TABLE 5.

Relationship between haplotype epistasis heritability and prediction accuracy for best haplotype prediction models.

Trait	HDL	LDL	TC	TG	HTO	Weight	BMIO
SNP model with additive values (A), MAF = 0.05
Additive heritability (${\widehat{\text{h}}}_{\mathrm{s1}}^2$ = ${\widehat{\text{h}}}_{\mathrm{\alpha }1}^2$)	0.409	0.469	0.409	0.312	0.773	0.493	0.424
SNP model with additive values (A), MAF = 0.10
Additive heritability (${\widehat{\text{h}}}_{\mathrm{s1}}^2$ = ${\widehat{\text{h}}}_{\mathrm{\alpha }1}^2$)	0.401	0.464	0.402	0.308	0.760	0.483	0.417
SNP model with additive and dominance values (A + D), MAF = 0.05
Additive heritability (${\widehat{\text{h}}}_{\mathrm{\alpha }2}^2$)	0.386	0.406	0.389	0.260	0.739	0.474	0.415
Dominance heritability (${\widehat{\text{h}}}_{\mathrm{\delta }}^2$)	0.121	0.174	0.102	0.125	0.198	0.088	0.044
SNP total heritability (${\widehat{\text{h}}}_{\text{s}}^2$)	0.507	0.580	0.491	0.385	0.937	0.562	0.459
SNP model with additive and dominance values (A + D), MAF = 0.10
Additive heritability (${\widehat{\text{h}}}_{\mathrm{\alpha }2}^2$)	0.378	0.404	0.381	0.257	0.724	0.462	0.407
Dominance heritability (${\widehat{\text{h}}}_{\mathrm{\delta }}^2$)	0.122	0.170	0.107	0.126	0.212	0.098	0.049
SNP total heritability (${\widehat{\text{h}}}_{\text{s}}^2$)	0.500	0.574	0.488	0.382	0.935	0.560	0.456
Haplotype prediction models
MAF	0.05	0.05	0.05	0.10	0.05	0.05	0.05
Best prediction model	A + D + H	H	D + H	H	A + D + H	A + D + H	A + H
Best haplotype blocking method	Genes	12 SNPs	50 Kb	50 Kb	200 Kb	12 SNPs	100 Kb
Accuracy increase (%)	2.76	8.12	3.15	3.29	2.18	1.86	2.17
SNP additive heritability (${\widehat{\text{h}}}_{\mathrm{\alpha }\mathrm{s}}^2$)	0.070	-	-	-	0.359	0.124	0.123
SNP dominance heritability (${\widehat{\text{h}}}_{\mathrm{\delta }\mathrm{s}}^2$)	0.094	-	0.077	-	0.147	0.057	-
Haplotype additive heritability (${\widehat{\text{h}}}_{\mathrm{\alpha }\mathrm{h}}^2$)	0.394	0.616	0.452	0.353	0.494	0.422	0.366
Total heritability (${\widehat{\text{h}}}_{\text{g}}^2$)	0.558	0.616	0.530	0.353	0.999	0.603	0.488
Estimates of haplotype epistasis heritability
Haplotype epistasis heritability (${\widehat{\text{h}}}_{\text{E}}^2$)	0.051	0.147	0.039	0.045	0.062	0.041	0.064
Relative haplotype epistasis heritability (${\widehat{\text{h}}}_{\text{Er}}^2$,%)	13.27	31.27	10.03	14.53	8.90	8.65	15.05

Accuracy increase is the percentage increase in observed prediction accuracy of the best haplotype model relative to the accuracy of the best SNP model (in bold face). A, SNP additive values; D, SNP dominance values; H, haplotype additive values; MAF, minor allele frequency; SNP total heritability is the sum of SNP additive and dominance heritabilities (Eq. 12). Total heritability is the sum of all heritabilities of genetic values in the model with haplotypes (Eqs. 7–10). Haplotype epistasis heritability was calculated using Eqs. 13–16. Relative haplotype epistasis heritability was calculated using Eqs. 17 and 18.