108 GENETICS AND EUGENICS 



to write out F2 ratios without going through the calculation 

 in detail either by algebra or by checkerboard. Thus, if 

 we take the expected completely recessive class as 1, each 

 class containing one dominant factor will be 3, each class 

 containing hvo dominant factors will be 9 {i. e., 3^) each class 

 containing three dominant factors will be 27 {i. e., 3^) etc. 

 Accordingly by mere inspection of a gametic series to ascer- 

 tain how many dominant factors each term contains, we may 

 at once assign to each the proportional number of r2 zygotes 

 in which it will be seen. See Table 8. 



TABLE 8 

 Relation between the Fi Gametic Series and the Expected F2 Zygotes 



Fi Gametic Series r2 Zygotes 



A + a 3A + la 



AB + Ab + aB + ab 9 AB + 3 Ab + 3 aB + 1 ab 



ABC + ABc + AbC + aBC \ f 27 ABC + 9 ABc + 9 AbC + 9 aBC 

 + Abe + aBc + abC + abc / \ + 3 Abe + 3 aBc + 3 abC + 1 abe 

 ABCD + ABCd + ete. 81 ABCD + 27 ABCd + etc. (let the reader 



supply the missing terms). 



Stated in general terms, as Mendel himself showed (and 

 as follows from the binomial formula), when the number of 

 unit-character differences between the parents is n,the visibly 

 different classes of offspring will be 2", the total different 

 sorts of zygotes will be 3", and the smallest number of in- 

 dividuals which may be expected to contain all of them will 



be 4». 



TABLE 9 



Table 9 shows what the size of these several classes is for 

 1-6 independent characters. 



