Xo. 562] THE PROBLEM OF INBREEDING 607 



result of self -fertilization; 1 ' with random cross-fertiliza- 

 tion there is no disappearance of any class whatever in 

 the offspring of the hybrids, but each class continues to be 

 reproduced in the same proportion." This is exactly the 

 point of distinction made above between self-fertilization 

 and all other forms of inbreeding. 



The objection will at once be raised that inbreeding is 

 not "random cross-fertilization." But r/ainrticnlli/ it is. 

 unless prevented from so being by some sort of associa- 

 tive mating on a gametic basis. As I have shown in an 

 earlier section the most general form of the concept of 

 inbreeding possible is that of the diminished number of 

 different actual ancestors in proportion to the maximum 

 number possible. But surely the existence of relatively 

 few ancestors in itself can involve no necessary implica- 

 tion as to the gametic constitution of those ancestors, so 

 far as concerns homozygosis or heterozygosis. 



Analytically the proof is as follows: Let us start with 

 the condition of complete heterozygosis, and consider 

 what will be the result of the closest possible inbreeding 

 (aside from self-fertilization), namely the continued 

 breeding of brother X sister, in a population all the indi- 

 viduals of which are heterozygous with reference to one 

 alternative character pair A and a, these characters 

 being, by hypothesis, not sex-linked. All the individuals 

 will then have the constitution Aa. This will be true of 

 all males and all females whether they stand in the rela- 

 tion to each other of brother and sister or not. Let all 

 matings be of the brother X sister type. The offspring 

 of the next generation will be in no wise affected by this 

 fact, of course, but only by the constitution of the indi- 

 viduals mated. We shall' then have the population of 

 mule progeny constituted as follows: 



The population of female progeny will evidently exhibit 

 exactly the same distribution, namely 



