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 F’, results are commonly abtained by selfing the /’; individuals 
in the case of plants, or interbreeding them in the case of animals, the 
F, 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 
F, zygotes: 
AABB + AABb+ AaBB + AaBb 
AABb + AaBb +AAbb + Aabb 
AaBB + AaBb + aaBB + aaBb 
AaBb + Aabb + aaBb + aabo 
F. genotypes: 
AABB +2AABb + 2AaBB + 4A4aBb + AAbb + 2Aabb + aaBB + 2aaBb + aabb 
Collecting these Ff: genotypes into their respective phenotypes we get 
the following results: 
9AB 3Ab 3aB lab 
1AABB 1A Abb laaBB laabb 
2AABb 2Aabb 2aaBb 
2AaBB 
4AaBb 
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 fF, phenotypic and 
genotypic distributions on the basis of the symmetrical relations displayed 
by them. The ratio of phenotypes in J’; in a cross involving n pairs of 
factors is conveniently obtained in cases of complete dominance by the 
expansion of the expression (3 + 1)” 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 + 1)” for values of n up to five 
have been given in condensed form. 
7 
Digitized by Microsoft® 
