A Measure of Sexual Dimorphism in Populations which are Univariate Normal Mixtures

Abstract

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.

Sexual size dimorphism and the rejection of Rensch’s rule in Diplopoda (Arthropoda)

“…Further studies of diplopod sexual dimorphism may include more taxa and make use of the length and width measurements to calculate volumes using the geometric morphometric approach shown here for finding causal relationships of dimorphism. The sexual dimorphism calculated here may be converted into alternative indices of sexual dimorphism in order to update its relevance, e. g. M I index [80,81] . It is worth noting sexual dimorphism and the selection pressures may be decoupled in time e. g. ostracodes [82] .…”

Dispersion dimorphism in human populations

“…The literature on dispersion dimorphism (Cope and Lacy, 1992;Ipiñ a and Durand, 2000;Kelley and Plavcan, 1998;LaVelle, 1995;Cheverud, 1982, 1985;Leutenegger and Larson, 1985;Marini et al, 1999;Meindl et al, 1985;Oxnard, 1987;Plavcan, 2000Plavcan, , 2001Plavcan and Cope, 2001;Plavcan and Kay, 1988;Tague, 1989Tague, , 1991Tague, , 1992Tague, , 1995Wood, 1976), directed toward the study of skeletal and dental traits in nonhuman primates and in humans, is characterized by discor-dant results sometimes obtained by inadequate statistical methods.…”

“…Am J Phys Anthropol 127: 342-350, 2005. Intrasexual variability is a distinct level within the hierarchical classification of variation, starting with the ontogeny of individuals and going through intrasexual, intersexual, interdemic, subspecific, and interspecific levels (Albrecht and Miller, 1997). As concerns the study of sexual dimorphism in primates, intrasexual variability has received sporadic consideration (Cope and Lacy, 1992;Ipiñ a and Durand, 2000;Kelley and Plavcan, 1998;LaVelle, 1995;Cheverud, 1982, 1985;Leutenegger and Larson, 1985;Marini et al, 1999;Meindl et al, 1985;Oxnard, 1987;Plavcan, 2000Plavcan, , 2001Plavcan and Cope, 2001;Plavcan and Kay, 1988;Tague, 1989Tague, , 1991Tague, , 1992Tague, , 1995Wood, 1976).…”

Inferential assessment of the MI index of sexual dimorphism: A comparative study with some other sexual dimorphism measures

“…In a previous study dealing with measures of sexual dimorphism, we proposed an index that was called MI whose definition, range and calculation were there established (Ipiña and Durand, 2000). To summarize, MI measures the overlap between the two functions composing a two normal mixture model, which is the same as saying that our proposed index calculates the overlap between two functions that represent the contribution of each sex in the mixture (see Fig.…”

“…In our previous study, the interested reader can consult the biological background that justifies both the proposal and the application of sexual dimorphism measures (Ipiña and Durand, 2000). In this study, we have analyzed the inferential structure of the MI index and constructed an interval estimate on the basis that the interval estimates of the mixture parameters have been calculated.…”