Study of the optimum haplotype length to build genomic relationship matrices

Abstract

Background

As genomic data becomes more abundant, genomic prediction is more routinely used to estimate breeding values. In genomic prediction, the relationship matrix ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{A}}$$\end{document} ), which is traditionally used in genetic evaluations is replaced by the genomic relationship matrix ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document} ). This paper considers alternative ways of building relationship matrices either using single markers or haplotypes of different lengths. We compared the prediction accuracies and log-likelihoods when using these alternative relationship matrices and the traditional \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document} matrix, for real and simulated data.

Methods

For real data, we built relationship matrices using 50k genotype data for a population of Brahman cattle to analyze three traits: scrotal circumference (SC), age at puberty (AGECL) and weight at first corpus luteum (WTCL). Haplotypes were phased with hsphase and imputed with BEAGLE. The relationship matrices were built using three methods based on haplotypes of different lengths. The log-likelihood was considered to define the optimum haplotype lengths for each trait and each haplotype-based relationship matrix.

Results

Based on simulated data, we showed that the inverse of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document} matrix and the inverse of the haplotype relationship matrices for methods using one-single nucleotide polymorphism (SNP) phased haplotypes provided coefficients of determination (R ²) close to 1, although the estimated genetic variances differed across methods. Using real data and multiple SNPs in the haplotype segments to build the relationship matrices provided better results than the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document} matrix based on one-SNP haplotypes. However, the optimal haplotype length to achieve the highest log-likelihood depended on the method used and the trait. The optimal haplotype length (7 to 8 SNPs) was similar for SC and AGECL. One of the haplotype-based methods achieved the largest increase in log-likelihood for SC, i.e. from −1330 when using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{G}}$$\end{document} to −1325 when using haplotypes with eight SNPs.

Conclusions

Building the relationship matrix by using haplotypes that comprise multiple SNPs will increase the accuracy of estimated breeding values. However, the optimum haplotype length that shows the correct relationship among individuals for each trait can be derived from the data.