SOME COMPLICATIONS OF MENDELIAN INHERITANCE 309 



more variable than the F\, and the tendency of most of the F 2 individuals 

 to be more or less intermediate. In some of these crosses, as in color in 

 wheat, the parent type does appear in the F 2 about as frequently as once 

 in 64 individuals. If it is argued that in other crosses the parent types are 

 much rarer than once in 64 individuals (in some they are practically never 

 obtained), we can refer to the ratios that would occur if four pairs or 

 five pairs of genes had been involved. 



Suppose that we are dealing with four pairs of multiple genes, A A BB 

 CC DD, and that each gene contributed one-eighth of the total effect. 

 There will be 16 kinds of germ cells produced by the F h and the F 2 will 



show : 



1 individual out of 256 with 8 genes 



8 individuals out of 256 with 7 genes 

 28 individuals out of 256 with 6 genes 

 56 individuals out of 256 with 5 genes 

 70 individuals out of 256 with 4 genes 

 56 individuals out of 256 with 3 genes 

 28 individuals out of 256 with 2 genes 



8 individuals out of 256 with 1 gene 



1 individual out of 256 with genes 



If five pairs of multiple genes, A A BB CC DD EE, were involved 

 and each gene contributed one-tenth of the total effect, there would be 

 32 kinds of germ cells produced by the F h and the F 2 would show: 



1 individual out of 1,024 with 10 genes 



10 individuals out of 1,024 with 9 genes 



45 individuals out of 1,024 with 8 genes 



120 individuals out of 1,024 with 7 genes 



210 individuals out of 1,024 with 6 genes 



252 individuals out of 1,024 with 5 genes 



210 individuals out of 1,024 with 4 genes 



120 individuals out of 1,024 with 3 genes 



45 individuals out of 1,024 with 2 genes 



10 individuals out of 1,024 with 1 gene 



1 individual out of 1,024 with genes 



The necessity of obtaining such large numbers 1 of F 2 individuals, 

 together with the difficulty of separating and classifying all the various 

 phenotypic classes, makes this type of inheritance difficult to study and 

 has necessitated a special statistical or biometrical technique. By this 

 means the multiple-factor hypothesis has been abundantly verified, 

 although many cases are far less simple than the ones outlined above. The 

 chief importance of multiple-factor inheritance lies in the fact that a 

 great many of the qualities desired by the practical breeder are inherited 



1 In actual breeding experiments, the number of F« individuals obtained should 

 be at least 10 times or, better, 25 times as large as the minimum number theoretically 

 required to allow each genotype to .show. 



