Beyond genomic selection: The animal model strikes back (one generation)!

Genome inheritance is by segments of DNA rather than by independent loci. We introduce the ancestral regression (AR) as a recursive system of simultaneous equations, with grandparental path coefficients as novel parameters. The information given by the pedigree in the AR is complementary with that provided by a dense set of genomic markers, such that the resulting linear function of grandparental BV is uncorrelated to the average of parental BV in the absence of inbreeding. AR is then connected to segmental inheritance by a causal multivariate Gaussian density for BV. The resulting covariance structure (sigma) is Markovian, meaning that conditional on the BV of parents and grandparents, the BV of the animal is independent of everything else. Thus, an algorithm is presented to invert the resulting covariance structure, with a computing effort that is linear in the number of animals as in the case of the inverse additive relationship matrix.