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physiological peculiarity. Thus, incipient species which were infertile together would have an advantage over other incipient species which were fertile, and, whenever the struggle for existence became severe, would prevail over them and take their place. Such infertility, being correlated with constitutional or structural differences, would probably, as already suggested, go on increasing as these differences increased ; and thus, by the time the new species became fully differentiated from its parent form (or brother variety) the infertility might have become as well marked as we usually find it to be between distinct species.

This discussion has led us to some conclusions of the greatest importance as bearing on the difficult problem of the cause of the sterility of the hybrids between distinct species. Accepting, as highly probable, the fact of variations in fertility occurring in correlation with variations in habits, colour, or structure, we see, that so long as such variations occurred only sporadically, and affected but a small proportion of the individuals in any area, the infertility could not be increased by natural selection, but would tend to die out almost as fast as it was produced. If, however, it was so closely correlated with physical variations or diverse modes of life as to affect, even in a small degree, a considerable proportion of the individuals of the two forms in definite areas, it would be preserved by natural selection, and the portion of the varying species thus affected would increase at the expense of those portions which were more fertile when crossed. Each further variation towards infertility between the two forms would be again preserved, and thus the incipient infertility of the hybrid offspring might be increased till it became so great as almost to amount to sterility. Yet further, we have seen that if several competing species in the same area were being simultaneously modified, those between whose varieties infertility arose would have an advantage over those whose varieties remained fertile inter se, and would ultimately supplant them.

The preceding argument, it will be seen, depends entirely upon the assumption that some amount of infertility characterises the distinct varieties which are in process of differentiation into species; and it may be objected that of such infertility there is no proof. This is admitted; but it is urged that facts have been adduced which render such infertility probable, at least in some cases, and this is all that is required. It is by no means necessary that all varieties should exhibit incipient infertility, but only some varieties; for we know that, of the innumerable varieties that occur but few become developed into distinct species, and it may be that the absence of infertility, to obviate the effects of intercrossing, is one of the usual causes of their failure. All I have attempted to show is, that when incipient infertility does occur in correlation with other varietal differences, that infertility can be, and in fact must be, increased by natural selection; and this, it appears to me, is a decided step in advance in the solution of the problem. 1

1 As this argument is a rather difficult one to follow, while its theoretical importance is very great, I add here the following briefer exposition of it, in a series of propositions ; being, with a few verbal alterations, a copy of what I wrote on the subject about twenty years back. Some readers may find this easier to follow than the fuller discussion in the text :-

Can Sterility of Hybrids have been Produced by Natural Selection ? 1. Let there be a species which has varied into two forms each adapted to certain existing conditions better than the parent form, which they soon supplant.

2. If these two forms, which are supposed to coexist in the same district, do not intercross, natural selection will accumulate all favourable variations till they become well suited to their conditions of life, and form two slightly differing species.

3. But if these two forms freely intercross with each other, and produce hybrids, which are also quite fertile inter se, then the formation of the two distinct races or species will be retarded, or perhaps entirely prevented ; for the offspring of the crossed unions will be more viyorous owing to the cross, although less adapted to their conditions of life than either of the pure breeds.

4. Now, let a partial sterility of the hybrids of some considerable proportion of these two forms arise ; and, as this would probably be due to some special conditions of life, we may fairly suppose it to arise in some definite portion of the area occupied by the two forms.

5. The result will be that, in that area, the hybrids (although continually produced by first crosses almost as freely as before) will not themselves increase so rapidly as the two pure forms ; and as the two pure forms are, by the terms of the problem, better suited to their several conditions of life than the hybrids, they will inevitably increase more rapidly, and will continually tend to supplant the hybrids altogether at every recurrent severe struggle for existence.

6. We may fairly suppose, also, that as soon as any sterility appears some disinclination to cross unions will appear, and this will further tend to the diminution of the production of liybrids.

