Prediction Formulae for General Combining Ability Selection Methods Utilizing One or Two Random-Mating Populations

Abstract

SummaryThis study is the first of a series in which theoretical comparisons are made among various general combining ability and specific combining ability selection methods. The particular purpose of this study is to set out the prediction formulae for all possible general combining ability selection methods which can be generated by one or two base populations.Prediction formulae are considered for various levels of genetic complexity; a single locus, two linked loci, and a generalized, genetic situation.To extend the prediction process to include a general combining ability selection procedure involving two different base populations, it is necessary to extend the gene model and variance partitioning to accommodate the hybrid population, and to define certain covariances between similar elements in different populations.When this is done, it is possible to predict the consequences of n cycles of selection followed by t generations of random mating without selection for each selection method. With the two·locus model it is possible to show how linkage and the additive X additive component of epistasis (as well as the additive genetic variance) enter into the prediction formulae when selection is applied. It is also possible to show, on relaxation from selection, that the disturbances due to linkage and epistasis tend to disappear.With the completely general genetic situation, it is demonstrated that the response to selection is a function of covariances among half· sibs. These parameters are defined either in a single population, or as a sum of cross-products involving two different populations, depending on the selection method involved.

Impact of Interpopulation Divergence on Additive and Dominance Variance in Hybrid Populations

“…In addition, a and d refer to the additive and dominance effects (Falconer and Mackay 1996). For the hybrid population p1 3 p2, s (Griffing 1962;Schnell 1965). Assume that both populations p1 and p2 are combined into one synthetic, which is randomly intermated for several generations so that linkage equilibrium is reached.…”

Comparisons of Potentials for General Combining Ability Selection Methods Utilizing One or Two Random-Mating Populations

“…) For a more detailed specification of the population parameters, selection values, and consequences of selection, the reader is referred to the previous study (Griffing 1962),…”

“…In the first paper of this series (Griffing 1962), the population and selection para· meters were given in detail. Hence ouly a brief outline will be made here.…”

“…This was demonstrated in the first paper of this series (Griffing 1962 [aik] = matrix of genotypic values, and…”

“…In the first paper (Griffing 1962) prediction formulae for genetic advance due to repeated cycles of selection were developed for each method. In this study the potentials inherent in the various methods are compared.…”