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 (Σ) 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.

Estimates of the actual relationship between half-sibs in a pig population.

Genomic relationships based on markers capture the actual instead of the expected (based on pedigree) proportion of genome shared identical by descent (IBD). Several methods exist to estimate genomic relationships. In this research, we compare four such methods that were tested looking at the empirical distribution of the estimated relationships across 6704 pairs of half-sibs from a cross-bred pig population. The first method based on multiple marker linkage analysis displayed a mean and standard deviation (SD) in close agreement with the expected ones and was robust to changes in the minor allele frequencies (MAF). A single marker method that accounts for linkage disequilibrium (LD) and inbreeding came second, showing more sensitivity to changes in the MAF. Another single marker method that considers neither inbreeding nor LD showed the smallest empirical SD and was the most sensible to changes in MAF. A higher mean and SD were displayed by VanRaden's method, which was not sensitive to changes in MAF. Therefore, the method based on multiple marker linkage analysis and the single marker method that considers LD and inbreeding performed closer to theoretical values and were consistent with the estimates reported in literature for human half-sibs.

A comparison of methods to estimate genomic relationships using pedigree and markers in livestock populations.

Accurate prediction of breeding values depends on capturing the variability in genome sharing of relatives with the same pedigree relationship. Here, we compare two approaches to set up genomic relationship matrices for precision of genomic relationships (GR) and accuracy of estimated breeding values (GEBV). Real and simulated data (pigs, 60k SNP) were analysed, and GR were estimated using two approaches: (i) identity by state, corrected with either the observed (GVR-O ) or the base population (GVR-B ) allele frequencies and (ii) identity by descent using linkage analysis (GIBD-L ). Estimators were evaluated for precision and empirical bias with respect to true pedigree IBD GR. All three estimators had very low bias. GIBD-L displayed the lowest sampling error and the highest correlation with true genome-shared values. GVR-B approximated GIBD-L 's correlation and had lower error than GVR-O . Accuracy of GEBV for selection candidates was significantly higher when GIBD-L was used and identical between GVR-O and GVR-B . In real data, GIBD-L 's sampling standard deviation was the closest to the theoretical value for each pedigree relationship. Use of pedigree to calculate GR improved the precision of estimates and the accuracy of GEBV.