RETRACTED: An elementary mathematical theory for the variability hypothesis (Retracted Article)

A selectivity theory is proposed to help explain how one gender of a species might tend to evolve with greater variability than the other gender. Briefly, the theory says that if one sex is relatively selective, then more variable subpopulations of the opposite sex will tend to prevail over those with lesser variability; and conversely, if one sex is relatively nonselective, then less variable subpopulations of the opposite sex will tend to prevail over those with greater variability. This theory makes no assumptions about differences in means between the sexes, nor does it presume that one sex is selective and the other nonselective. Two mathematical models are presented: a statistical analysis using normally distributed fitness values, and a deterministic analysis using exponentially distributed fitness levels and a standard system of coupled ordinary differential equations. The theory is applied to the classical greater male variability hypothesis.