MATHEMATICAL. CONSIDERATIONS 97 



since the heterozygous individuals are more vigorous than 

 the homozygous, selection either unconscious or purpose- 

 ful would favor the more heterozygous so that actual 

 approach to homozygosity is quite likely not to proceed 

 at as fast a rate as the theoretical curve would indicate. 



Self- fertilization is the quickest and surest means of 

 obtaining complete homozygosity for the reason that 

 whenever any pair of allelomorphs becomes homozygous 

 it must always remain so, as long as self-fertilization takes 

 place, whereas in brother and sister mating a homozygote 

 may be mated to a heterozygote. The approach to homo- 

 zygosity in self-fertilization when one pair of contrasted 

 characters is considered and fecundity does not vary pro- 

 ceeds as follows : 



Generation F^ F^ F^ F^ 



Parent type A A 1/4 3/8 7/16 1/2 AA^ =.492 



Parent type aa 1/4 3/8 7/16 1/2 aa, =.492 



Hybrid type Aa 1 1/2 1/4 1/8 Aa^ =.008 



In brother and sister mating the procedure is 

 as follows; 



Generation F^ F^ F^ F^ F^ 



Parent type ^^ 1/4 2/8 5/16 11/32 1/2 ^^,,=.490+ 



Parent type aa 1/4 2/8 5/16 11/32 1/2 aa^, =.490+ 



Hybridtype^a 1 1/2 2/4 3/8 5/16 Aa^^=mS-\- 



These figures have definite numerical relations to each 

 other and formulae have been obtained by Jennings ^^^ for 

 calculating the condition in any generation. It will be seen 

 from the above figures that 6 generations of self-fertiliza- 

 tion are more effective than 17 generations of brother and 

 sister matings in bringing about homozygosis. 



Of parent by offspring matings there are several 

 7 



