MATHEMATICAL CONSIDERATIONS 99 



ability only indirectly by changing the vigor of the organ- 

 isms so that they may react differently to dilTerent 

 environments. 



Assuming, then, that the loss of the stimulation ac- 

 companying heterozygosity is correlated with the reduc- 

 tion in the number of heterozygous factors we should 

 expect to find the decrease of heterosis greatest in the first 

 generations, rapidly becoming less until no further loss 

 is noticeable in any number of subsequent generations 

 of self-fertilization, and that on the average the decrease 

 will become negligible from the seventh to the twelfth 

 generation and from then on no further marked change 

 will take place. Segregation of characters and appearance 

 of new types and reduction in variability will also follow 

 the same course. Some cases are to be expected in whioh 

 stability is reached earlier, and some cases in which it is 

 reached later; or, theoretically it may never be reached. 

 With these points in mind, let us see what are the actual 

 results of long-continued inbreeding. 



