1. The phenomenon of frequency-dependent selection with an advantage for the rare type over the common type is intriguing because it implies balancing selection. Thus the high level of genetic variability as found in natural populations can be explained without the necessity of considerable genetic load. Rare male mating advantage is here defined as frequency-dependent male sexual fitness with the rare type of male favoured. Such a rare male effect has been found to be very widespread in insects, at least under laboratory conditions, but there are several problems associated with this phenomenon which will be discussed in this review.

2. To determine whether male mating success is frequency-dependent, the quantity to be considered, most appropriately, is male sexual fitness of the one type relative to the other type (KM). Other approaches are discussed and it is shown that they confound differential mating success with frequency dependence of mating success. Moreover, it is shown that Levene's indices, previously designed as a measure of differential mating success, confound mating success with assortment, making these indices less useful.

3. The theoretical relationship between frequency dependence of male mating success and total sexual fitness is more complicated than would be expected beforehand. Some examples are given to clarify this issue.

4. Statistical tests to determine frequency dependence of male mating success have often been carried out in the past by determining the significance of deviations from random mating for each male type frequency separately. This procedure must be considered incorrect, because a change in male mating success over frequencies has to be tested. A correct way to do this is by testing all frequencies together in one single statistic, with only a moderate assumption about the type of frequency dependence. When mating success depends on frequency in a more irregular way, alternative tests are available, in which mating success at one frequency can be tested against any other frequency.

5. The rare male effect has been studied most thoroughly in Drosophila, and has been demonstrated for many Drosophila species. The effect has been demonstrated for some other insects as well, and also for vertebrates. The rare male effect has been found for types of males differing in specific genotype (visible mutants, karyotypes), genetic background and geographic origin. A rare male effect has also been demonstrated for non-genetic properties such as temperature of rearing. Though much less common than rare male mating advantage, there are some examples of rare female mating advantage. The expression of the rare male effect may be affected by several factors, such as age of the females, temperature or experimental approach.

6. Only a few studies on rare type mating advantage in Nature have been carried out, but some positive evidence is available.

7. It is pointed out that mating success will be frequency-dependent if both types of males differ pronouncedly in mating behaviour, but the nature of this frequency dependence may vary. If one type of male is more vigorous than the other type, a one-sided rare male effect can be explained on the basis of male–male competition. Quite often, though, a two-sided rare male effect has been found for males not greatly differing in mating behaviour or mating success. Three types of explanations are considered: (a) The females prefer to choose the rare type of male; (b) The rare type of male compensates for its rarity by becoming more sexually active; (c) No individual behaviour is altered.

8. As to the question whether the rare male effect could be an artefact of the experimental setup, the following points are relevant;

(a) Biases as a result of alternate marking resulting in rare male mating advantage are theoretically possible, but are shown to be unimportant in explaining the rare male effect for Drosophila.

(b) An effect analogous to the effect of alternate marking due to finite sample size is conceivable, but probably less important than suggested by Bryant et al. (1980).

(c) When males are not sampled randomly with respect to place in the vial, bias may be introduced, resulting in a spurious rare male effect.

(d) We feel that the standpoint of Bryant et al. (1980) that there is not yet any good evidence for the existence of a rare male effect is not sustained. Positive proof in favour of the existence of the rare male effect is that the effect can be modified by changing only one factor, such as odour. The artifacts just mentioned cannot explain why a rare male effect should be present in the one but absent in the other situation.