FUTURE OF THE SCIENCE OF BREEDING 177 



This indeed is the general experience of those who have 

 studied crosses involving quantitative characters, whether 

 in animals or plants. The first crosses are more or less 

 intermediate in size between the parental breeds, while at 

 the same time their range of variability is relatively small. 

 When they are bred together they give rise to an F 2 

 generation in which the mean, as in the F x individuals, is 

 roughly intermediate between those of the original strains 

 used. The great difference between the F x and F 2 generations 

 is that, whereas in the former the range of variation is com- 

 paratively small, in the latter it is very large, overlapping 

 and sometimes even exceeding the range found in the two 

 parental strains. The salient feature about such an F 2 

 generation is that the curve of variation is apparently con- 

 tinuous. Even the closest scrutiny will not enable us to 

 separate them into definite groups, as was possible with our 

 sweet peas. 



How are we to bring such cases into line with those in 

 which the phenomena can be explained in terms of definite 

 factors each producing a definite qualitative result ? A 

 form of explanation favoured by many genetic workers is 

 that recently termed the theory of multiple factors, of which 

 the conception was originally due to Nilsson-Ehle. On this 

 theory a cross may involve a difference between the original 

 parents of several factors, each independently producing a 

 similar effect and each transmitted in the normal way. 



Perhaps the simplest way of making this clear is to take 

 a simple imaginary example (Fig. 9). Let us suppose that a 

 cross is made between two animals of which one is homozygous 

 for three independent factors A, A 1 and A 2 , the other lacking 

 in all three. Let us also make the following assumptions : 



(1) That each factor by itself produces a similar effect in 

 increasing the size. 



(2) That a double dose of any of the three factors pro- 

 duces twice as great an effect as that resulting from a single 

 dose. 



(3) That the independent effects produced by the three 

 factors are cumulative. 



N 



