A measure of sexual dimorphism in populations which are univariate normal mixtures

Measures of sexual dimorphism have been used extensively to predict the social organization and ecology of animal and human populations. There is, however, no universally accepted measure of phenotypic differences between the sexes. Most indices of sexual dimorphism fail to incorporate all of the information contained in a random data set. In an attempt to have a better alternative, an index is proposed to measure sexual dimorphism in populations that are distributed according to a probabilistic mixture model with two normal components. The index calculates the overlap between two functions that represent the contribution of each sex in the mixture. In order to assess such an index, sample means, variances and sizes of each sex are needed. As a consequence, the sample information used is greater than that used by other indices that take intrasexual variability into account. By evaluating some examples, our proposed index appears to be a more realistic measure of sexual dimorphism than other measures currently used.