228 GENETICS 



have seven size gradations containing respectively o, i, 2, 

 3, 4, 5 or 6 of the "size genes" AABBCC, the different 

 grades showing the following relative numbers of indi- 

 viduals: 



No. of Size Factors 0123456 



No. of Individuals i 6 15 20 15 6 1=64 



Here the relative numbers of individuals in each of the 

 grades is given by the expansion of the binomial (i + i)^« 

 The relative numbers for any other number of "size genes" 

 can be written out directly. For four pairs the series is given 

 by (i -|- i)^, and for n pairs it is (i + i)^°- 



Thus when there is a cross between races differing quanti- 

 tatively in size, depth of color, or the like, the difference 

 being due to a diversity in several pairs of genes, the gen- 

 eral results are as follows: 



(i) The Fi generation is uniform (except in so far as 

 there are variations due to environmental conditions), and 

 is intermediate between the two parental types. 



(2) The F2 generation is varied in constitution. It con- 

 sists of a series of grades, varying from the larger to the 

 smaller parent. If the number of gene pairs in which the 

 original parents differ is n, the number of grades is 2n -{- i. 



(3) The number of individuals is largest in the inter- 

 mediate grades, and decreases toward the more extreme 

 grades, in both directions. 



(4) The relative numbers of individuals in the differ- 

 ent grades, from smallest to largest, are given by the ex- 

 pansion of the binomial (i + i)^"- 



(5) Since most of the individuals fall in the intermedi- 

 ate grades, the general effect is to give the impression that 

 F2, like Fi, is intermediate, so that the inheritance appears 

 to be of the blending type. This is particularly true if only 

 small numbers of individuals are available for study; most 

 or all of these fall in the intermediate classes. 



