Frequency-dependent sexual selection.
Sexual selection by female choice is expected to give rise to a frequency-dependent sexual advantage in favour of preferred male phenotypes: the rarer the preferred phenotypes, the more often they are chosen as mates. This 'rare-male advantage' can maintain a polymorphism when two or more phenotypes are mated preferentially: each phenotype gains an advantage when it is rarer than the others; no preferred phenotype can then be lost from the population. Expression of preference may be complete or partial. In models of complete preference, females with a preference always mate preferentially. Models of partial preference are more realistic: in these models, the probability that a female mates preferentially depends on the frequency with which she encounters the males she prefers. Two different 'encounter models' of partial preference have been derived: the O'Donald model and the Charlesworth model. The encounter models contain the complete preference model as a limiting case. In this paper, the Charlesworth model is generalized to allow for female preference of more than one male phenotype. Levels of frequency dependence can then be compared in the O'Donald and Charlesworth models. The complete preference model and both encounter models are formulated in the same genetical terms of preferences for dominant and recessive male phenotypes. Polymorphic equilibria and conditions for stability are derived for each of the three models. The models are then fitted to data of frequencies of matings observed in experiments with the two-spot ladybird. The complete preference model gives as good a fit as the encounter models to the data of these and other experiments. The O'Donald and Charlesworth encounter models are shown to produce a very similar frequency-dependent relation. Generally, as females become less choosy, they express their preference with more dependence on male frequency, whereas the resulting selection of the males becomes less frequency dependent. More choosy females are more constant in expressing their preference, producing greater frequency dependence in the selection of the males.