The value of genomic relationship matrices to estimate levels of inbreeding

Abstract

Background Genomic relationship matrices are used to obtain genomic inbreeding coefficients. However, there are several methodologies to compute these matrices and there is still an unresolved debate on which one provides the best estimate of inbreeding. In this study, we investigated measures of inbreeding obtained from five genomic matrices, including the Nejati-Javaremi allelic relationship matrix (FNEJ), the Li and Horvitz matrix based on excess of homozygosity (FL&H), and the VanRaden (methods 1, FVR1, and 2, FVR2) and Yang (FYAN) genomic relationship matrices. We derived expectations for each inbreeding coefficient, assuming a single locus model, and used these expectations to explain the patterns of the coefficients that were computed from thousands of single nucleotide polymorphism genotypes in a population of Iberian pigs. Results Except for FNEJ, the evaluated measures of inbreeding do not match with the original definitions of inbreeding coefficient of Wright (correlation) or Malécot (probability). When inbreeding coefficients are interpreted as indicators of variability (heterozygosity) that was gained or lost relative to a base population, both FNEJ and FL&H led to sensible results but this was not the case for FVR1, FVR2 and FYAN. When variability has increased relative to the base, FVR1, FVR2 and FYAN can indicate that it decreased. In fact, based on FYAN, variability is not expected to increase. When variability has decreased, FVR1 and FVR2 can indicate that it has increased. Finally, these three coefficients can indicate that more variability than that present in the base population can be lost, which is also unreasonable. The patterns for these coefficients observed in the pig population were very different, following the derived expectations. As a consequence, the rate of inbreeding depression estimated based on these inbreeding coefficients differed not only in magnitude but also in sign. Conclusions Genomic inbreeding coefficients obtained from the diagonal elements of genomic matrices can lead to inconsistent results in terms of gain and loss of genetic variability and inbreeding depression estimates, and thus to misleading interpretations. Although these matrices have proven to be very efficient in increasing the accuracy of genomic predictions, they do not always provide a useful measure of inbreeding.

Correlation of Genomic and Pedigree Inbreeding Coefficients in Small Cattle Populations

“…Bjelland et al [ 21 ] estimated a correlation between Fmg and Froh similar to ours which was 0.81 in the USA’s Holstein cattle. Caution should be exercised when using Fmg because Villanueva et al [ 37 ] mentioned that Fmg can lead to inconsistent results in terms of the gain and loss of genetic variability, and, thus, to misleading interpretations, and do not always provide a useful measure of inbreeding.…”

How to achieve a higher selection plateau in forest tree breeding? Fostering heterozygote × homozygote relationships in optimal contribution selection in the case study of Populus nigra

“…Using alternative formulations might even lead to different long‐term performance when used in the context of OCS (Gebregiwergis et al, 2020 ). However, a matrix that increases accuracy of genomic predictions does not necessarily measure inbreeding efficiently (Villanueva et al, 2021 ), so developing different formulations for different purposes seems preferable. Indeed, genomic information has been used differently in different contexts (as reviewed in Maltecca et al, 2020 ): minimum coancestry mating (Fernández et al, 2021 ), selection against unfavorable alleles (Upperman et al, 2019 ), or genomic selection with dominance effects (Sun et al, 2014 ).…”

Estimating inbreeding depression for growth and reproductive traits using pedigree and genomic methods in Argentinean Brangus cattle

“…Recently, Villanueva et al (2021) showed that the diagonal elements of matrix G, as are computed in our study (VanRaden, 2008, method 1), cannot be interpreted as inbreeding coefficients. First, inbreeding coefficients were computed using an HMM approach (ZooRoH) and not from G. Second, inbreeding depression models the mean of an individual, whereas the selfrelationship models its variance.…”