Quantitative genetics of doubled haploid populations and application to the theory of line development.

The line value of a genotype is defined as the expected value of all lines that can be derived from this genotype. Specific genetic effects are defined for this value: only additive and additive by additive epistatic effects are necessary. There is no dominance effect for such a value. A general expression for the covariances between related lines is given. From a design with several lines per haplodiploidized plant taken at random from a population it is possible to estimate the additive variance for line value and the variance of additive by additive epistasis for line value. Variances of higher order epistasis can be estimated with a two-factor mating design in which a cross is replaced by the population of lines that can be derived from it. With a diallel or a factorial design a direct test for the presence of homozygous by homozygous epistasis is possible. The application of the concept of line value to the theory of line development leads to simple expressions of genetic advance in one cycle of recurrent selection according to the testing system. A brief consideration of these expressions leads to the conclusion that single doubled haploid descent recurrent selection will be one of the most efficient methods for low heritabilities and with a rapid development of doubled haploid lines.