Sample size required for marker assisted selection in improving quantitative traits of self-fertilizing species

The efficiency of selection for desired trait genotypes in a molecular marker assisted selection for a quantitative trait in self-fertilizing crop is considered. The QTLs controlling the trait were assumed to be unlinked. It was supposed that the selection starts in F-2, derived from a cross between inbred lines, and this selection will terminate if one or more plants with the desired trait genotype is found. If no plant with the desired trait genotype is found in F-2 then the selection is continued in the F-3 progeny that is derived from a single selected F-2 plant. Which F-2 plant is to be selected was determined according to the rank which is related to the marker genotype of the F-2 plants. And this rank was based on the expected frequency of the desired trait genotype in the progeny. The plant with the top rank among all F-2 plants is then selected with the first priority. Additionally the number of F-3 plants in the progeny was set to be equal to the number of plants that are required for detecting one or more plants with the desired trait genotype with a given probability. The probability of getting at least one plant with the desired trait genotype is expressed as a function of the number of F-2 plants (N). The required value for N and the total number of plants (T) in F-2 and F-3 for detecting at least one plant with the desired trait genotype were calculated for different situations. T was always smaller for a single marker than for flanking markers. The minimum of T and monotonous decrease of N can be observed when the cumulative-expected-frequency of selected marker genotypes of F-2 plants increased.