Physiological Selection. Another form of infertility has been suggested by Professor G. J. Romanes as having aided in bringing about the characteristic infertility or sterility of hybrids. It is founded on the fact, already noticed, that certain individuals of some species possess what may be termed selective sterility—that is, while fertile with some individuals of the species they are sterile with others, and this altogether independently of any differences of form, colour, or structure. The phenomenon, in the only form in which it has been observed, is that of “infertility or absolute sterility between two individuals, each of which is perfectly fertile with all other individuals ;” but Mr. Romanes thinks that "it would not be nearly so remarkable, or physiologically improbable, that such incompatibility should run through a whole race or strain.”1 Admitting that this may be

7. In the other part of the area, however, where hybridism occurs with perfect freedom, hybrids of various degrees may increase till they equal or even exceed in number the pure species—that is, the incipient species will be liable to be swamped by intercrossing.

8. The first result, then, of a partial sterility of crosses appearing in one part of the area occupied by the two forms, will be—that the great majority of the individuals will there consist of the two pure forms only, while in the remaining part these will be in a minority,- which is the same as saying that the new physiological variety of the two forms will be better suited to the conditions of existence than the remaining portion which has not varied physiologically.

9. But when the struggle for existence becomes severe, that variety which is best adapted to the conditions of existence always supplants that which is imperfectly adapted ; therefore, by natural selection the varieties which are sterile when crossed will become established as the only ones.

10. Now let variations in the amount of sterility and in the disinclination to crossed unions continue to occur—also in certain parts of the area : exactly the same result must recur, and the progeny of this new physiological variety will in time occupy the whole area.

11. There is yet another consideration that would facilitate the process. It seems probable that the sterility variations would, to some extent, concur with, and perhaps depend upon, the specific variations ; so that, just in proportion as the two forms diverged and became better adapted to the conditions of existence, they would become more sterile when intercrossed. If this were the case, then natural selection would act with double strength ; and those which were better adapted to survive both structurally and physiologically would certainly do so.

i Cases of this kind are referred to at p. 155. It must, however, be noted, that such sterility in first crosses appears to be equally rare between different species of the same genus as between individuals of the same species. Mules and other hybrids are freely produced between very distinct species, but are

so, though we have at present no evidence whatever in support of it, it remains to be considered whether such physiological varieties could maintain themselves, or whether, as in the cases of sporadic infertility already discussed, they would necessarily die out unless correlated with useful characters. Mr. Romanes thinks that they would persist, and urges that “whenever this one kind of variation occurs it cannot escape the preserving agency of physiological selection. Hence, even if it be granted that the variation which affects the reproductive system in this particular way is a variation of comparatively rare occurrence, still, as it must always be preserved whenever it does occur, its influence in the manufacture of specific types must be cumulative.The very positive statements which I have italicised would lead most readers to believe that the alleged fact had been demonstrated by a careful working out of the process in some definite supposed cases. This, however, has nowhere been done in Mr. Romanes' paper; and as it is the vital theoretical point on which any possible value of the new theory rests, and as it appears so opposed to the self-destructive effects of simple infertility, which we have already demonstrated when it occurs between the intermingled portion of two varieties, it must be carefully examined. 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 themselves infertile or quite sterile ; and it is this infertility or sterility of the hybrids that is the characteristic--and was once thought to be the criterion

-of species, not the sterility of their first crosses. Hence we should not expect to find any constant infertility in the first crosses between the distinct strains or varieties that formed the starting - point of new species, but only a slight amount of infertility in their mongrel offspring. It follows, that Mr. Romanes' theory of Physiological Selection—which assumes sterility or infertility between first crosses as the fundamental fact in the origin of species --does not accord with the general phenomena of hybridism among animals.

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. The probabilities are, therefore, that ninetenths 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 98,180 pairs of the normal variety to 12201 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.

A mathematical friend has pointed out that in the preceding calculation I have omitted two factors which influence the result without altering its character. These are, the few crosses that may occur between the newly produced physio1 The exact number is 1219.51, but the fractions are omitted for clearness.

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