Compatibility of pedigree-based and marker-based relationship matrices for single-step genetic evaluation

Ole F Christensen

doi:10.1186/1297-9686-44-37

Abstract

BackgroundSingle-step methods provide a coherent and conceptually simple approach to incorporate genomic information into genetic evaluations. An issue with single-step methods is compatibility between the marker-based relationship matrix for genotyped animals and the pedigree-based relationship matrix. Therefore, it is necessary to adjust the marker-based relationship matrix to the pedigree-based relationship matrix. Moreover, with data from routine evaluations, this adjustment should in principle be based on both observed marker genotypes and observed phenotypes, but until now this has been overlooked. In this paper, I propose a new method to address this issue by 1) adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix instead of the reverse and 2) extending the single-step genetic evaluation using a joint likelihood of observed phenotypes and observed marker genotypes. The performance of this method is then evaluated using two simulated datasets.ResultsThe method derived here is a single-step method in which the marker-based relationship matrix is constructed assuming all allele frequencies equal to 0.5 and the pedigree-based relationship matrix is constructed using the unusual assumption that animals in the base population are related and inbred with a relationship coefficient γ and an inbreeding coefficient γ / 2. Taken together, this γ parameter and a parameter that scales the marker-based relationship matrix can handle the issue of compatibility between marker-based and pedigree-based relationship matrices. The full log-likelihood function used for parameter inference contains two terms. The first term is the REML-log-likelihood for the phenotypes conditional on the observed marker genotypes, whereas the second term is the log-likelihood for the observed marker genotypes. Analyses of the two simulated datasets with this new method showed that 1) the parameters involved in adjusting marker-based and pedigree-based relationship matrices can depend on both observed phenotypes and observed marker genotypes and 2) a strong association between these two parameters exists. Finally, this method performed at least as well as a method based on adjusting the marker-based relationship matrix.ConclusionsUsing the full log-likelihood and adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix provides a new and interesting approach to handle the issue of compatibility between the two matrices in single-step genetic evaluation.

Highlights

Single-step methods for genetic evaluation [1,2,3] have recently become popular because they provide an approach to incorporate genomic information into genetic evaluations that is both coherent and conceptually simple
This work explores two possibilities to solve the problem, i.e. 1) in which the pedigree-based relationship matrix is adjusted to the marker-based relationship matrix and 2) in which the single-step genetic evaluation is extended by using a joint likelihood of observed phenotypes and observed marker genotypes. This results in a single-step method in which the marker-based relationship matrix is constructed assuming all allele frequencies are equal to 0.5 and the pedigree-based relationship matrix is constructed using the unusual assumption that animals in the base population are related and inbreed with a relationship coefficient γ and an inbreeding coefficient γ /2
The first term is the REML-log-likelihood for the phenotypes conditional on the observed marker genotypes and the second term is the log-likelihood for the observed marker genotypes

Summary

Introduction

Single-step methods for genetic evaluation [1,2,3] have recently become popular because they provide an approach to incorporate genomic information into genetic evaluations that is both coherent and conceptually simple. These adjustments consisted of scaling and adding a number to all elements in the marker-based relationship matrix based on equating means of diagonal and off-diagonal elements in the two matrices, and it was demonstrated that accuracy of prediction increased and bias decreased In relation to this problem of compatibility between markerbased and pedigree-based relationship matrices, with data from routine evaluations, selection affects the allele frequencies over time, and in principle both observed marker genotypes and observed phenotypes contain information about allele frequencies in the base population. I propose a new method to address this issue by 1) adjusting the pedigree-based relationship matrix to be compatible with the marker-based relationship matrix instead of the reverse and 2) extending the single-step genetic evaluation using a joint likelihood of observed phenotypes and observed marker genotypes. The performance of this method is evaluated using two simulated datasets

Methods

Results

Discussion

Conclusion