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Background  Genomic prediction of purebred animals for crossbred performance can be based on a model that estimates effects of single nucleotide polymorphisms (SNPs) in purebreds on crossbred performance. For crossbred performance, SNP effects might be breed-specific due to differences between breeds in allele frequencies and linkage disequilibrium patterns between SNPs and quantitative trait loci. Accurately tracing the breed-of-origin of alleles (BOA) in three-way crosses is possible with a recently developed procedure called BOA. A model that accounts for breed-specific SNP effects (BOA model), has never been tested empirically on a three-way crossbreeding scheme. Therefore, the objectives of this study were to evaluate the estimates of variance components and the predictive accuracy of the BOA model compared to models in which SNP effects for crossbred performance were assumed to be the same across breeds, using either breed-specific allele frequencies (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Amodel) or allele frequencies averaged across breeds (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  Bmodel). In this study, we used data from purebred and three-way crossbred pigs on average daily gain (ADG), back fat thickness (BF), and loin depth (LD).    Results  Estimates of variance components for crossbred performance from the BOA model were mostly similar to estimates from models    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Aand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  B. Heritabilities for crossbred performance ranged from 0.24 to 0.46 between traits. Genetic correlations between purebred and crossbred performance (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{r}}_{\text{pc}}$$\end{document}    r  pc) across breeds ranged from 0.30 to 0.62 for ADG and from 0.53 to 0.74 for BF and LD. For ADG, prediction accuracies of the BOA model were higher than those of the    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Aand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  Bmodels, with significantly higher accuracies only for one maternal breed. For BF and LD, prediction accuracies of models    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Aand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  Bwere higher than those of the BOA model, with no significant differences. Across all traits, models    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Aand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  Byielded similar predictions.    Conclusions  The BOA model yielded a higher prediction accuracy for ADG in one maternal breed, which had the lowest    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{r}}_{\text{pc}}$$\end{document}    r  pc(0.30). Using the BOA model was especially relevant for traits with a low    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{r}}_{\text{pc}}$$\end{document}    r  pc. In all other cases, the use of crossbred information in models    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{A}}$$\end{document}    G  Aand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${\text{G}}_{\text{B}}$$\end{document}    G  B, does not jeopardize predictions and these models are more easily implemented than the BOA model.    Electronic supplementary material  The online version of this article (doi:10.1186/s12711-017-0350-1) contains supplementary material, which is available to authorized users.

Genomic evaluation for a three-way crossbreeding system considering breed-of-origin of alleles