Effects of ignoring inbreeding in model‐based accuracy for BLUP and SSGBLUP

Abstract

Model‐based accuracy, defined as the theoretical correlation between true and estimated breeding value, can be obtained for each individual as a function of its prediction error variance (PEV) and inbreeding coefficient F, in BLUP, GBLUP and SSGBLUP genetic evaluations. However, for computational convenience, inbreeding is often ignored in two places. First, in the computation of reliability = 1‐PEV/(1 + F). Second, in the set‐up, using Henderson's rules, of the inverse of the pedigree‐based relationship matrix A. Both approximations have an effect in the computation of model‐based accuracy and result in wrong values. In this work, first we present a reminder of the theory and extend it to SSGBLUP. Second, we quantify the error of ignoring inbreeding with real data in three scenarios: BLUP evaluation and SSGBLUP in Uruguayan dairy cattle, and BLUP evaluations in a line of rabbit closed for >40 generations with steady increase of inbreeding up to an average of 0.30. We show that ignoring inbreeding in the set‐up of the A‐inverse is equivalent to assume that non‐inbred animals are actually inbred. This results in an increase of apparent PEV that is negligible for dairy cattle but considerable for rabbit. Ignoring inbreeding in reliability = 1‐PEV/(1 + F) leads to underestimation of reliability for BLUP evaluations, and this underestimation is very large for rabbit. For SSGBLUP in dairy cattle, it leads to both underestimation and overestimation of reliability, both for genotyped and non‐genotyped animals. We strongly recommend to include inbreeding both in the set‐up of A‐inverse and in the computation of reliability from PEVs.

Genetic Diversity in the Portuguese Mertolenga Cattle Breed Assessed by Pedigree Analysis

“…Controlling the rate of inbreeding is usually one of the major targets in conservation and selection programs [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], and more so when selection decisions take family or genomic information into account, such as in BLUP, GBLUP (Genomic best linear unbiased prediction) and ssGBLUP (Single-step genomic BLUP) [32][33][34][35][36], or when reproductive biotechnology (Embryo transfer-ET, in-vitro fertilization-IVF and Multiple Ovulation Embryo Transfer-MOET) is used [37]. The evaluation of genetic diversity of populations has evolved over the years, with the advantage that we can now benefit from methodologies, criteria and concepts proposed longer ago and those implemented more recently.…”

Genotype-by-environment interactions for reproduction, body composition, and growth traits in maternal-line pigs based on single-step genomic reaction norms

“…The accuracy of genomic estimated breeding values (GEBV) of animal for a trait was calculated following [ 42 ] as: where is the standard error (SE) of the coefficient for the RNM intercept or slope for animal (square root of the diagonal elements of the inverse of the left-hand side), is the inbreeding coefficient of animal , and is the variance of the coefficient for the RNM intercept or slope for animal . An estimate of the correlation of GEBV between traits and ( ) was obtained using the weighted Pearson correlation coefficient of GEBV, as described in [ 43 ]: with and , where and are the GEBV of traits and , respectively, and is the accuracy-based weighting of animal , calculated as .…”

Definition of Environmental Variables and Critical Periods to Evaluate Heat Tolerance in Large White Pigs Based on Single-Step Genomic Reaction Norms

“…where SD i is the posterior standard deviation of GEBV for animal i for the RN of t, being t the intercept or slope terms, F i is the inbreeding coefficient, and σ2 a is the estimated variance of animal additive effect for the intercept or slope (Aguilar et al, 2020).…”