Thomas Belt suggested that the frequent limitation of mimicry in butterflies to the female resulted from sexual selection. Because female butterflies store sperm they can be fully fertile after only one mating; the reproductive success of a male is proportional to the number of times he mates. Sexual selection is therefore much stronger in males than females, with selection coefficients being greater by a small multiple of the number of times a female is courted during her life (long-lived species) or of the reciprocal of the female mortality rate between courtships (short-lived species). As butterflies of both sexes respond to colour when courting, sexual selection resists colour changes especially strongly in males. As a result, genes conferring new mimetic colour patterns can often become established in a butterfly population much more readily if their expression is initially limited to females; when the population size of a Batesian mimic, its model, and its predator fluctuates, such sex-limited genes have an enhanced probability of ultimate fixation in the population, and a reduced chance of loss; this effect is accentuated by the selection of modifiers which improve the mimicry. When the establishment of unimodal mimicry (expressed in both sexes) is favoured in a Batesian mimic, the gene tends to rise to an equilibrium frequency at which modifiers suppressing the expression of the mimicry only in males and'modifiers enhancing the mimicry only in females are favoured. The outcome is female-limited mimicry, or unimodal mimicry with better mimicry in the females, the males either retaining some of their sexual colour or the selective behaviour of the females becoming altered. In a Muellerian mimic there is no such equilibrium and selection ultimately favours expression of mimicry in both sexes and an appropriate alteration in the courtship responses. Hence Muellerian mimicry is seldom female-limited. Exceptional cases appear to result from the sexes flying in separate habitats. The genetical evidence in Papilio and Heliconius favours initial limitation of expression over subsequent modification as the usual basis for female-limited mimicry.
Other explanations of female-limited mimicry can be found wanting in various ways; a higher predation rate on females could produce sex-limitation, but is probably not a strong factor. But the greater variability of the female in Lepidoptera may indicate lesser developmental stability, which could result in greater penetrance of mutants in the female, and hence account for the initial female-limitation. At very high densities of a mimetic species which has no non-mimetic form, mimicry tends to deteriorate more rapidly in a unimodal than in an otherwise identical sex-limited species. Although by itself this would equally favour male-limitation, and hence cannot explain the predominance of female-limitation, this effect may over evolutionary time be causing a slight increase in the proportion of sex-limited species among mimics.
The stability of some mimetic polymorphisms is investigated by linear approximation: in some instances a stable equilibrium can be changed into an oscillating equilibrium by changes in the population size.