Determining the minimum sample size required to obtain sufficient progeny with a desired genotype at two quantitative trait loci

In this paper we determine the minimum progeny sample size n needed to obtain, with probability α, at least m individuals of a desired two-locus genotype [Symbol: see text] affecting quantitative traits. The two quantitative trait loci (QTLs) of interest may be linked or independent, with or without epistatic interaction between them. Parental genotypes may be known or unknown, and gene action at either locus may range from additive to overdominance. To reduce the required sample size, mating patterns that will produce a high proportion of desired progeny are suggested for different progeny genotypes and dominance levels. Based on the assumption of normally distributed quantitative trait expression, individuals can be classified into a genotype or genotypic group according to their phenotypic expressions. This technique is used to select both parents and progeny with unknown genotypes. Choice of parental classification criteria for a given quantitative trait affects classification accuracy, and hence the probability of obtaining progeny of the desired genotype. The complexity of this probability depends on the dominance level at each locus, the recombination fraction, and the awareness of parental genotypes. The procedure can be expanded to deal with more than two loci.