An algorithm to compute optimal genetic contributions in selection programs with large numbers of candidates.

A novel algorithm, OCSELECT, is presented for the calculation of optimal genetic contributions with a restricted rate of inbreeding when the number of selection candidates is very large. The calculation of optimal genetic contributions requires the relationship matrix between the candidates and its inverse. The relationship matrix was written as: A = ZA(p)Z' + D, where A(p) is the relationship matrix of the parents, D is a diagonal matrix of Mendelian sampling variances, and Z contains genetic contributions from parents to offspring. Therefore, A(-1) = d(-1) - d(-1)Z(Z'd(-1)Z + A(P)(-1))(-1) Z'd(-1), requires only inversion of matrices of the size of the number of parents instead of the number of offspring. The new algorithm was compared with the software package GENCONT on a salmon data set containing 39,214 selection candidates and 45,846 pedigreed fish in total. Because GENCONT could not handle such a large data set, this data set was split into 19 smaller data sets. Both algorithms gave the same solution with respect to the genetic gain and very similar solutions with respect to the number of selected animals. The OCSELECT algorithm was able to calculate the optimal contributions for the complete data set of 39,214, and therefore no preselection of the 39,214 fish was necessary before entering the fish into the new optimal contribution selection procedure.