312 THE VARIATION OF ANIMALS IN NATURE 



legitimate to assume the occurrence of rare, beneficial mutants, 

 any mathematical treatment of the conditions under which 

 they spread demands further assumptions as to their selective 

 advantage and as to the amount of intercrossing within the 

 species. We have pointed out the difficulty of attributing a 

 constant selective advantage to a mutant which has to make 

 its way in a fluctuating environment, in a checker-board of 

 different habitats and in a species which is far from being 

 genetically homogeneous. Again, apart from the great 

 variety of factors which may produce partial isolation, the 

 mere fact that an animal is small, while the range of the species 

 is often large, introduces a measure of purely spatial isolation. 

 The result is that, in order to obtain the uniform conditions 

 necessary for mathematical calculations, a relatively small 

 subdivision of the species can alone be treated, and here the 

 unknown rate of mutation begins at once to be significant. 

 The mathematical treatment of Natural Selection cannot tell 

 us whether or not the theory is true, but it might be used to 

 give us some idea of the time-limits for evolutionary changes 

 and the limits and results of various types of selection. We 

 feel, however, that the fundamental assumptions are still 

 very insecure and we need scarcely be bound by any purely 

 mathematical restrictions. 



Finally, we have considered the indirect evidence for the 

 theory. We have intentionally thrown our net wide and 

 included material which not all zoologists would regard 

 as relevant to the Natural Selection problem. At one time 

 or another almost all biological phenomena have been supposed 

 to provide some sort of evidence for the theory, and our choice 

 was chiefly influenced by the thoroughness with which par- 

 ticular lines of inquiry had been explored. The first half of 

 the section deals with a variety of phenomena such as protec- 

 tive coloration or adaptation to life in torrents, which suggest 

 that evolutionary divergence may have been due to a selective 

 process, while in the second half we are concerned with the 

 problem of species and how far their characteristics are ex- 

 plicable on the assumption that specific divergence is mainly 

 dependent on Natural Selection. 



In our examination of numerous examples of protective 

 coloration we take the view that a generalised colouring of 

 this nature is probably fundamental in all groups. It may be 



