Metafounders are related to F st fixation indices and reduce bias in single-step genomic evaluations

Abstract

Background Metafounders are pseudo-individuals that encapsulate genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses the estimation and usefulness of metafounder relationships in single-step genomic best linear unbiased prediction (ssGBLUP).ResultsWe show that ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, such as fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals and pedigree. Simple methods for their estimation include naïve computation of allele frequencies from marker genotypes or a method of moments that equates average pedigree-based and marker-based relationships. Complex methods include generalized least squares (best linear unbiased estimator (BLUE)) or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer coefficients from marker data have not been developed for related individuals. We derived a genomic relationship matrix, compatible with pedigree relationships, that is constructed as a cross-product of {−1,0,1} codes and that is equivalent (apart from scale factors) to an identity-by-state relationship matrix at genome-wide markers. Using a simulation with a single population under selection in which only males and youngest animals are genotyped, we observed that generalized least squares or maximum likelihood gave accurate and unbiased estimates of the ancestral relationship parameter (true value: 0.40) whereas the naïve method and the method of moments were biased (average estimates of 0.43 and 0.35). We also observed that genomic evaluation by ssGBLUP using metafounders was less biased in terms of estimates of genetic trend (bias of 0.01 instead of 0.12), resulted in less overdispersed (0.94 instead of 0.99) and as accurate (0.74) estimates of breeding values than ssGBLUP without metafounders and provided consistent estimates of heritability.ConclusionsEstimation of metafounder relationships can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships reduces bias of genomic predictions with no loss in accuracy.

A fast indirect method to compute functions of genomic relationships concerning genotyped and ungenotyped individuals, for diversity management

“…This assumption can be removed using the metafounder approach [ 21 ], which postulates that the pedigree-based additive relationship between any pair of founders is equal to a positive parameter (from 0 to 2) that summarizes the situation of the pedigree base in reference to the genomic base [ 10 ]. This parameter can be estimated from genomic data [ 22 ], and represents the homozygosity across founders in the pedigree that would yield observed genomic relationships in , where is computed as the cross-product with containing {− 1, 0, 1} values. Furthermore, Garcia-Baccino et al [ 22 ] showed that the value of is relative to a theoretical genomic base that displays maximum variability at each marker locus (allelic frequencies 0.5), thus giving rise by drift to the pedigree base and to differentiation of frequencies in the genotyped population.…”

Efficient and accurate computation of base generation allele frequencies

“…The accuracy for such cases could be improved by taking into account the different base populations by implementing the GLS_Sparse method with genetic groups. This could be done by replacing the vector 1 in the different formulae by a matrix Q that contains the expected fraction of each genetic group for each geno- with μ i being a vector of estimates of base allele frequencies for all genetic groups (Gengler et al, 2007;VanRaden, 2008;Makgahlela et al, 2013;Garcia-Baccino et al, 2017). .…”

“…The GLS equivalent uses the method proposed by McPeek et al (2004) and implemented by Strandén et al (2017) and Garcia-Baccino et al (2017) in which for the ith SNP…”

“…The first method was to run, for each SNP, a BLUP in which the heritability was close to 1 (e.g., 0.99 or smaller; Gengler et al, 2007). The second method was, for each SNP, a general least squares (GLS) estimator using either sparse or dense matrices for the computation of the inverse of pedigree relationship submatrices (McPeek et al, 2004;Garcia-Baccino et al, 2017;Strandén et al, 2017). The BLUP and GLS methods are expected to be very similar because both use pedigree information, but we did not expect them to be exactly the same, although theoretically equivalent (e.g., Henderson, 1984;Mrode, 2005;Garcia-Baccino et al, 2017) differences between estimates of BLUP and GLS methods could be due to the heritability different from 1 and the iterative solver used in the BLUP method.…”

“…The second method was, for each SNP, a general least squares (GLS) estimator using either sparse or dense matrices for the computation of the inverse of pedigree relationship submatrices (McPeek et al, 2004;Garcia-Baccino et al, 2017;Strandén et al, 2017). The BLUP and GLS methods are expected to be very similar because both use pedigree information, but we did not expect them to be exactly the same, although theoretically equivalent (e.g., Henderson, 1984;Mrode, 2005;Garcia-Baccino et al, 2017) differences between estimates of BLUP and GLS methods could be due to the heritability different from 1 and the iterative solver used in the BLUP method. The objective of this study was to determine the most efficient and accurate method for estimating base generation allele frequencies when different scenarios likely to occur in real data are considered, including missing genotypes, genotyping errors, and incomplete pedigree.…”