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Abstract
Markov chain Monte Carlo (MCMC) methods have been proposed to overcome computational problems in linkage and segregation analyses. This approach involves sampling genotypes at the marker and trait loci. Among MCMC methods, scalar-Gibbs is the easiest to implement, and it is used in genetics. However, the Markov chain that corresponds to scalar-Gibbs may not be irreducible when the marker locus has more than two alleles, and even when the chain is irreducible, mixing has been observed to be slow. Joint sampling of genotypes has been proposed as a strategy to overcome these problems. An algorithm that combines the Elston-Stewart algorithm and iterative peeling (ESIP sampler) to sample genotypes jointly from the entire pedigree is used in this study. Here, it is shown that the ESIP sampler yields an irreducible Markov chain, regardless of the number of alleles at a locus. Further, results obtained by ESIP sampler are compared with other methods in the literature. Of the methods that are guaranteed to be irreducible, ESIP was the most efficient.
Highlights
QTL mapping includes the estimation of the locations of QTL, of the magnitudes of the QTL effects, and of the frequencies of QTL alleles
Results obtained by the ESIP and Sheehan-Thomas samplers were compared to the true marginal probabilities
Sheehan and Thomas [24] explained that there is a trade-off between the size of the relaxation parameter and efficiency of the algorithm
Summary
QTL mapping includes the estimation of the locations of QTL, of the magnitudes of the QTL effects, and of the frequencies of QTL alleles. When QTL genotypes cannot be observed, marker genotypes are used together with trait phenotypes to map QTL by marker-QTL linkage analysis. The mixed model of inheritance is used in linkage analyses. Under this model, the trait is assumed to be influenced by a single QTL linked to a marker (MQTL) and the remaining QTL are assumed to be unlinked to the marker (RQTL). The additive effects of the RQTL are usually assumed to be normally distributed. Under this model the marker-MQTL parameters can be estimated by likelihood or Bayesian approaches
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