In doing so, I will suppose that the required variation is not of "rare occurrence," but of considerable amount, and that it appears afresh each year to about the same extent, thus giving the theory every possible advantage.
Let us then suppose that a given species consists of 100,000 individuals of each sex, with only the usual amount of fluctuating external variability.

Let a physiological variation arise, so that 10 per cent of the whole number--10,000 individuals of each sex--while remaining fertile _inter se_ become quite sterile with the remaining 90,000.

This peculiarity is not correlated with any external differences of form or colour, or with inherent peculiarities of likes or dislikes leading to any choice as to the pairing of the two sets of individuals.

We have now to inquire, What would be the result?
Taking, first, the 10,000 pairs of the physiological or abnormal variety, we find that each male of these might pair with any one of the whole 100,000 of the opposite sex.

If, therefore, there was nothing to limit their choice to particular individuals of either variety, the probabilities are that 9000 of them would pair with the opposite variety, and only 1000 with their own variety--that is, that 9000 would form sterile unions, and only _one_ thousand would form fertile unions.
Taking, next, the 90,000 normal individuals of either sex, we find, that each male of these has also a choice of 100,000 to pair with.