182 



APPENDIX I DIVERGENT EVOLUTION. 



The following solutions, as well as those given in Table V, are 

 obtained by substituting values for M, m, and c in formula (2) : 

 When M = 4, m = 3, then if 



c 

 c 

 c 

 c 

 c 



%, half-breeds 

 , half-breeds 

 \, half-breeds 

 4-, half-breeds 

 , half-breeds 



: pure-breeds x f . 

 : pure-breeds x f. 



pure-breeds x -|. 

 : pure-breeds x y. 



pure-breeds x I 



TABLE V. From Formula (2). 



OBSERVATIONS ON TABLE V. 



This mathematical analysis of the effects of positive segregation 

 and segregate fecundity when cooperating brings distinctly into view 

 several important relations. 



First. Incomplete forms of positive segregation, that avail little 

 or nothing in preventing a form from being absorbed in the course of 

 time, become very efficient when strengthened by moderate degrees 

 of mutual sterility. Take, for instance, the line of the table in which 



c If i in every 100 unions is a cross with some other form, 



100 



