Different versions of genomic models are proposed to predict breeding values for animals using dense markers. However, so far little attention has been payed to estimating the genomic explained variance from the data, or to compare ”genomic” heritability estimates with pedigree- based heritability estimates. One group of genomic models is based on mixed models, using markers to build genomic relationship matrices (e.g., Garrick (2007), VanRaden (2008)). These models could be straightforwardly applied to estimate genomic (co)variances and heritabilities by REML, but have limited possibilities for extensions. For instance, extensions to multi-trait estimation, to add interaction variances, or to estimate genomic (co)variances by chromosome would result in an unmanageably large number of relationship matrices and (co)variance components to deal with. Also, these genomic relationship matrices may be singular, requiring bending which effectively reduces the off-diagonals, and then could be expected to lead to biases in genomic variance estimates.

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