Minimising inbreeding in small populations by rotational mating with frozen semen

Mating plans are investigated in order to minimize inbreeding in small populations when frozen semen is available. For a single dam line it was found that specific sire rotations minimized the asymptotic level of inbreeding when semen is used repeatedly from certain generations. When semen of N foundation (G0) sires is used rotationally over generations it is shown that the inbreeding level asymptotes to 1/(2(N+1) - 2). However, if only G0 sires are used then all genes will eventually descend from the founder sires. Inbreeding can be reduced further by using sires from generation one (G1) and later as this retains genes from the founder dams in the long-term gene pool. If semen from NG0 sires and N unrelated G1 sons is used rotationally then inbreeding asymptotes to (2(N-1) + 1)/(2(2N+1) - 2). When there are more founder dams than sires, the asymptotic inbreeding can be reduced even further by using the semen of half-sib G1 sires in rotation. Optimal rotations using full-sib G1 sires or generation 2 (or later) sires will lower the asymptotic inbreeding also, but generally not by much. It was found that when unlimited frozen semen from a specified group of sires was available, the optimal mating plan was achieved by selecting each generation the sire with the least co-ancestry with the current female of the dam line.