Metafounders are Fst fixation indices and reduce bias in single step genomic evaluations

Abstract

BACKGROUNDMetafounders are pseudo-individuals that condense the genetic heterozygosity and relationships within and across base pedigree populations, i.e. ancestral populations. This work addresses estimation and usefulness of metafounder relationships in Single Step GBLUP.\n\nRESULTSWe show that the ancestral relationship parameters are proportional to standardized covariances of base allelic frequencies across populations, like Fst fixation indexes. These covariances of base allelic frequencies can be estimated from marker genotypes of related recent individuals, and pedigree. Simple methods for estimation include naive computation of allele frequencies from marker genotypes or a method of moments equating average pedigree-based and marker-based relationships. Complex methods include generalized least squares or maximum likelihood based on pedigree relationships. To our knowledge, methods to infer Fst coefficients and Fst differentiation have not been developed for related populations.\n\nA compatible genomic relationship matrix constructed as a crossproduct of {-1,0,1} codes, and equivalent (up to scale factors) to an identity by state relationship matrix at the markers, is derived. Using a simulation with a single population under selection, in which only males and youngest animals were 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 other two (naive and method of moments) were biased (estimates of 0.43 and 0.35). We also observed that genomic evaluation by Single Step GBLUP using metafounders was less biased in terms of accurate genetic trend (0.01 instead of 0.12 bias), slightly overdispersed (0.94 instead of 0.99) and as accurate (0.74) than the regular Single Step GBLUP. Single Step GBLUP using metafounders also provided consistent estimates of heritability.\n\nCONCLUSIONSEstimation of metafounder relationship can be achieved using BLUP-like methods with pedigree and markers. Inclusion of metafounder relationships improves bias of genomic predictions with no loss in accuracy.