Additive Variation Maintained under Stabilizing for Two Quantitative Characters Selection: a Two-locus Model of Pleiotropy

A model with two diallelic loci controlling two additive quantitative characters is suggested. One of the loci has a similar effect on both characters, whereas the second locus has an antagonistic effect on the two characters. Both characters experience direct stabilizing selection. The model yields a stable polymorphic state, with both characters maintaining genetic variation. The genetic correlation between the characters at the equilibrium is zero, in spite of the pleiotropic effects of the loci controlling them. HE question about the amount of genetic variation that can be maintained T in a population under stabilizing selection is prominent in theoretical population genetics; however, an answer to this question is far from being certain. Starting from the work by FISHER (1930), who showed that genetic variation is always reduced by stabilizing selection, it has been amply demonstrated that, in the absence of other forces, no genetic variation can be permanently maintained under stabilizing selection for an additive quantitative character controlled by several loci having similar effects on the character (except for the variation due to a maximum of one segregating locus if the number of loci is odd) (BULMER 1971; KOJIMA 1959; LEWONTIN 1964; ROBERTSON 1956; WRIGHT 1935). A number of models have been developed that incorporate mutations as a source of variation, and suggestions have been made that mutation-selection balance can possibly account for the relatively high levels of genetic variation maintained in natural populations (BULMER 1972; KIMURA 1965; LANDE 1976; LATTER 1960; TURELLI 1984). The mutation-selection balance hypothesis, however, has not won unanimous acceptance. One of the main arguments against it is that mutation rates must be very high and selection very weak in order for mutation-selection balance to maintain the levels of genetic variation found in natural populations. The argument could have been settled if reliable estimates were available of mutation and selection parameters for quantitative characters in real populations. Unfortunately, the difficulties in obtaining reGenetics 112: 717-725 March, 1986