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 ( F NEJ ), the Li and Horvitz matrix based on excess of homozygosity ( F L&H ), and the VanRaden (methods 1, F VR 1 , and 2, F VR 2 ) and Yang ( F YAN ) 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 F NEJ , 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 F NEJ and F L&H led to sensible results but this was not the case for F VR 1 , F VR 2 and F YAN . When variability has increased relative to the base, F VR 1 , F VR 2 and F YAN can indicate that it decreased. In fact, based on F YAN , variability is not expected to increase. When variability has decreased, F VR 1 and F VR 2 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.