Computing inbreeding coefficients accounting for unknown parents using pedigree-based metafounders

Missing pedigrees result in underestimated numerator relationship and inbreeding coefficients in a closed population. Recursive algorithms have been proposed to derive nonzero inbreeding coefficients accounting for unknown parents but can be computationally ineffective with a deep pedigree. In this report, we proposed a pedigree-based metafounder (MF) approach to calculate nonzero inbreeding. Unknown parents were assigned to MF based on the birth year of their offspring. The MF were assumed to have self-relationships equaling twice the average inbreeding coefficients of the animals with both parents known and born in the same year. The relationships between 2 MF were set as a function (i.e., minimum, harmonic mean, or maximum) of their self-relationships. Inbreeding coefficients were then computed using Sargolzaei and Iwaisaki's (2004) algorithm modified to account for MF, and the relationship matrix of MF was constructed iteratively until convergence. The algorithm was tested and compared with a recursive algorithm using a pedigree of 8.6 million Japanese Holsteins (average longest ancestral path = 11) and a simulated pedigree with 11,550,500 animals across 40 generations. For the Holstein pedigree, one iteration took ∼300 s with the recursive algorithm and 70 s with the proposed algorithm. If the relationships between MF were assumed to equal the maximum of their self-relationships, both algorithms converged to the same results. Simulation results further confirmed that the maximum assumption yielded the best correlation between the estimated and true inbreeding. The discussion highlights how different assumptions regarding the relationships between MF affect the resulting numerator relationship and inbreeding coefficients. With the MF approach, the subsets of the numerator relationship matrix accounting for unknown parents can also be derived quickly.