OPPORTUNITY FOR SELECTION: AN APPROPRIATE MEASURE FOR EVALUATING VARIATION IN THE POTENTIAL FOR SELECTION?

The opportunity for selection (1) is a ratio of the variance in fitness (reproductive success) to the square of mean fitness (equivalent to the square of one-hundredth ofthe coefficient ofvariation in fitness; 1= [CV/ lOOP). It has been proposed as an index of the extent ofvariation that could be subject to selection in a given population (Crow, 1958, 1962; Wade and Arnold, 1980; Arnold, 1986; Endler, 1986). Presumably the magnitude of I would index the potential for selection: small values would indicate little opportunity for selection, whereas large values would indicate greater opportunities for selection. Since I has no units, it has been used to make comparisons between sexes and between species. Such comparisons may allow one to make inferences regarding the relationship between opportunities for selection and, say, mating systems (Payne, 1984; Trail, 1985; Hafernik and Garrison, 1986). Since increased opportunities for selection imply a greater potential for evolutionary change, much attention has been given to the measurement of I values in a number of species (Wade and Arnold, 1980; Clutton-Brock, 1983; McCauley, 1983; Arnold and Wade, 1984; Payne, 1984; Price, 1984; Houck et aI., 1985; Trail, 1985; Fincke, 1986; Hafernik and Garrison, 1986). As a ratio, I changes when either of its components change: the variance may actually change (increase or decrease); and/or the mean may change (see Atchley et aI., 1976). For a given measure of fitness (such as the number of matings, mates, offspring, or clutches), mean fitness values of less than 1.0 will have a particularly dramatic effect on I. Under such circumstances, the square of the mean is less than the mean, and I is therefore amplified. Furthermore, since changes in I are assumed to reflect changes in the variance in fitness, I is presumed to be independent of the mean. If such independence between I and mean fitness does not occur, the validity ofany comparisons between I values is questionable. For example, if the distribution of matings among males of a species follows a Poisson distribution then variation in 1 is predictable. In a Poisson distribution, the variance is equal to the mean (Sokal and Rohlf, 1981) and therefore 1 will vary as the inverse of the mean (l = variance/mean= mean/mean= l/mean). While we do not expect that the mating pattern ofany animal should necessarily follow a Poisson distribution, we can use it as a reference, because it specifies the relationship between the mean and variance. To illustrate how I can vary even when patterns of mate choice do not, assume there are 100 males in a population and that mating occurs at random (Poisson distribution for numbers of matings by individual males). If few females mate (N = 5), then the mean fitness of males during a given interval (mean number of matings per male) will be 0.05, and I will be 20.0 (= 1.0/0.05). If many females mate (N = 50), then the mean fitness of males will be 0.5, and I will be 2.0. In both cases, mating is random, but I varies by an order of magnitude, reflecting the variation in number of mating females. If this is the case, variation in I would , not indicate biologically important differences in the opportunity for selection, that is, changes in the variance in reproductive success among males due to changes in patterns of mate choice. In our study ofseasonal variation in sexual selection in the mottled sculpin (Cottus bairdi), we found that total opportunities for selection among males was very highly correlated with the total mean fitness of males in each time interval that selection on males was evaluated (Downhower et aI., 1987). Observed fitness variation among individual males was largely a product of differences between males in mating success, but variation in the mean fitness of males at different times in a given breeding season was due, in part, to changes in the total number of females available as mates at different times (Downhower et aI., 1987). In addition, set rules of mate choice in this species (Downhower and Brown, 1980; Brown, 1981; Downhower et aI., 1983) fix the relationship between mean fitness and fitness variation, so opportunity for selection (1) becomes a function of mean fitness. Clutton-Brock and his co-workers have collected data on annual and age-dependent variation in I in red deer (Cervuselaphus) (Fig. I). In both sets ofdata, variation in I is significantly and negatively correlated with the mean. Although both lines lie above the values expected for a Poisson, it should be noted that the values for mean fitness in six of seven annual estimates and in three of the nine age-class estimates are less than 1.0. In red deer, the relationship between annual variation in I and the mean annual reproductive success of all males is different from the relationship between agespecific male reproductive success and age-specific measures of opportunity for selection (1) (Fig. I). In the former instance, the slope of the regression is less