EVOLUTIONARY MECHANISMS 285 



Other. In general terms the theory is obviously true. The points which 

 require discussion are, firstly, whether species contain hereditary 

 varieties which leave different numbers of offspring, and if so how are 

 such varieties inherited; and, secondly, exactly what are the quantita- 

 tive results of natural selection, and how far can they provide a theory 

 of evolution adequate to explain the distribution of animal and plant 

 species. We can give a fairly complete qualitative answer to the first 

 question, and a discussion of the consequences of natural selection in 

 exact mathematical terms is at present being worked out by several 

 authors; but our quantitative knowledge, about the amount of variation 

 found in natural species, the degree of selective advantage involved, and 

 the rate of evolutionary change, is still extremely small. 



A great deal of the discussion of evolution has been concerned with 

 the discovery of particular cases which are either easy to explain on the 

 basis of the theories held by the author, or, more often, seem difficult 

 to explain on the theories held by his opponents. We shall not have 

 space to discuss many of these problems here. The realm of Nature is 

 so manifold, that we must expect to, and do, find the most extraordinary 

 things in it, such as small bugs with an undeniable facial resemblance 

 to crocodiles. Many of these peculiar phenomena can still be given no 

 very plausible explanation on any hypothesis. It is more important to try 

 to form a theory which will deal adequately with the normal and 

 straightforward evolution such as we see it in the majority of species 

 and in the palaeontological record. 



2. Variation Within a Population 



We have seen that environmental factors may cause the splitting of 

 a species into more or less separate populations whose hereditary 

 material does not mix. Natural selection can cause one of these races 

 to replace the other, but it cannot transform one of the populations 

 unless there are other hereditable variations within that population for 

 it to work on. We are here concerned with the nature of the variation 

 within an interbreeding population, which can be selected for or 

 against in such a way as to change the average appearance of the group. 



If we draw a large random sample from an interbreeding population 

 and measure some character, we shall always find some variation be- 

 tween the different individuals. If we plot, against any particular value 

 X of the measurement, the number of individuals in which that value 

 is found, we obtain a curve giving the frequency distribution of the 

 population with respect to the charaaer. The distribution is usually 

 represented by a bell-shaped curve; there are a majority of individuals 



