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 {73} 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 2/3 × 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 {74} 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]. * * * * * {75} CHAPTER VII THE CASE OF _PAPILIO POLYTES_