INDEPENDENT MENDELIAN INHERITANCE 97 



fortunately the limits of experimental facilities usually preclude the pos- 

 sibility of working with large numbers of factors in any single experi- 

 ment, so that it rarely becomes necessary to handle any large number of 

 combinations. 



Since FZ results are commonly obtained by selfing the F\ individuals 

 in the case of plants, or interbreeding them in the case of animals, the 

 Fz ratios ordinarily represent the product of two like gametic series each 

 consisting of all possible combinations of the different factors involved. 

 There are several methods of obtaining these ratios, each of which has 

 its special advantages. The simplest of these is the algebraic method 

 which merely depends upon the multiplication of the two series together 

 as illustrated in the following general example for two factor differences. 



Female gametes AB + Ab + aB + ab 

 Male gametes AB + Ab + aB + ab 



Ft zygotes: 



AABB + AABb + AaBB + AaBb 



AABb + AaBb +AAbb + Aabb 



AaBB + AaBb + aaBB + aaBb 



AaBb + Aabb + aaBb + aabo 



F-i genotypes: 

 AABB + 2 AABb + 2AaBB + 4AaBb + A Abb + 2 Aabb + aaBB + 2aaBb + aabb 



Collecting these FZ genotypes into their respective phenotypes we get 

 the following results: 



9AB 3Ab 3aB lab 



1AABB lAAbb laaBB laabb 



2 AABb 2 Aabb 2aaBb 



2AaBB 

 4 AaBb 



This tabulation of the genotypes since it shows that the genotypes 

 within a phenotype are in definite ratios to each other immediately sug- 

 gests the method of progression of writing down the FZ phenotypic and 

 genotypic distributions on the basis of the symmetrical relations displayed 

 by them. The ratio of phenotypes in FZ in a cross involving n pairs of 

 factors is conveniently obtained in cases of complete dominance by the 

 expansion of the expression (3 + l) n or by continuously dividing the 

 terms of a simpler ratio in the ratio 3 : 1 until the number of pairs of factor 

 differences involved is satisfied. In the following table the phenotypic 

 ratios obtained by the expansion of (3 + l) n for values of n up to five 

 have been given in condensed form. 

 7 



