Multi-Allelic Haplotype Model to Integrate Functional Genomic Information with Genomic Prediction and Variance Component Estimation

A multi-allelic haplotype model treating each haplotype as an ‘allele’ was developed to include SNP haplotypes as a vehicle to integrate functional genomic information with genomic prediction and estimation. For h haplotypes, h(h+1)/2 breeding values are possible and can be expressed as: a = W_αhα_h, where a = [h(h+1)/2]×1 column vector of breeding values, α_h = (h−1)×1 column vector of average effects of gene substitution (AEGS) and W_αh = [h(h+1)/2]×(h−1) model matrix of α_h. Each element in W_αh takes one of the following three values: 2p_k, −(1−2p_k) or −2(1−p_k), where p_k = frequency of haplotype k. With appropriate changes of matrix dimensions, the haplotype genomic additive relationship matrix can be defined as: G_αh = T_αhT_αhʹ, where T_αh = W_αh/(s^1/2), and s is the average of the diagonal elements of W_αhW_αhʹ. The dominance formulations of haplotype blocks are derived similarly. For a sample of n individuals, the limit number of effects is 2n−1 for AEGS and is the number of heterozygous genotypes for dominance effects. We tested this model with additive haplotype effects using all 27,732 human autosome genes as haplotype blocks of the 500K SNP data from the Framingham Heart Study. After adding 2Kb to either end of each gene and merging overlapping genes, 18,656 gene blocks were defined. This number was reduced to 10,857 after merging gene blocks <25Kb apart, covering 35% of the human genome with block sizes of 4.1Kb-1.64Mb. This multi-allelic haplotype model increased the prediction accuracy for most phenotypes in the test dataset.