Design and comparison of gene-pyramiding schemes in animals

Marker-assisted gene pyramiding provides a promising way to develop new animal breeds or lines, in which genes responsible for certain favorable characters identified in different breeds or lines are incorporated. In consideration of features of animal populations, we proposed five schemes for pyramiding three genes, denoted Scheme A-E, and five schemes for pyramiding four genes, denoted Scheme F-J. These schemes are representative of the possible alternatives. We also provided an algorithm to compute the population sizes needed in each generation. We compared these schemes with respect to the total population size and the number of generations required under different situations. The results show that there is no scheme that is optimal in all cases. Among the schemes for pyramiding three genes from three lines (L1, L2 and L3), Scheme D (a three-way cross between the three lines are first performed, followed by a backcross to L1 and a subsequent intercross to obtain the desired genotype) has a significant advantage over the other schemes when the recombination rate between adjacent genes ranges from 0.1 to 0.4, while Scheme A (a two-way cross between L1 and L2 and a subsequent intercross are performed, followed by a cross with L3 and a subsequent intercross to obtain the desired genotype) is optimal when recombination rate is 0.5. Among schemes for pyramiding four genes from four lines (L1, L2, L3 and L4), Scheme I (seperately, a two-way cross between L1 and L2 (L3 and L4) followed by a backcross to L1 (L3) and a subsequent intercross are performed, then the offspring from the two sides are crossed and followed by a backcross to L1 and a subsequent intercross to obtain the desired genotype) is optimal when the recombination rate ranges from 0.1 to 0.4, while Scheme F (cross and subsequent intercross between the four lines are performed successively) is the optimal when the recombination rate is 0.5. We also disscuss how the animals' reproductive capacity, the probabilities of obtaining the desired genotypes and genetic distance between adjacent genes would affect the design of an optimal scheme.