Understanding factors influencing the estimated genetic variance and the distribution of breeding values

This study investigated the main factors influencing the genetic variance and the variance of breeding values (EBV). The first is the variance of genetic values in the base population, and the latter is the variance of genetic values in the population under evaluation. These variances are important as improper variances can lead to systematic bias. The inverse of the genetic relationship matrix (K ^-1) and the phenotypic variance are the main factors influencing the genetic variance and heritability (h²). These factors and h² are also the main factors influencing the variance of EBVs. Pedigree- and genomic-based relationship matrices (A and G as K) and phenotypes on 599 wheat lines were used. Also, data were simulated, and a hybrid (genomic-pedigree) relationship matrix (H as K) and phenotypes were used. First, matrix K underwent a transformation (K* = w K + α 11' + β I), and the responses in the mean and variation of diag(K ^-1) and offdiag(K ^-1) elements, and genetic variance in the form of h² were recorded. Then, the original K was inverted, and matrix K ^-1 underwent the same transformations as K, and the responses in the h² estimate and the variance of EBVs in the forms of correlation and regression coefficients with the EBVs estimated based on the original K ^-1 were recorded. In response to weighting K by w, the estimated genetic variance changed by 1/w. We found that μ(diag(K)) - μ(offdiag(K)) influences the genetic variance. As such, α did not change the genetic variance, and increasing β increased the estimated genetic variance. Weighting K ^-1 by w was equivalent to weighting K by 1/w. Using the weighted K ^-1 together with its corresponding h², EBVs remained unchanged, which shows the importance of using variance components that are compatible with the K ^-1. Increasing β I added to K ^-1 increased the estimated genetic variance, and the effect of α 11' was minor. We found that larger variation of diag(K ^-1) and higher concentration of offdiag(K ^-1) around the mean (0) are responsible for lower h² estimate and variance of EBVs.