108 ANALYSIS OF THE FOUR PRINCIPLES. 



Undoubtedly the latter is the one we need to represent the result 

 toward which the given conditions tend, though before the eighteenth 

 generation is reached the degree of segregate breeding will have 

 become more stringent. 



Having obtained a formula giving the results that would be reached 

 if the ratios of cross-breeding and of attendant infertility were con- 

 tinued at a given level for a number of generations, we next inquire 

 whether there is any reason to believe that the degrees of segregate 

 breeding will become more stringent in successive generations, and 

 whether the infertility of cross-breeds will be increased. 



17. Cumulative Segregation Resulting from Segregative Endowments. 



Let us consider a partially segregated variety of a plant species in 

 which there is some variation in the segregative endowments. We 

 will suppose that the species is one whose pollen is freely distributed 

 by the wind and whose stigma is susceptible of fertilization for ten 

 hours. 



Though the individuals of the new and partially segregated variety 

 are very few as compared with the original stock, yet the pollen of the 

 new kind reaches every stigma of the same kind before the ten hours 

 of its susceptibility have passed, while pollen of the original kind, be- 

 ing far more abundant, is sure to reach every stigma soon after their 

 flowers have opened. 



The positive segregation of the new variety we will suppose is se- 

 cured by prepotence of the pollen of the variety on the stigmas of the 

 same variety, one variation being prepotent for about five hours, 

 with the result that one-half of the individuals breed pure and one-half 

 are crossed ; that is, c = % ; while another variation is prepotent for 

 about 6 hours, with the result that two-thirds of the individuals 

 breed pure and one-third are crossed ; that is c -- J. 



The negative segregation of the new variety we will suppose is se- 

 cured by segregate survival; for the pure-breeds, through different 

 degrees of adaptation to the new station, enjoy different degrees of 

 success in leaving offspring that come to maturity, the less adapted 

 variations being multiplied by i in each generation, and the better 

 adapted multiplied by 2 in each generation, while the cross-breeds 

 are so lacking in adaptation as to be multiplied by ^ in each genera- 

 tion. We therefore have two values for M, each occurring under 

 c = %, and again under c = 3. In one variation we have M=- i, and 

 m =- 4, the proportion being as M " 10, and m = 2 ; and in the other 

 variation we have M = 2, and m -- 4-, the proportion being as M = 10 

 and m = i. 



