Computing inbreeding coefficients and the inverse numerator relationship matrix in large populations of honey bees. (17th July 2018) - Bernstein, Richard
Abstract: The inbreeding coefficients are considered in breeding decisions, and the inverse numerator relationship matrix A −1 is a prerequisite for breeding value estimation. Polyandry and haploid males are among the specifics of relationships between honey bees. Brascamp and Bijma (2014) averaged out the manifold possible relationships among honey bees that appear to have the same parents in a pedigree and assigned a single entry in A to animals that behave as a unit, for example, the workers of a hive. Their methods of calculation connected full‐sibs in the variance matrix of the Mendelian sampling terms D, via nonzero off‐diagonal elements. This impedes the inversion of A and the closely connected calculation of inbreeding coefficients, because efficient algorithms for this task take D to be a diagonal matrix. Memory limitations necessitate their use for large data sets. We adapted the quickest of them to the block diagonal matrix D, that is postulated for the honey bee. To our knowledge, the presented algorithm is the first one that facilitates the method of Brascamp and Bijma (2014) on large data sets.