## Abstract

Selection of animals based on the conditional mean of the genotype given all data maximizes expected genetic progress. The genotypic model used for marker assisted selection leads to a conditional distribution that is the weighted sum of normal densities. The conditional mean is the weighted sum of conditional means, and the likelihood of the data is the sum of weighted normal likelihoods.' In all of the above, the sum is over all possible kn marked QTL genotypes, where k is the number of genotypes at the marked QTL, and n the number of animals. In human genetics, computable algorithms for the likelihood have been devised by writing it as the product of conditional densities. Such algorithms are not available for the conditional mean. Approximations for the conditional mean and likelihood are discussed.

*Proceedings of the World Congress on Genetics Applied to Livestock Production*, Volume XIII. Plenary lectures, molecular genetics and mapping, selection, prediction and estimation., , 433–436, 1990

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