Impact of prior specifications in a shrinkage-inducing Bayesian model for quantitative trait mapping and genomic prediction.

BACKGROUND: In quantitative trait mapping and genomic prediction, Bayesian variable selection methods have gained popularity in conjunction with the increase in marker data and computational resources. Whereas shrinkage-inducing methods are common tools in genomic prediction, rigorous decision making in mapping studies using such models is not well established and the robustness of posterior results is subject to misspecified assumptions because of weak biological prior evidence. METHODS: Here, we evaluate the impact of prior specifications in a shrinkage-based Bayesian variable selection method which is based on a mixture of uniform priors applied to genetic marker effects that we presented in a previous study. Unlike most other shrinkage approaches, the use of a mixture of uniform priors provides a coherent framework for inference based on Bayes factors. To evaluate the robustness of genetic association under varying prior specifications, Bayes factors are compared as signals of positive marker association, whereas genomic estimated breeding values are considered for genomic selection. The impact of specific prior specifications is reduced by calculation of combined estimates from multiple specifications. A Gibbs sampler is used to perform Markov chain Monte Carlo estimation (MCMC) and a generalized expectation-maximization algorithm as a faster alternative for maximum a posteriori point estimation. The performance of the method is evaluated by using two publicly available data examples: the simulated QTLMAS XII data set and a real data set from a population of pigs. RESULTS: Combined estimates of Bayes factors were very successful in identifying quantitative trait loci, and the ranking of Bayes factors was fairly stable among markers with positive signals of association under varying prior assumptions, but their magnitudes varied considerably. Genomic estimated breeding values using the mixture of uniform priors compared well to other approaches for both data sets and loss of accuracy with the generalized expectation-maximization algorithm was small as compared to that with MCMC. CONCLUSIONS: Since no error-free method to specify priors is available for complex biological phenomena, exploring a wide variety of prior specifications and combining results provides some solution to this problem. For this purpose, the mixture of uniform priors approach is especially suitable, because it comprises a wide and flexible family of distributions and computationally intensive estimation can be carried out in a reasonable amount of time.

Genetic analysis of complex traits via Bayesian variable selection: the utility of a mixture of uniform priors.

A new estimation-based Bayesian variable selection approach is presented for genetic analysis of complex traits based on linear or logistic regression. By assigning a mixture of uniform priors (MU) to genetic effects, the approach provides an intuitive way of specifying hyperparameters controlling the selection of multiple influential loci. It aims at avoiding the difficulty of interpreting assumptions made in the specifications of priors. The method is compared in two real datasets with two other approaches, stochastic search variable selection (SSVS) and a re-formulation of Bayes B utilizing indicator variables and adaptive Student's t-distributions (IAt). The Markov Chain Monte Carlo (MCMC) sampling performance of the three methods is evaluated using the publicly available software OpenBUGS (model scripts are provided in the Supplementary material). The sensitivity of MU to the specification of hyperparameters is assessed in one of the data examples.

Adaptive potential of northernmost tree populations to climate change, with emphasis on Scots pine (Pinus sylvestris L.).

The adaptive potential of the northernmost Pinus sylvestris L. (and other northern tree) populations is considered by examining first the current patterns of quantitative genetic adaptive traits, which show high population differentiation and clines. We then consider the postglacial history of the populations using both paleobiological and genetic data. The current patterns of diversity at nuclear genes suggest that the traces of admixture are mostly visible in mitochondrial DNA variation patterns. There is little evidence of increased diversity due to admixture between an eastern and western colonization lineage, but no signal of reduced diversity (due to sequential bottlenecks) either. Quantitative trait variation in the north is not associated with the colonizing lineages. The current clines arose rapidly and may be based on standing genetic variation. The initial phenotypic response of Scots pine in the north is predicted to be increased survival and growth. The genetic responses are examined based on quantitative genetic predictions of sustained selection response and compared with earlier simulation results that have aimed at more ecological realism. The phenotypic responses of increased growth and survival reduce the opportunity for selection and delay the evolutionary responses. The lengthening of the thermal growing period also causes selection on the critical photoperiod in the different populations. Future studies should aim at including multiple ecological and genetic factors in evaluating potential responses.

Demographic history has influenced nucleotide diversity in European Pinus sylvestris populations.

To infer the role of natural selection in shaping standing genetic diversity, it is necessary to assess the genomewide impact of demographic history on nucleotide diversity. In this study we analyzed sequence diversity of 16 nuclear loci in eight Pinus sylvestris populations. Populations were divided into four geographical groups on the basis of their current location and the geographical history of the region: northern Europe, central Europe, Spain, and Turkey. There were no among-group differences in the level of silent nucleotide diversity, which was approximately 0.005/bp in all groups. There was some evidence that linkage disequilibrium extended further in northern Europe than in central Europe: the estimates of the population recombination rate parameter, rho, were 0.0064 and 0.0294, respectively. The summary statistics of nucleotide diversity in central and northern European populations were compatible with an ancient bottleneck rather than the standard neutral model.