COMPUTATIONS OF EFFECTS. 



177 



.5. Computation of the Effects 0} 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 = 0.1, M z= 2, m = 1 (see Table II). 



Table I. 



Variety No. 1 , pure-breeds. 



1,000 = A. 

 1.8 



Of what gener- 

 ation. 



1,800 

 1.8 



A (I. 8) 



3,240 =A(l.S)~. 



1.8 



5,832 = A(i.8)< 



357-05= (1.8) 10 comput- 

 ed by log. .-.357.050 = 

 A(i.8) 10 



39,347^7:? = (1.8) 18 



• '•39,347.272 = A(i.8) ls 



; Initial number 

 1 st generation. 

 2d generation. 

 3d generation. 



10th generation 

 1 8th generation 



Half of the 

 half-breeds. 



Three- 

 quarter 

 breeds 

 on one 

 side. 



Variety No. 2, 

 pure- breeds. 



IOO 



260 



532 



20 



/ - 



35.688 

 3,934- 725 



i, 800 



3, 240 



5. S3 2 



357, 50 



39.347. 272 



Explanation ok 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), ;'. <\, 

 180 — ■ 10 = 170. Adding these two sums together we have 90 -j- 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 18th 

 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. 



