570 ])r. F. A. Dix^s reply to Mr. G. A. K. Marsliall 



the type. These omissions destroy the remainder of the 

 foundation on which his a iiriori fabric is based. 



But periiaps, after all, it was unnecessary to offer one's 

 own reasons for dissenting from Mr. Marshall's conclusions, 

 for he has himself made two admissions which virtually 

 undermine his case. 



The first of these is that, as he puts it with great 

 candour, " two lines of argument, based on the same data, 

 have led to diametrically opposite results " (p. 101). This 

 is a somewhat striking phenomenon, and ought of itself 

 to suggest caution in dealing with these problems by 

 numerical methods. In giving his view of the cause of 

 the discrepancy, he fully recognises that his arithmetical 

 argument is entirely competent to prove the advantage, 

 to both sides, of any Miillerian combination once effected ; 

 though he holds that it does not succeed in accounting for 

 the process of for motion of such an assemblage, except in 

 the case of considerable disparity of numbers. But when 

 the process is complete, his ditticulty ceases. 



How is it then that he finds in the formation of a 

 Miillerian assemblage a stumbling-block of this kind ? 

 The reason is that he is himself labouring under the error 

 of which he accuses his opponents, viz., that in the repre- 

 sentation of the case the intermediate stages are not 

 adequately taken into account. The truth of the matter 

 is that so soon as the aposeme of species B occurs in any 

 of the individuals of species A, the Miillerian association 

 B + A' is already formed, and A' enjoys its advantage. On 

 Mr. Marshall's own showing, A' now virtually belongs to B, 

 which class is strengthened by its accession; and whatever 

 may be A"s chances of survival as compared with typical 

 A, it has at any rate found a place in an assemblage which 

 has so far been able to maintain itself. If its new diameter 

 is of such a kind as to be subject to Mendelian laws of 

 inheritance, there is no reason why it should not persist 

 under the shelter of B, even in the absence of reinforce- 

 ment from its original stock. 



But a much more important consideration than the 

 above is the fact that the first appearance of aposeme B 

 is consistent with the persistence of aposeme A : a fact 

 which is constantly overlooked, though it is really implicit 

 in the statement that the Darwinian idea of the evolution 

 of a case of mimicry (which is that accepted by Mr. Mar- 

 shall) " involves the assumption that it has been built up 



