The variances of the distributions of the combinations of the sexes within mammalian litters: Notes to mark the centenary of the problem

It is 100 years since Gini noted that in some samples of litters of mice and rabbits, the variances of the distributions of the combinations of the sexes are sub-binomial. In other words, in contrast with binomial expectation, there are too many litters in which the sexes are equally balanced, and there are too few unisexual litters. In the intervening years, this finding has been replicated in a number of further species, but no explanation has become established. Potential explanations are reviewed here, and it is suggested that the most likely cause is that, at the time of formation of the zygotes, p, the probability that a zygote will be male, varies from one zygote to another within litters, thus constituting an example of Poisson variation. And it is a standard result in probability theory that such variation causes sub-binomial variance.