A modified indirect method for computing inbreeding coefficients

The performance of existing methods for computing inbreeding coefficients-including tabular-based methods, Cholesky decomposition-based methods, and indirect methods-has been limited by either memory usage, pedigree depth, or average half-sib family size. In this note, we present a modified indirect method that efficiently identifies, computes, and stores the necessary elements for computing inbreeding coefficients. The algorithm was tested on pedigrees of 8.6 million Japanese Holsteins born from 1901 to 2023, with an average longest ancestral path number of 17 and 42,120 sires with progenies. Compared to a previous indirect method, the modifications reduced computation time from 103.4 to 7.2 s. When parallelized using 32 threads, the computation completed in 1.1 s. Simulation results suggested that the proposed method is less affected by pedigree depth or family size, making it practical for most livestock populations reproduced via artificial insemination.