Is drift 'directional'? Unequal breeding sex ratio revisited

Unequal breeding sex ratio can significantly reduce effective population size, allowing a rare neutral allele to jump to a high frequency through genetic drift. However, this one-way alteration to allele frequency appears inconsistent with the concept that drift is non-directional. Based on binomial sampling distribution, this study developed a method to directly and exhaustively measure drift by calculating the mean deviation of change in allele frequency, then applied it to cases of unequal breeding sex ratio. The result shows that, under those cases, (1) the mean deviation can always be divided into two halves that are equal in size but opposite in direction; (2) each half consists of one or several categories represented by various allele proportions in the rare sex; (3) this proportion is another factor that determines the outcome of drift, in addition to effective population size and allele frequency; (4) drift is non-directional on a global scale, but whether an allele will drift up or down can be predicted based on the above factors. This method enables us to dissect every component of the expected change in allele frequency caused by drift and to find out the combined effect of population size, allele frequency and allele proportion in the rarer sex under neutrality but unequal breeding sex ratio.