## Measuring the Sex Difference in Fitness Variance

Most research on sexual selection and its effects on mating systems has focused either on the context in which sexual selection occurs (i.e., via male combat or female choice), or on the evolutionary outcome of sexual selection (i.e., on descriptions of sexual dimorphism or mating behavior). This research has led to fascinating results; it is the same approach used by Darwin himself; but unfortunately, these results do not consider either the process or the extent to which sexual selection may achieve its evolutionary effects. To understand whether and to what degree the sexes may become distinct within a species, and to understand if sexual selection could be responsible for such divergence among related species, it is necessary to measure the fitness variance for males and females within as well as among species. This method illustrates when and why sexual selection can be strong enough to overwhelm the effects of natural selection and, therefore, how it can produce the sex-specific phenotypes researchers find so compelling.

Consider a hypothetical population, say of albatrosses or penguins, consisting of 20 individuals and a sex ratio equal to 1. If, in a given breeding season, a single ovum from each of the 10 females in the population is fertilized by a different male, the total number of offspring, ^ototal, equals (1 ovum) x (10 females) = 10. Because each mating pair produces 1 offspring, the total offspring produced by all females, NO,, equal the total offspring produced by all males, NO? = 10. Because there are 10 females and 10 males in our population, the average offspring per female, O,, equal NOtotal/N, = 1, which equals the average offspring per male, O?, evaluated similarly as NOtotal/ N? = 1. Also, because each individual in the population produces the same number of offspring (=1), no variance in offspring numbers can exist for either sex. Thus, if Vq, and VO? equal the variance in offspring numbers among females and among males, respectively, VO, = VO? = 0. This example shows that, regardless of whether the number of fertilized ova each female produces is 1, or 106, when each female is mated by a single male and the sex ratio equals 1, barring sex differences in juvenile viability, there can be no sex difference in the variance in fitness between the sexes.

This example goes a long way toward explaining why wind-pollinated plants, marine species with external fertilization, and even hermaphroditic organisms, all tend to show little sexual dimorphism. In each of these cases, population sex ratios equal to or are nearly 1, and pollen or sperm are either so widespread or so restricted in their distribution that individual males and individual females both have similar probabilities of reproduction and tend to contribute approximately equally to the next generation. In the case of hermaphrodites, both sexes are represented in each individual, thus reproduction by one sex means reproduction by the other, and unless some individuals emphasize one sex or the other sex (as occurs in some marine flatworms), the population-wide variance in fitness through male and female functions is approximately equivalent. When such conditions apply, neither sex is likely to become distinct from the other, except as is specifically required for the production of ova or sperm.

Now consider a case in which 1 of the 10 males secures 2 mates instead of just 1. The total offspring produced by our population, NOtotal = 10, remains unchanged. Similarly, because N? = N, = 10, the average offspring per male, O? = NOtotal/N? = 1, equal the average offspring per female, O, = NOtotal/N, = 1. Because each female still secures 1 mate with whom she produces a single brood, the variance in offspring numbers for females, Vq, = 0. However, because 1 male has 2 mates, 1 male must be excluded from mating. When this happens, the variance in offspring numbers among males, VO?, must increase.

If paternity data were available for our population, we could estimate the magnitude of the increase in VO? simply by calculating the statistical variance in offspring numbers for males. When such data are available, this is indeed the simplest approach. However, as is more often the case, when paternity data are lacking, an equally accurate and in fact more informative approach involves partitioning the variance in offspring numbers within and among the classes of mating and nonmating individuals. In the example above, only males were variable in their numbers of mates, but in many species, both sexes may vary in mate numbers, and in sex-role-reversed species, including certain sea spiders, giant water bugs, and pipefish, females are consistently more variable in mate numbers than males. Although they are seldom used for this purpose, the data necessary to calculate the mean and variance in mate numbers for males, and the mean and variance in offspring numbers for females, are often available in standard life history analyses. This quantitative approach allows us to measure the fitness variance within each sex, which is proportional to the intensity of selection. The sex difference in selection intensity, in turn, estimates the degree to which the sexes will diverge in phenotype.