160 A BOOK OF INSECTS 



livery may be. But it is clear that if several uneatable 

 species resemble one another so closely that they are prac- 

 tically indistinguishable, the relative loss sustained by 

 each as a result of " experimental tasting " will be greatly 

 lessened. Supposing the species to be equally numerous 

 in individuals, the whole matter is reducible to a simple 

 calculation in arithmetic, subject, of course, to the law of 

 average. Thus, if two similarly coloured species are con- 

 cerned, the loss sustained by each will be halved ; if four 

 are concerned, it will be quartered ; and so on. Moreover, 

 when two species unequal in numerical importance are 

 involved, the rarer of the two has the advantage. Dr. 

 Midler's demonstration of this was essentially as follows: 

 Suppose that the birds of a region have to destroy 1200 

 butterflies of a distasteful species before it becomes recog- 

 nised as such, and that there exist in this region 2000 

 individuals of species A and 10,000 of species B ; then, if 

 they are different in appearance, each will lose 1200 indi- 

 viduals ; but if they are deceptively alike, this loss will be 

 divided among them in proportion to their numbers, and 

 A will lose 200 and B 1000. A accordingly saves 1000, 

 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 1 to 5, the 

 relative advantage from their resemblance is as 25 to 1. 

 In view of these facts it is clearly advantageous for num- 

 bers of different species to resemble one another closely — 

 to converge, as it were, upon a single type ; and this is 

 why we find a general similarity in colour and pattern 

 among great groups of species in all parts of the world. 

 The experience gained by a young insectivorous creature 

 at the expense of one species holds good for another 

 species that resembles it superficially, and so on through- 

 out the whole range of similarly coloured species, dis- 



