model are extremely simple, in contrast with IBD methods. Extensions of the model to genomic selection and multi-QTL mapping are straightforward.</p

Comparison of alternative approaches to single-trait genomic prediction using genotyped and non-genotyped Hanwoo beef cattle.

BackgroundGenomic predictions from BayesA and BayesB use training data that include animals with both phenotypes and genotypes. Single-step methodologies allow additional information from non-genotyped relatives to be included in the analysis. The single-step genomic best linear unbiased prediction (SSGBLUP) method uses a relationship matrix computed from marker and pedigree information, in which missing genotypes are imputed implicitly. Single-step Bayesian regression (SSBR) extends SSGBLUP to BayesB-like models using explicitly imputed genotypes for non-genotyped individuals.MethodsCarcass records included 988 genotyped Hanwoo steers with 35,882 SNPs and 1438 non-genotyped steers that were measured for back-fat thickness (BFT), carcass weight (CWT), eye-muscle area, and marbling score (MAR). Single-trait pedigree-based BLUP, Bayesian methods using only genotyped individuals, SSGBLUP and SSBR methods were compared using cross-validation.ResultsMethods using genomic information always outperformed pedigree-based BLUP when the same phenotypic data were modeled from either genotyped individuals only or both genotyped and non-genotyped individuals. For BFT and MAR, accuracies were higher with single-step methods than with BayesB, BayesC and BayesCπ. Gains in accuracy with the single-step methods ranged from +0.06 to +0.09 for BFT and from +0.05 to +0.07 for MAR. For CWT, SSBR always outperformed the corresponding Bayesian methods that used only genotyped individuals. However, although SSGBLUP incorporated information from non-genotyped individuals, prediction accuracies were lower with SSGBLUP than with BayesC (π = 0.9999) and BayesB (π = 0.98) for CWT because, for this particular trait, there was a benefit from the mixture priors of the effects of the single nucleotide polymorphisms.ConclusionsSingle-step methods are the preferred approaches for prediction combining genotyped and non-genotyped animals. Alternative priors allow SSBR to outperform SSGBLUP in some cases

An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops

<p>Abstract</p> <p>Background</p> <p>Marginal posterior genotype probabilities need to be computed for genetic analyses such as geneticcounseling in humans and selective breeding in animal and plant species.</p> <p>Methods</p> <p>In this paper, we describe a peeling based, deterministic, exact algorithm to compute efficiently genotype probabilities for every member of a pedigree with loops without recourse to junction-tree methods from graph theory. The efficiency in computing the likelihood by peeling comes from storing intermediate results in multidimensional tables called cutsets. Computing marginal genotype probabilities for individual <it>i </it>requires recomputing the likelihood for each of the possible genotypes of individual <it>i</it>. This can be done efficiently by storing intermediate results in two types of cutsets called anterior and posterior cutsets and reusing these intermediate results to compute the likelihood.</p> <p>Examples</p> <p>A small example is used to illustrate the theoretical concepts discussed in this paper, and marginal genotype probabilities are computed at a monogenic disease locus for every member in a real cattle pedigree.</p