Short communication: Methods to compute genomic inbreeding for ungenotyped individuals.

The genomic measure of inbreeding is closer to the actual inbreeding than the pedigree-based measure. However, it cannot be computed for ungenotyped animals. An estimate of genomic inbreeding comes from the diagonal of matrix H used in single-step methods. This matrix projects genomic relationships to all ungenotyped members of the pedigree. The diagonal element of H gives an estimate of the genomic inbreeding coefficient. However, so far no computational methods are available to compute the diagonal of H. Here we propose 3 exact methods to compute this diagonal. The first uses an already-existing algorithm to compute, for each ungenotyped individual, products of the form Hx to obtain the corresponding diagonal element of H. The second method computes, for each ungenotyped individual, a term that can be written as a quadratic form involving pedigree and genomic relationships. For both methods, the computational burden is linear in the number of ungenotyped animals. The last method reorders the computations of the second method so that they become linear in the number of genotyped animals, which is usually much smaller. We tested the methods in 3 small data sets (with ~2,000 genotyped animals and 30,000-500,000 animals in pedigree) and in a large simulated population (with 1,220,000 animals in pedigree and 36,000 genotyped animals). Tests resulted in satisfactory computing times (<10 min in the largest example using 10 parallel threads). Computing times were much shorter for the third method, as expected. Using these methods, estimates of genomic inbreeding in ungenotyped animals can be obtained on a regular basis.