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

Abstract

SummaryThis study is concerned with comparisons of potentials exhibited by the entire class of general combining ability methods which can be generated by one or two random-mating populations. By potential is meant the greatest value the population mean assumes with continued application of a given selection method initially applied to a population of specified genetic constitution. The argument is restricted to an arbitrary number of alleles at a single locus, and it is assumed that the populations are infinite in size.Considerable attention is devoted to the situation of overdominance. In this case, the potential of a mating system depends on whether or not a stable equilibrium is possible. The equilibrium theory for multiple alleles is used to demonstrate that a stable equilibrium state exists for a general combining ability test in which the popu· lation undergoing selection, itself, is used as tester. However, when the population undergoing selection is tested by some other population, the solution is more complicated. For example, with reciprocal selection, it is shown that the eqUilibrium (if it exists) in the hybrid population is unstable. This leads to fixation of alleles in the parent popUlations. However, if there are more than three alleles at the locus, more than one fixable region exists on the topography generated by the hybrid popu· lation mean. In this situation, reciprocal selection carries the hybrid population to one of several genotypic values which may. or may not, be the greatest value in the population.These equilibrium results are used in making comparisons among the various selection methods in terms of their potentials for the overdominant situation.Similarly. potentials of the mating systems are compared for the case of partial dominance.From these considerations of potentials, selection programmes are suggested for the situations in which heterosis is, or is not, used.

Computer simulation of reciprocal recurrent selection with overdominant gene action

“…This result should not be interpreted to mean that, in practice, selection utilizing an inbred tester (RST) would always be superior to RRS. While initial selection response may be more rapid for RST, this method does not, in contrast to RRS, allow maximum utilization of non-overdominant loci (Comstock et ah, 1949;Griffing, 1963) and thus has a lower expected selection limit.…”

“…Dickerson (1952) has pointed out that when both populations involved in RRS are initially at equilibrium frequencies for the same over-dominant loci, the cross progenies display the same gene frequency, and selection for cross performance is likely to have little effect in the first few generations. While the genetic equilibrium of over-dominant alleles under selection for intrapopulation performance is a stable one, it can be shown that selection for cross performance between such populations will render these equilibria unstable (Griffing, 1963). Small perturbations of equilibrium gene frequencies in either or both populations may then lead to genetic change under selection for cross performance.…”

Evaluation of three grain maize composites developed from broad-base synthetics by divergent selection on three complementary testers

“…On theoretical data, Cress (1966) found that, at overdominant loci, the maximum hybrid combination could not be obtained by maintaining separate populations. Griffing (1963) (fig 1).…”

Response to eight cycles of full-sib reciprocal recurrent selection for grain yield and standability in BS10 and BS11 maize populations

“…Russell and Eberhart (1975) proposed the use of inbred lines derived from each of the two populations as testers, which would increase the variance among testcross families and would avoid sampling problems. Griffing (1963) and claimed that the full potential of reciprocal selection could not be achieved unless the favorable alleles are present in both populations. Since no improvement on loci, which are already fixed in at least one of the parental populations, is possible.…”