Bayesian adaptive Markov chain Monte Carlo estimation of genetic parameters.

Accurate and fast estimation of genetic parameters that underlie quantitative traits using mixed linear models with additive and dominance effects is of great importance in both natural and breeding populations. Here, we propose a new fast adaptive Markov chain Monte Carlo (MCMC) sampling algorithm for the estimation of genetic parameters in the linear mixed model with several random effects. In the learning phase of our algorithm, we use the hybrid Gibbs sampler to learn the covariance structure of the variance components. In the second phase of the algorithm, we use this covariance structure to formulate an effective proposal distribution for a Metropolis-Hastings algorithm, which uses a likelihood function in which the random effects have been integrated out. Compared with the hybrid Gibbs sampler, the new algorithm had better mixing properties and was approximately twice as fast to run. Our new algorithm was able to detect different modes in the posterior distribution. In addition, the posterior mode estimates from the adaptive MCMC method were close to the REML (residual maximum likelihood) estimates. Moreover, our exponential prior for inverse variance components was vague and enabled the estimated mode of the posterior variance to be practically zero, which was in agreement with the support from the likelihood (in the case of no dominance). The method performance is illustrated using simulated data sets with replicates and field data in barley.

Bayesian prediction of breeding values by accounting for genotype-by-environment interaction in self-pollinating crops.

In self-pollinating populations, individuals are characterized by a high degree of inbreeding. Additionally, phenotypic observations are highly influenced by genotype-by-environment interaction effects. Usually, Bayesian approaches to predict breeding values (in self-pollinating crops) omit genotype-by-environment interactions in the statistical model, which may result in biased estimates. In our study, a Bayesian Gibbs sampling algorithm was developed that is adapted to the high degree of inbreeding in self-pollinated crops and accounts for interaction effects between genotype and environment. As related lines are supposed to show similar genotype-by-environment interaction effects, an extended genetic relationship matrix is included in the Bayesian model. Additionally, since the coefficient matrix C in the mixed model equations can be characterized by rank deficiencies, the pseudoinverse of C was calculated by using the nullspace, which resulted in a faster computation time. In this study, field data of spring barley lines and data of a 'virtual' parental population of self-pollinating crops, generated by computer simulation, were used. For comparison, additional breeding values were predicted by a frequentist approach. In general, standard Bayesian Gibbs sampling and a frequentist approach resulted in similar estimates if heritability of the regarded trait was high. For low heritable traits, the modified Bayesian model, accounting for relatedness between lines in genotype-by-environment interaction, was superior to the standard model.