Bayesian methods for estimating GEBVs of threshold traits

Abstract

Estimation of genomic breeding values is the key step in genomic selection (GS). Many methods have been proposed for continuous traits, but methods for threshold traits are still scarce. Here we introduced threshold model to the framework of GS, and specifically, we extended the three Bayesian methods BayesA, BayesB and BayesCp on the basis of threshold model for estimating genomic breeding values of threshold traits, and the extended methods are correspondingly termed BayesTA, BayesTB and BayesTCp. Computing procedures of the three BayesT methods using Markov Chain Monte Carlo algorithm were derived. A simulation study was performed to investigate the benefit of the presented methods in accuracy with the genomic estimated breeding values (GEBVs) for threshold traits. Factors affecting the performance of the three BayesT methods were addressed. As expected, the three BayesT methods generally performed better than the corresponding normal Bayesian methods, in particular when the number of phenotypic categories was small. In the standard scenario (number of categories ¼ 2, incidence ¼ 30%, number of quantitative trait loci ¼ 50, h 2 ¼ 0.3), the accuracies were improved by 30.4%, 2.4%, and 5.7% points, respectively. In most scenarios, BayesTB and BayesTCp generated similar accuracies and both performed better than BayesTA. In conclusion, our work proved that threshold model fits well for predicting GEBVs of threshold traits, and BayesTCp is supposed to be the method of choice for GS of threshold traits.

Bayesian methods for jointly estimating genomic breeding values of one continuous and one threshold trait

“…It has been generally accepted that the number of QTL controlling traits of interest affects the accuracy of genomic prediction by Bayesian methods [8,11,25,26]. This was also confirmed by our results.…”

Priors in Whole-Genome Regression: The Bayesian Alphabet Returns

“…An almost empty hiatus spans from letters D to R (Erbe et al 2012) with Bayes RS emerging even more recently (Brondum et al 2012). Wang et al (2013) presented Bayes TA, TB, and TCp, extensions of the corresponding letters to threshold models. The upper bound of the alphabet seems to have been defined by Larry Schaeffer (personal communication, Interbull Meeting, Guelph, 2011) when he threatened attendants of this conference with Bayes Z-D, although full details have not been published yet.…”

Fast Genomic Predictions via Bayesian G-BLUP and Multilocus Models of Threshold Traits Including Censored Gaussian Data

“…, Meijering and Gianola 1985; Wang et al 2013). The problem with the former procedure is that it loses the information contained by the extra categories, whereas in the latter method the model is in effect not compatible with the data.…”

“…A threshold model for BLUP with fixed thresholds has been covered by Gianola (1982) and with unknown, estimated threshold positions by Sorensen et al (1995). Multilocus association models of binary and ordinal traits have been considered by Hoti and Sillanpää (2006), Iwata et al (2009), González-Recio et al (2009), González-Recio and Forni (2011), and Wang et al (2013). Furthermore, the threshold approach for censored observations has been considered by Broman (2003), within BLUP context by Sorensen et al (1998), and with multilocus association models by Sillanpää and Hoti (2007) and Iwata et al (2009).…”

“…, Park and Casella 2008; Kärkkäinen and Sillanpää 2012a) as a representative of a multilocus association model with variable regularization, and show that in case of a binary, ordinal, or censored Gaussian phenotype the same additional latent variable layer can be plugged into both types of the genomic selection models. In fact, the additional latent variable layer can be subsumed into legions of different linear Gaussian models; Wang et al (2013) have used it with BayesA, BayesB, and BayesC π , whereas in our previous work (Kärkkäinen and Sillanpää 2012a) we incorporated a binary threshold-based latent layer into 13 distinct models, including a Bayesian G-BLUP, BayesA, BayesB and both hierarchical and nonhierarchical Bayesian LASSO. In this work, we exemplify the threshold method with a hierarchical Bayesian LASSO as it proved the best working model in the aforementioned previous work and, on the other hand, we did not want to pick anything lesser known, such as the extended Bayesian LASSO (introduced by Mutshinda and Sillanpää 2010, used successfully, e.g.…”