Though it is difficult to regard Batesian mimicry as produced by the accumulation of small variations through natural selection, it is perhaps rather more plausible to suppose that such a process may happen in connection with the numerous instances of Müllerian mimicry. For since the end result is theoretically to the advantage of both species instead of but one, it is possible to argue that the process would be simplified by their meeting one another halfway, as Müller[[34]] himself originally suggested. Variations on the part of each in the direction of the other would be favourably selected, the mimicry being reciprocal.
Difficulties, however, begin to arise when we inquire into the way in which this unification of pattern may be conceived of as having come about. By no one have these difficulties been more forcibly presented than by Marshall[[35]] in an able paper published a few years ago, and perhaps the best way of appreciating them is to take a hypothetical case used by him as an illustration.
Let us suppose that in the same area live two equally distasteful species A and B, each with a conspicuous though distinct warning pattern, and each sacrificing 1000 individuals yearly to the education of young
birds. Further let it be supposed that A is a common species of which there are 100,000 individuals in the given area, while B is much rarer, and is represented by 5000. The toll exacted by young birds falls relatively more lightly upon A than upon B, for A loses only 1%, whereas B's loss is 20%. Clearly if some members of B varied so that they could be mistaken for A it would be greatly to their advantage, since they would pass from a population in which the destruction by young birds was 20% to one in which it would now be rather less than 1%. Moreover, as the proportion of B resembling A gradually increased owing to this advantage, the losses suffered by those exhibiting the original B pattern would be relatively heavier and heavier until the form was ultimately eliminated. In other words, it is theoretically conceivable that of two distasteful species with different patterns the rarer could be brought to resemble the more abundant.
We may consider now what would happen in the converse case in which the more numerous species exhibited a variation owing to which it was confused with the rarer. Suppose that of the 100,000 individuals of A 10,000 shewed a variation which led to their being mistaken for B, so that there are 90,000 of the A pattern and 15,000 of the B pattern of which 10,000 belong to species A. A will now lose 1000 out of the 90,000 having the A pattern, and ⅔ × 1000 out of the 10,000 of species A which exhibit the B pattern. The toll of the birds will be 1⁄90 of those keeping the original A pattern, and 2⁄30 of those of species A which have
assumed the B pattern. The mortality among the mimetic members of A is six times as great as among those which retain the type form. It is clear therefore that a variation of A which can be mistaken for B is at a great disadvantage as compared with the type form[[36]], and consequently it must be supposed that the Müllerian factor, as the destruction due to experimental tasting by young birds is termed, cannot bring about a resemblance on the part of a more numerous to a less numerous species. Further, as Marshall goes on to shew, there can be no approach of one species to the other when the numbers are approximately equal. A condition essential for the establishing of a mimetic resemblance on Müllerian lines, no less than on Batesian, is that the less numerous species should take on the pattern of the more numerous. Consequently the argument brought forward in the earlier part of this chapter against the establishing of such a likeness by a long series of slight variations is equally valid for Müllerian mimicry[[37]].