Abstract
BackgroundThe amount of functional genomic information has been growing rapidly but remains largely unused in genomic selection. Genomic prediction and estimation using haplotypes in genome regions with functional elements such as all genes of the genome can be an approach to integrate functional and structural genomic information for genomic selection. Towards this goal, this article develops a new haplotype approach for genomic prediction and estimation.ResultsA multi-allelic haplotype model treating each haplotype as an ‘allele’ was developed for genomic prediction and estimation based on the partition of a multi-allelic genotypic value into additive and dominance values. Each additive value is expressed as a function of h − 1 additive effects, where h = number of alleles or haplotypes, and each dominance value is expressed as a function of h(h − 1)/2 dominance effects. For a sample of q individuals, the limit number of effects is 2q − 1 for additive effects and is the number of heterozygous genotypes for dominance effects. Additive values are factorized as a product between the additive model matrix and the h − 1 additive effects, and dominance values are factorized as a product between the dominance model matrix and the h(h − 1)/2 dominance effects. Genomic additive relationship matrix is defined as a function of the haplotype model matrix for additive effects, and genomic dominance relationship matrix is defined as a function of the haplotype model matrix for dominance effects. Based on these results, a mixed model implementation for genomic prediction and variance component estimation that jointly use haplotypes and single markers is established, including two computing strategies for genomic prediction and variance component estimation with identical results.ConclusionThe multi-allelic genetic partition fills a theoretical gap in genetic partition by providing general formulations for partitioning multi-allelic genotypic values and provides a haplotype method based on the quantitative genetics model towards the utilization of functional and structural genomic information for genomic prediction and estimation.
Highlights
The amount of functional genomic information has been growing rapidly but remains largely unused in genomic selection
Genomic best linear unbiased prediction (GBLUP) using genome-wide single nucleotide polymorphism (SNP) markers can utilize a wealth of theoretical results and computational strategies of best linear unbiased prediction (BLUP) [1] that has become a standard approach for genetic evaluation, with dairy cattle having the most widespread use of BLUP worldwide [2,3,4,5]
The implementation of GBLUP within the BLUP framework is made possible by a genomic relationship matrix that replaces the pedigree relationship matrix in BLUP [6]
Summary
The amount of functional genomic information has been growing rapidly but remains largely unused in genomic selection. Genomic prediction and estimation using haplotypes in genome regions with functional elements such as all genes of the genome can be an approach to integrate functional and structural genomic information for genomic selection. With the factorization of a = Wαα and d = Wδδ, genomic additive relationship is a function of WαWα ' and genomic dominance relationship is a function of WδWδ ' [9]. This approach for defining genomic relationships was only available for bi-allelic loci. General factorization formulations for an arbitrary number of alleles were unavailable, and a method using such multi-allelic haplotype model for genomic prediction and estimation was unavailable
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