THROUGH CUMULATIYE SEaREGATIOT^. 



259 



Observations on Tahle V. 



This mathematical analysis of the effects of Positive Segregation 

 and Segregate Eecundity when co-operating brings distinctly into 

 view several important relations. 



1st. Incomplete forms of 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 = y^-^. If 1 in every 100 unions is a cross with 

 some other form, the form will in time be overwhelmed, unless 

 other causes come in to counteract ; but here we see that, if 

 Segregate Fecundity occurs in the ratio of 10 to 9, the pure 

 form becomes 12 times as numerous as the half-breeds ; and if in 

 the ratio of 10 to 5, it becomes 100 times as numerous. 



2nd. Again, if we take the proportional differences between 

 the different terms of the top line opposite c=|, we shall find 

 them very unlike the differences that appear in the bottom line 

 opposite c = Y(h'5' -'-^ former the first term is 9 times as 

 large as the last ; while in the latter the first term is more than 

 80 times as large as the last. This shows that when Segregation 

 is intense, differences in the degree of Segregate Fecundity pro- 

 duce greater contrasts than the same differences do when the 

 Segregation is slight. 



3rd. A similar distinction is found when we compare the right- 

 hand column with the left-hand column. The smallest term in 

 the former is to the largest term in the same column as 1 to 899, 

 while in the left-hand column the greatest difference is as 1 to 

 100. This shows that when Segregate Fecundity is strongly 

 developed, differences in the degrees of Segregation produce 

 greater contrasts than the same differences produce when the 

 Segregate Fecundity is but slightly developed. 



4th. Once more let us consider the relations to each other of 

 the four terms that stand in the upper left-hand corner of the 

 table. Suppose that of some one variety of a plant species, cha- 

 racterized by Prepotential Segregation and Segregate Fecundity, 

 we have occurring in equal numbers four variations whose rela- 

 tions to other varieties are indicated by the figures given in these 

 four terms, while in their relations to each other they are com- 

 pletely fertile and not Segregated. Which variation will leave 

 the greatest number of pure offspring, that is the greatest number 



