220 THE VARIATION OF ANIMALS IN NATURE 



internal rather than external relations is required. There 

 may be competition between different degrees of organisation 

 rather than passive selection by the external environment. 

 But we shall return to this question in our last two chapters. 



Again, it may be questioned whether the pathological 

 character of many of the mutants is not a more important 

 feature than the small structural details by which they have 

 actually been identified. If this is so, the statement that 

 even the minute structural changes seen in Drosophila mutants 

 involve loss of viability, is a truism obscured by the way it is 

 expressed. It is possible that we ought rather to say that even 

 the pathological mutations of Drosophila produce visible struc- 

 tural variations. In its natural environment it is possible 

 that an animal can throw considerably larger mutations 

 which have no ill effect at all. 



The mathematical analysis of Natural Selection and of 

 the multiplication of variants is necessary and desirable, and 

 has, we believe, already led to important results. The most 

 important, as must be expected from the novelty of the methods, 

 are a reorientation of old evidence and the indication of 

 new problems, rather than any far-reaching ' explanation ' of 

 evolution. 



We are not competent to criticise from the mathematical 

 side the methods of the various writers, but, on general grounds, 

 it appears that three main assumptions have to be made before 

 mathematical analysis can begin. These are : 



(a) A definite mutation-rate. 



(b) A definite, even if only average, survival value for a 



given mutant. 



(c) A system of random mating. 



We shall consider these assumptions in the above order. 



(a) The mutation-rate. — It is much to be regretted that our 

 present knowledge of the frequency of gene-mutations is very 

 limited. Almost all our information (gleaned in somewhat 

 exceptional circumstances) is derived from observations on 

 mutation in Drosophila and Gammarus, 1 and we have no means 



1 It is not quite certain how long Nabours's protracted observations on the 

 genetical behaviour of the colour-pattern in the grouse-locusts have been carried 

 on, but it seems that they have been at least twenty years in hand (Nabours, 1929, 

 p. 55). During that time only one mutation has been detected (Nabours, 1930, 



P- 350- 



