Predicting the impact of genotype-by-genotype interaction on the purebred–crossbred genetic correlation from phenotype and genotype marker data of parental lines

Abstract

Background

The genetic correlation between purebred (PB) and crossbred (CB) performances ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} ) partially determines the response in CB when selection is on PB performance in the parental lines. An earlier study has derived expressions for an upper and lower bound of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} , using the variance components of the parental purebred lines, including e.g. the additive genetic variance in the sire line for the trait expressed in one of the dam lines. How to estimate these variance components is not obvious, because animals from one parental line do not have phenotypes for the trait expressed in the other line. Thus, the aim of this study was to propose and compare three methods for approximating the required variance components. The first two methods are based on (co)variances of genomic estimated breeding values (GEBV) in the line of interest, either accounting for shrinkage (VC _GEBV-S) or not (VC _GEBV). The third method uses restricted maximum likelihood (REML) estimates directly from univariate and bivariate analyses (VC _REML) by ignoring that the variance components should refer to the line of interest, rather than to the line in which the trait is expressed. We validated these methods by comparing the resulting predicted bounds of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} estimated from PB and CB data for five traits in a three-way cross in pigs.

Results

With both VC _GEBV and VC _REML, the estimated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} (plus or minus one standard error) was between the upper and lower bounds in 14 out of 15 cases. However, the range between the bounds was much smaller with VC _REML (0.15–0.22) than with VC _GEBV (0.44–0.57). With VC _GEBV-S, the estimated \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} was between the upper and lower bounds in only six out of 15 cases, with the bounds ranging from 0.21 to 0.44.

Conclusions

We conclude that using REML estimates of variance components within and between parental lines to predict the bounds of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} resulted in better predictions than methods based on GEBV. Thus, we recommend that the studies that estimate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{pc}$$\end{document} with genotype data also report estimated genetic variance components within and between the parental lines.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12711-022-00773-z.