204 ENTOMOLOGY 



of Batesian mimicry. Bates noted that none of the pierid mimics were 

 so abundant as their heliconiid models. If they were, their protection 

 would be less; and should the mimic exceed its model in numbers, 

 the former would be more subject to attack than the latter. Some- 

 times, indeed, as Miiller found, the mimic actually is more common than 

 the model; in which event, the consequent extra destruction of the 

 mimic would at least theoretically reduce its numbers back to the 

 point of protection. 



In Miillerian mimicry, however, the inevitable variation in abun- 

 dance of two or more converging and protected species is far less dis- 

 astrous; though when two species, equally distasteful, are involved, 

 the rarer of the two has the advantage, as Fritz Miiller has shown. His 

 lucid explanation is essentially as follows : 



Suppose that the birds of a region have to destroy 1,200 butter- 

 flies of a distasteful species before it becomes recognized as such, and 

 that there exist in this region 2,000 individuals of species A and 10,000 

 of species B; then, if they are different in appearance, each will lose 

 1,200 individuals, but if they are deceptively alike, this loss will be di- 

 vided among them in proportion to their numbers, and A will lose 200 

 and B 1,000. A accordingly saves 1,000, or 50 per cent, of the total 

 number of individuals of the species, and B saves only 200, or 2 per cent. 

 Thus, while the relative numbers of the two species are as i to 5, the 

 relative advantage from their resemblance is as 25 to i. 



If two or more distasteful species are equally numerous, their re- 

 semblance to one another brings nearly equal advantages. In cases of 

 this kind and many are known it is sometimes impossible to dis- 

 tinguish between model and mimic, as all the participants seem to 

 have converged toward a common protective appearance, through an 

 interchange of features the " reciprocal mimicry" of Dr. Dixey. 



Marshall argues, however, against this diaposematism, maintaining 

 that in the case of two participants in Miillerian mimicry the evolution 

 of the mimetic pattern has been in one direction only toward the more 

 abundant species any variations in the opposite direction being dis- 

 advantageous. 



From this explanation, the superior value of Miillerian as compared 

 with Batesian mimicry is evident. 



The fourth condition that the imitators differ from the bulk of 

 their allies holds true to such a degree that even the two sexes of the 

 same species may differ extremely in coloration, owing to the fact that 

 the female has assumed the likeness of some other and protected species. 



