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. The probabilities are, therefore, that nine-tenths of them—that is, 81,000—would pair with their normal fellows, while 9000 would pair with the opposite abnormal variety forming the above-mentioned sterile unions.
Now, as the number of individuals forming a species remains constant, generally speaking, from year to year, we shall have next year also 100,000 pairs, of which the two physiological varieties will be in the proportion of eighty-one to one, or 98,780 pairs of the normal variety to 1220[64] of the abnormal, that being the proportion of the fertile unions of each. In this year we shall find, by the same rule of probabilities, that only 15 males of the abnormal variety will pair with their like and be fertile, the remaining 1205 forming sterile unions with some of the normal variety. The following year the total 100,000 pairs will consist of 99,984 of the normal, and only 16 of the abnormal variety; and the probabilities, of course, are, that the whole of these latter will pair with some of the enormous preponderance of normal individuals, and, their unions being sterile, the physiological variety will become extinct in the third year.
If now in the second and each succeeding year a similar proportion as at first (10 per cent) of the physiological variety is produced afresh from the ranks of the normal variety, the same rate of diminution will go on, and it will be found that, on the most favourable estimate, the physiological variety can never exceed 12,000 to the 88,000 of the normal form of the species, as shown by the following table:—
1st Year. 10,000 of physiological variety to 90,000 of normal variety.
2d " 1,220 + 10,000 again produced.
3d " 16 + 1,220 + 10,000 do. = 11,236
4th " O + 16 + 1,220 + 10,000 do. = 11,236
5th " O + 16 + 1,220 + 10,000 = 11,236
and so on for any number of generations.
In the preceding discussion we have given the theory the advantage of the large proportion of 10 per cent of this very exceptional variety arising in its midst year by year, and we have seen that, even under these favourable conditions, it is unable to increase its numbers much above its starting-point, and that it remains wholly dependent on the continued renewal of the variety for its existence beyond a few years. It appears, then, that this form of inter-specific sterility cannot be increased by natural or any other known form of selection, but that it contains within itself its own principle of destruction. If it is proposed to get over the difficulty by postulating a larger percentage of the variety annually arising within the species, we shall not affect the law of decrease until we approach equality in the numbers of the two varieties. But with any such increase of the physiological variety the species itself would inevitably suffer by the large proportion of sterile unions in its midst, and would thus be at a great disadvantage in competition with other species which were fertile throughout. Thus, natural selection will always tend to weed out any species with too great a tendency to sterility among its own members, and will therefore prevent such sterility from becoming the general characteristic of varying species, which this theory demands should be the case.
On the whole, then, it appears clear that no form of infertility or sterility between the individuals of a species, can be increased by natural selection unless correlated with some useful variation, while all infertility not so correlated has a constant tendency to effect its own elimination. But the opposite property, fertility, is of vital importance to every species, and gives the offspring of the individuals which possess it, in consequence of their superior numbers, a greater chance of survival in the battle of life. It is, therefore, directly under the control of natural selection, which acts both by the self-preservation of fertile and the self-destruction of infertile stocks—except always where correlated as above, when they become useful, and therefore subject to be increased by natural selection.
Summary and Concluding Remarks on Hybridity.
The facts which are of the greatest importance to a comprehension of this very difficult subject are those which show the extreme susceptibility of the reproductive system both in plants and animals. We have seen how both these classes of organisms may be rendered infertile, by a change of conditions which does not affect their general health, by captivity, or by too close interbreeding. We have seen, also, that infertility is frequently correlated with a difference of colour, or with other characters; that it is not proportionate to divergence of structure; that it varies in reciprocal crosses between pairs of the same species; while in the cases of dimorphic and trimorphic plants the different crosses between the same pair of individuals may be fertile or sterile at the same time. It appears as if fertility depended on such a delicate adjustment of the male and female elements to each other, that, unless constantly kept up by the preservation of the most fertile individuals, sterility is always liable to arise. This preservation always occurs within the limits of each species, both because fertility is of the highest importance to the continuance of the race, and also because sterility (and to a less extent infertility) is self-destructive as well as injurious to the species.
So long therefore as a species remains undivided, and in occupation of a continuous area, its fertility is kept up by natural selection; but the moment it becomes separated, either by geographical or selective isolation, or by diversity of station or of habits, then, while each portion must be kept fertile inter se, there is nothing to prevent infertility arising between the two separated portions. As the two portions will necessarily exist under somewhat different conditions of life, and will usually have acquired some diversity of form and colour—both which circumstances we know to be either the cause of infertility or to be correlated with it,—the fact of some degree of infertility usually appearing between closely allied but locally or physiologically segregated species is exactly what we should expect.