For multivariate, single-step genomic best linear unbiased prediction analyses fitting a breeding value model, it is often assumed that the proportions of total genetic variance accounted for by genomic markers and residual polygenic effects are the same for all traits. Different covariance matrices for the two types of genetic effects are readily taken into account by fitting them separately. However, this can lead to slow convergence rates in iterative solution schemes. We propose an alternative computing strategy which – exploiting a canonical transformation – allows for trait-specific covariances whilst directly fitting total genetic effects only. Its effects on convergence rates and gains in accuracy and bias of genomic evaluation compared to analyses assuming proportionality of covariance matrices are examined using a small simulation study. Results show comparatively little improvement in accuracies but worthwhile reductions in overdispersion of predicted genetic merits for genotyped individuals without phenotypes.

Simulation was used to illustrate the effects of genomic selection on estimates of genetic parameters, comparing values when genomic relationships were ignored with those obtained accounting for the joint relationship matrix of genotyped and non-genotyped individuals. Analyses were carried out with increasing truncation of earlier records, pedigrees and genotype information. Results showed that estimates from pedigree only analyses could be markedly biased downwards as more historical data is ignored, especially with strong genomic selection, causing predicted breeding values for selection candidates in the last generation to be under-dispersed.

Context. A common problem in mixed model-based genetic evaluation schemes for livestock is that cohorts of animals differ systematically in mean genetic merit, for example, due to missing pedigree. This can be modelled by fitting genetic groups. Single-step genomic evaluation (ssGBLUP) combining information from genotyped and non-genotyped individuals has become routine, but little is known of the effects of unknown parents in this context.

Aims. To investigate the effects of missing pedigrees on accuracy and bias of predicted breeding values for ssGBLUP analyses.

Methods. A simulation study was used to examine alternative ways to account for genetic groups in ssGBLUP, for multi-generation data with strong selection and rapidly increasing numbers of genotyped animals in the most recent generations.

Key results. Results demonstrated that missing pedigrees can markedly impair predicted breeding values. With selection, alignment of genomic and pedigree relationship matrices is essential when fitting unknown parent groups (UPG). Genomic relationships are complete; that is, they 'automatically' reference the genomic base, which typically differs from the genetic base for pedigreed animals. This can lead to biased comparisons between genotyped and non-genotyped animals with unknown parents when the two categories of animals are assigned to the same UPG. Allocating genotyped individuals to a separate UPG across all generations for each strain or breed was shown to be a simple and effective way to reduce misalignment bias. In contrast, fitting metafounders modified pedigree-based relationships to account for ancestral genomic relationships and inbreeding rather than the genomic relationship matrix. Thus, no bias due to different types of animals assigned to the same metafounders was apparent. Overall, fitting metafounders yielded slightly higher correlations between true and predicted breeding values than did UPG models, which assume genetic groups to be unrelated.

Conclusions. Missing pedigrees are more problematic with ssGBLUP than for analyses considering pedigree-based relationships only. UPG models with separation of genotyped and non-genotyped individuals and analyses fitting metafounders yielded comparable predictions of breeding values in terms of accuracy and bias.

Implications. A previously unidentified incompatibility between alignment of founder populations and assignment of genotyped and non-genotyped animals to the same UPG has been reported. Implementation of the proposed strategy to reduce 'double counting' is straightforward and can improve results of ssGBLUP analyses.

WOMBAT is a freely available software package for linear mixed model analyses in quantitative genetics, distributed since 2006. Its main focus is the estimation of covariance components and genetic parameters via restricted maximum likelihood (REML) and the prediction of individuals' genetic merit. It predominantly targets models and tasks common to animal breeding applications, but is well suited to and used in other areas of quantitative genetics.

We highlight its key characteristics and capabilities, some unique features and selected, recent extensions to better accommodate analyses utilising genomic information. Specific topics considered are parsimonious models for multivariate analyses, REML estimation subject to a penalty on the likelihood to reduce sampling variation, pooling of results from analyses by parts, construction of relationship matrices and their inverses, genome wide association screens and so-called single step analyses. In addition we outline computational strategies employed and the scope for large scale analyses with modern hardware.

Restricted maximum likelihood estimation of genetic parameters accounting for genomic relationships has been reported to impose computational burdens which typically are many times higher than those of corresponding analyses considering pedigree based relationships only. This can be attributed to the dense nature of genomic relationship matrices and their inverses. We outline a reparameterisation of the multivariate linear mixed model to principal components and its effects on the sparsity pattern of the pertaining coefficient matrix in the mixed model equations. Using two data sets we demonstrate that this can dramatically reduce the computing time per iterate of the widely used 'average information' algorithm for restricted maximum likelihood. This is primarily due to the fact that on the principal component scale, the first derivatives of the coefficient matrix with respect to the parameters modelling genetic covariances between traits are independent of the relationship matrix between individuals, i.e. are not afflicted by a multitude of genomic relationships.