GENERAL RELATIONS IN INHERITANCE 289 



aBCd, aBcD, abCD, Abed, aBcd, abCd, abcD and abed. If 

 the number of heterozygotic pairs is n, the number of dif- 

 ferent types of germ cells is 2°. 



These 16 different types of germ cells unite, each with 

 all the others in equal proportions. If we should represent 

 the results of these unions, we should have for the constitu- 

 tion of generation F2 a square table like that of table 2, 

 Chapter V, but showing 256 combinations instead of 16. 

 But as in table 2, there would be certain duplicates among 

 the combinations; the total number of diverse combinations 

 would be found to be in this case 81, or 3^. In general, for 

 any number « of heterozygotic gene pairs in Fi, the number 

 of different gene combinations in the zygotes that form F2 



is 3°- ^ _ 



(The derivation of this value 3° may be seen as follows. 

 If a single pair, as Aa, is heterozygotic in Fi, this yields in 

 F2 the three different combinations AA, Aa and aa, (table i, 

 page 113). If a second pair Bb is heterozygotic, this also 

 yields three combinations BB, Bb and bb, and since any com- 

 bination from the first pair may unite with any combination 

 from the second, the total number of diverse combinations 

 is 3^, or 9. Every pair added multiplies the result by 3, so 

 that for n pairs the number of different combinations is 3°.) 



Thus, even though we begin with but two differing stocks, 

 in their descendants there may be produced a great number 

 of different stocks, with diverse combinations of genes and 

 of characteristics. 



Relation to inequalities among the genes: The relations 

 just set forth acquire special biological significance in con- 

 sequence of the fact that many of the variations among the 

 genes are of importance for the vigor and survival of the 

 individuals that carry them. Many of the gene modifica- 

 tions, as we have before seen, are in the nature of defects. 

 This is more particularly the case with recessive genes. 

 Often it is true that of the genes of a particular pair the 



