Genomic Analysis Combining Genotyped and Non-genotyped Individuals

Genomic prediction and genome-wide association studies (GWAS) are relatively straightforward when individuals have both phenotypic and genotypic data.  In many breeding applications, genotyped individuals have descendants or other relatives that have been phenotyped but not genotyped.  One common approach to use information on these relatives is to use all pedigree and performance data to estimate breeding values and then deregress this information on genotyped animals to use as data in genomic prediction or GWAS.  Another approach is to use a single-step analysis (Legarra et al, 2009; Aguilar et al, 2010) that involves creation of a genetic variance-covariance matrix among all animals using information on both genotyped and non-genotyped animals.  That approach requires brute force inversion of two matrices of order equal to the number of genotyped animals, and requires the genomic and pedigree-based relationship matrices to have the same definition of base or founder animals.  We have proposed an alternative formulation for this problem, that does not require matrix inversion, and is therefore practical for problems with hundreds of thousands of genotyped individuals.  This formulation includes the conventional single-step model as a special case, and when so parameterized provides identical solutions.  However, it is easily extended to other classes of models, including those that use variable selection.