# An evolutionary theory for the variability hypothesis

An elementary mathematical theory based on “selectivity” is proposed to address a question raised by Charles Darwin, namely, how one gender of a sexually dimorphic species might tend to evolve with greater variability than the other gender. Briefly, the theory says that if one sex is relatively selective then from one generation to the next, more variable subpopulations of the opposite sex will tend to prevail over those with lesser variability; and conversely, if a sex is relatively non-selective, 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 non-selective. Two mathematical models are presented: a discrete-time one-step statistical model using normally distributed fitness values; and a continuous-time deterministic model using exponentially distributed fitness levels.

That is from a new paper by Theodore P. Hill, via Derek. Here is some of the history behind the paper, which ended up being “spiked.” And here is Andrew Gelman’s take. Here are relevant emails to the dispute.