Approximate estimation of minimal sample size required for marker-assisted backcross breeding.

Backcross breeding is a useful method to transfer favorable alleles from a donor parent into a recipient parent. Marker-assisted selection (MAS) can speed up the process. To make an appropriate plan before using MAS in a breeding program, breeders need to know the minimal sample size of the progeny generation required. A method to estimate the minimal sample size required for marker-assisted backcross breeding when both foreground selection and background selection are conducted is proposed. On the basis of a simplified assumption that the target loci are introgressed and the genetic background are independent, the probability of selecting individuals with desired genotypes in each generation is approximately estimated combining analytical approach (for foreground selection) and simulation according to the graphic genotypes of backcrossing parents (for background selection). The minimal sample size required to obtain at least one desired individual with a given probability is estimated. Application of the method is demonstrated with hypothesized examples. The method can be conveniently applied to practical backcross breeding programs.