COMPUTATIONS OF EFFECTS. 



177 



5. Computation of the Effects of Different Degrees of Positive Segregation 

 Cooperating with Different Degrees of Segregate Survival. 



Of the tables which are herewith presented Table I is an arithmet- 

 ical computation, showing the number of half-breeds as contrasted 

 with the pure-breeds, when nine-tenths of each variety form unions 

 among themselves and double with each generation, while the off- 

 spring of the one-tenth that form mixed unions simply equal the 

 number of the parents by which they are produced; in other words 

 when c=o.i,M = 2, m = i (see Table II). 



Table I. 



Variety No. 1, pure-breeds. 



1,000 = A 



1.8 



1,800 = A (1.8) 



1.8 



3,240 = A(i.8) = 



1.8 



5,832 =A(i.8)« 



357-05= (i.8)'° comput- 

 ed by log. .-.357.050 = 

 A (1.8)1" 



39.347-272 = (1-8)1' 

 .•-39,347.272 = A (1.8)1' 



of what gener- 

 ation. 



Initial number 

 ist generation. 

 2d generation. 

 3d generation. 



loth generation 

 1 8th generation 



Half of the 

 half-breeds. 



260 



532 



35,688 

 3,934.725 



Three- 

 quarter 

 breeds 

 on one 

 side. 



72 



Variety No. 2, 

 pure-breeds. 



1,000 

 I, 800 

 3,240 

 5,832 



357,050 

 39,347,272 



ExPL.^NATioN OP Table I. 



The 2d generation of the half-breeds is found by taking nine-tenths of the pre- 

 vious half-breeds, i. e., 100 X 0.9 = 90, and one-tenth of the previous pure-breeds 

 (the one-tenth that form mixed unions), minus one- tenth of the previous half- 

 breeds (because one-tenth of the half-breeds consort with an equal number of 

 pure-breeds, and so produce not half-breeds but three-quarter breeds), i. k., 

 180 — 10 ^ 170. Adding these two suras together we have 90 -f- 170 = 260 = 

 the 2d generation of half-breeds. 



As in this table the computation commences without any half-breeds, the fol- 

 lowing generations of half-breeds are all a little less than one-tenth as large as the 

 corresponding generations of pure-breeds. When, however, we come to the 1 8th 

 generation the difference is less than one in a million, and we may consider the 

 result as practically corresponding with the formula for the nth generation given 

 in Table III. 



