Genomic Heritability: A Ragged Diagonal Between Bias and Variance

Many important traits in plants, animals, and microbes are polygenic and are therefore difficult to improve through traditional marker-assisted selection. Genomic prediction addresses this by enabling the inclusion of all genetic data in a mixed model framework. The main method for predicting breeding values is genomic best linear unbiased prediction (GBLUP), which uses the realized genomic relationship or kinship matrix (K) to connect genotype to phenotype. The use of relationship matrices allows information to be shared for estimating the genetic values for observed entries and predicting genetic values for unobserved entries. One of the key parameters of such models is genomic heritability [Formula], or the variance of a trait associated with a genome-wide sample of DNA polymorphisms. Here we discuss the relationship between several common methods for calculating the genomic relationship matrix and propose a new matrix based on the average semivariance that yields accurate estimates of genomic variance in the observed population regardless of the focal population quality as well as accurate breeding value predictions in unobserved samples. Notably, our proposed method is highly similar to the approach presented by Legarra (2016) despite different mathematical derivations and statistical perspectives and only deviates from the classic approach presented in VanRaden (2008) by a scaling factor. With current approaches, we found that the genomic heritability tends to be either over- or underestimated depending on the scaling and centering applied to the marker matrix (Z), the value of the average diagonal element of K, and the assortment of alleles and heterozygosity (H) in the observed population and that, unlike its predecessors, our newly proposed kinship matrix KASV yields accurate estimates of [Formula] in the observed population, generalizes to larger populations, and produces BLUPs equivalent to common methods in plants and animals.