The soul of many an anti-Darwinian will have been cheered by Mr. A.W. Bennett’s paper on ‘The Theory of Natural Selection from a Mathematical Point of View.’ It is, in fact, a very admirable piece of special pleading, based on a skilful assumption of premisses which, to a careless or biassed observer, might seem indisputable.
The tendency to variation is spoken of as something very mysterious, of which no adequate account has ever yet been given. Yet the very simple explanation is no bad one,—that where two parents are concerned in the production of any offspring, the product in part resembling each of the producers must of necessity also in part differ from each of them. Between the parents themselves, Mr. Herbert Spencer has shown that differences of age and external circumstances would ensure the requisite want of resemblance in the absence of any other cause.
‘The rigid test of mathematical calculation’ is then applied to the case of mimetic butterflies, with the view of showing that they could not have been produced simply according to the laws of variation, inheritance, and natural selection. In the application of this rigid test, the very first step is a perfectly gratuitous assumption, ‘that it would require, at the very lowest calculation, one thousand steps to enable the normal Leptalis to put on its protective form.’ Who is to prove that fifty differences would be insufficient? An interval of a thousand years might be granted for establishing each one of these variations. Suppose even fifty thousand, instead of only fifty steps, to be necessary, it is another gratuitous assumption that ‘the smallest change in the direction of the Ithomia, which we can conceive on any hypothesis to be beneficial to the Leptalis, is at the very lowest one-fiftieth of the change required to produce perfect resemblance.’ How small a difference must decide the choice made by a donkey placed equidistant between two bundles of hay! Certainly, then, a bird on the wing, having to choose amidst myriads of butterflies, may be determined by an almost infinitesimal distinction. Further, though the whole change may be produced by an immense number of small changes, it is not necessary to suppose that all the changes will be equally small. It is merely begging the question to assume that the first change could not possibly be large enough to be of any use. And if it may be of use, the whole mathematical calculation, based on its being useless, breaks down from the beginning. Again, since the Leptalis may have spent one million years in arriving at its present likeness to the present Ithomia, it is impossible to assert that the normal forms of the two butterflies were as wide apart at the beginning of that period as they are at present. The mimicry having once set in, might be retained by parallel variations. This, indeed, cannot fail to be the case, if the protection is to be a lasting one; for when the Ithomia varies in outward appearance, unless the Leptalis varies in the same direction, the resemblance will be lost. This progressive mimicry would be more valuable than an imitation in which no changes occurred, since the enemies of a mimetic species would in time become aware of a fraud which had no variations at its command, as birds are said now-a-days to pounce without hesitation upon caterpillars which very much resemble twigs67. Even ‘a rough imitation’ may be useful in the first instance, and yet when hostile eyes have long been exercised, and have acquired greater and greater sharpness, finally nothing less than absolute identity of appearance may be thoroughly effective. Thus the perfecting of the resemblance will be no ‘mere freak of Nature,’ nor shall we be ‘landed in the dilemma that the last stages are comparatively useless’ in this procedure.
The array of figures brought forward to prove that the Leptalis could not have made twenty steps of variation in the direction of the Ithomia by chance, would be much to the purpose if any exponent of the theory of Natural Selection had ever argued or supposed that it could. The calculation takes it for granted that the theory is erroneous, instead of proving it to be in error. Upon this assumption, it might have been put far more strongly, only that a stronger way of putting it would have borne on the face of it the suspicion of some inherent fallacy. It begins by supposing that there are ‘twenty different ways in which a Leptalis may vary, only one of these being in the direction ultimately required;’ it might quite as truthfully, or even more so, have said a thousand instead of twenty, and then the second step would have given the chance as only one in a million, instead of one in four hundred. But while the theory of Natural Selection speaks of numerous minute useful variations, Mr. Bennett will not allow that combination of terms. Let them be numerous and minute, if you will, he says; but if small, they cannot be useful; if useful, they cannot be small. He claims to have Mr. Darwin’s own word for it, that a large variation would not be permanent, as though Mr. Darwin had said, ‘living creatures have come to be what they are by successive useful deviations of structure permanently propagated, but no large deviations are permanent, and no small ones are useful.’ It is quite obvious that in the use of relative terms, such as great and small, Mr. Darwin neither intended to stultify himself nor has done so. A thing may be large enough to be useful without being large as compared with something twenty times its own size; and a man may be said to have a huge brain in a very small body, although the body in solid content far exceeds the brain. When Mr. Darwin says that ‘Natural Selection always acts with extreme slowness’, he does not imply that its steps must therefore be so numerous as to be too small to confer any advantage. This would be a contradiction in terms. But the steps may be exceedingly small notwithstanding, and also sometimes separated by enormous intervals of time from one another.
In introducing his own explanation of things, Mr. Bennett affirms that ‘resemblances, and resemblances of the most wonderful and perfect kind’ in the vegetable kingdom, ‘are in no sense mimetic or protective.’ This may be so, but it can hardly be said to be proved. When he speaks of ‘man’s reason’ having ‘assisted him so to modify his body as to adapt himself to the circumstances with which he is surrounded,’ and suggests that the instinct of animals may have assisted them also to modify their bodies by slow and gradual degrees to the same purpose, it is difficult to imagine the process intended, and still more difficult to see how ‘the slow and gradual degrees’ will escape the rigid test of mathematical calculation which Mr. Bennett has elsewhere applied; for if the steps are great, they ought not to be permanent; and if small, they ought not to be useful. A theory which makes it possible for a bee to ‘modify its proboscis’ by instinct, or for a man to treat his nose in the same manner by reason, seems harder of digestion than the Darwinian.
Torquay, Nov. 12, 1870.
