The value of genomic relationship matrices to estimate levels of inbreeding.

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.

Estimates of recent and historical effective population size in turbot, seabream, seabass and carp selective breeding programmes.

BACKGROUND: The high fecundity of fish species allows intense selection to be practised and therefore leads to fast genetic gains. Based on this, numerous selective breeding programmes have been started in Europe in the last decades, but in general, little is known about how the base populations of breeders have been built. Such knowledge is important because base populations can be created from very few individuals, which can lead to small effective population sizes and associated reductions in genetic variability. In this study, we used genomic information that was recently made available for turbot (Scophthalmus maximus), gilthead seabream (Sparus aurata), European seabass (Dicentrarchus labrax) and common carp (Cyprinus carpio) to obtain accurate estimates of the effective size for commercial populations. METHODS: Restriction-site associated DNA sequencing data were used to estimate current and historical effective population sizes. We used a novel method that considers the linkage disequilibrium spectrum for the whole range of genetic distances between all pairs of single nucleotide polymorphisms (SNPs), and thus accounts for potential fluctuations in population size over time. RESULTS: Our results show that the current effective population size for these populations is small (equal to or less than 50 fish), potentially putting the sustainability of the breeding programmes at risk. We have also detected important drops in effective population size about five to nine generations ago, most likely as a result of domestication and the start of selective breeding programmes for these species in Europe. CONCLUSIONS: Our findings highlight the need to broaden the genetic composition of the base populations from which selection programmes start, and suggest that measures designed to increase effective population size within all farmed populations analysed here should be implemented in order to manage genetic variability and ensure the sustainability of the breeding programmes.

Maintenance of genetic diversity in subdivided populations using genomic coancestry matrices.

For both undivided and subdivided populations, the consensus method to maintain genetic diversity is the Optimal Contribution (OC) method. For subdivided populations, this method determines the optimal contribution of each candidate to each subpopulation to maximize global genetic diversity (which implicitly optimizes migration between subpopulations) while balancing the relative levels of coancestry between and within subpopulations. Inbreeding can be controlled by increasing the weight given to within-subpopulation coancestry (λ). Here we extend the original OC method for subdivided populations that used pedigree-based coancestry matrices, to the use of more accurate genomic matrices. Global levels of genetic diversity, measured as expected heterozygosity and allelic diversity, their distributions within and between subpopulations, and the migration pattern between subpopulations, were evaluated via stochastic simulations. The temporal trajectory of allele frequencies was also investigated. The genomic matrices investigated were (i) the matrix based on deviations of the observed number of alleles shared by two individuals from the expected number under Hardy-Weinberg equilibrium; and (ii) a matrix based on a genomic relationship matrix. The matrix based on deviations led to higher global and within-subpopulation expected heterozygosities, lower inbreeding and similar allelic diversity than the second genomic and pedigree-based matrices when a relatively high weight was given to the within-subpopulation coancestries (λ ≥ 5). Under this scenario, allele frequencies moved only slightly away from the initial frequencies. Therefore, the recommended strategy is to use the former matrix in the OC methodology giving a high weight to the within-subpopulation coancestry.

Changes in Allele Frequencies When Different Genomic Coancestry Matrices Are Used for Maintaining Genetic Diversity.

A main objective in conservation programs is to maintain genetic variability. This can be achieved using the Optimal Contributions (OC) method that optimizes the contributions of candidates to the next generation by minimizing the global coancestry. However, it has been argued that maintaining allele frequencies is also important. Different genomic coancestry matrices can be used on OC and the choice of the matrix will have an impact not only on the genetic variability maintained, but also on the change in allele frequencies. The objective of this study was to evaluate, through stochastic simulations, the genetic variability maintained and the trajectory of allele frequencies when using two different genomic coancestry matrices in OC to minimize the loss of diversity: (i) the matrix based on deviations of the observed number of alleles shared between two individuals from the expected numbers under Hardy-Weinberg equilibrium (θLH); and (ii) the matrix based on VanRaden's genomic relationship matrix (θVR). The results indicate that the use of θLH resulted in a higher genetic variability than the use of θVR. However, the use of θVR maintained allele frequencies closer to those in the base population than the use of θLH.