GENETIC SYSTEM: RELATION TO CHARACTERISTICS 121 



parents are interbred that differ in four or more charac- 

 ters depending on four or more different pairs of auto- 

 somes. If the number of pairs of autosomes is called n, the 

 following relations hold : 



If parents differ in n autosomes : 



(i) The number of diverse types of gametes produced 

 by the individuals of the Fi generation is 2". 



(2) The number of different combinations (genotypes) 

 in the zygotes of F2, formed by mating the 2° gametes 

 from Fi, is 3°. 



(3) The number of different phaenotypes produced in 

 F2 is 2". 



These relations yield very great numbers of diverse com- 

 binations, in cases where the number of pairs of autosomes 

 is large. Thus in man, with 23 pairs of autosomes, if all 

 the autosomes differed in the two parents, the number of 

 types of germ cells produced by the Fi individuals would 

 be 2-^, or many millions, the number of possible diverse 

 genotypes in F2 would be 3-^, or many billions, and the 

 number of possible different phaenotypes would be 2-^. 

 (As will appear later, the number of different possible com- 

 binations is greatly increased by the exchange of parts by 

 the members of a pair of chromosomes.) 



Thus typical Mendelian inheritance, dependent on dif- 

 ferences between different pairs of autosomes, can be 

 treated to a certain extent mathematically. The individuals 

 in F2 and later generations occur in proportions repre- 

 sented by simple mathematical ratios. These are dealt with 

 in Chapter IX. 



It will be worth while to formulate the main facts that 

 we have brought out as to autosomal inheritance: 



I. Some single pairs of characters, dominant and reces- 

 sive, follow in inheritance the method of distribution of a 

 single pair of autosomes. 



