Univariate estimates of sexual dimorphism: the effects of intrasexual variability

The difference between male and female values of quantitative traits depends on the distribution of the variables within each sex, increasing with the rise in the difference between male and female average values and with the decrease of the dispersion of measurements in both sexes. This paper deals with the sensitivity of some widely used indices (relative difference between male and female mean values (MDI), Student's t, and the so-called Bennett-Chakraborty-Majumder D coefficient) with respect to intrasexual variability. The Kolmogorov-Smirnov distance (KS) is suggested here as a further index of dimorphism, although it is not usually utilized for this purpose. The theoretical approach is accompanied by the analysis of empirical data (metric variables obtained from a sample of present Sardinians) and by computer simulations under various assumptions. Indices based on the difference between male and female average values are not able to evaluate fully the various aspects of dimorphism. Student's t proved to be an adequate measure of whole sex differences, both in real and in simulated samples, as intrasexual variability is included in its formulation. The D index also proved to be a good measure of undivided sexual dimorphism, as it is the result of formal examination, and from application to empirical or to simulated cases. The Kolmogorov-Smirnov distance gave the best performance both in formal examination and in the whole simulation results, as it takes into account intrasexual variability, and is applicable to any kind of distribution. In simulated cases it was sensitive to variations of means and variances, and it was able to evaluate variance dimorphism. Since the last three indices measure the combined effect of size and variance dimorphism, the joint use of the MDI index is suggested in order to isolate the relative contribution of the difference between the means.