Directional selection on a quantitative character is predicted to decr
ease genetic variance and lead to rapid fixation of alleles. However,
many traits vary in a dichotomous manner although the underlying genet
ic determination is polygenic. This paper presents a theoretical exami
nation of the effects of directional selection on a dimorphic trait. S
uch selection can change the incidence of the selected morph from 50 p
er cent to 99 per cent within 20 generations. However, after an initia
l decline heritability is predicted to rise back to its original value
. The consequences of a finite number of alleles and loci on this pred
iction are examined using a simulation model. These simulations show t
hat, unlike the case of directional selection on a continuously distri
buted trait, there is little loss of genetic variance even when the tr
ait is controlled by only three loci with two alleles per locus.