CUMULATIVE SEGREGATION THE RESULT. 109 
Solution reached by means of Table V.—Looking in Table V,* we find 
that when c = 4, and M ~1o, 
(var. 1) then with m = 2, half-breeds = pure-breeds = 2; 
(var. 2) and with m = 1, half-breeds = pure-breeds = a 
that when c = }, and M = io, 
(var. 3) then with m = 2, half-breeds = pure-breeds < 25 
(var. 4) and with m = 1, half-breeds = pure-breeds x a 
Now, it is evident that the influence on the next generation of the 
variation marked as var. 4, which is the most highly segregated, will 
be much greater than that of any other one of the variations. 
Solution reached by means of Table A.—If we consult Table A, we 
shall find an equal contrast, for it gives for 
(var. 1) cross-breeds = pure-breeds x 2; 
(var. 2) cross-breeds = pure-breeds x ae 
Be 
(4? 
(var. 4) cross-breeds = pure-breeds = +. 
Solution reached by direct computation —A similar conclusion may 
be reached by computing the result for a few generations. Let us 
suppose that for one-half of the new variety the average prepotence 
allows one-half of the individuals to form cross-unions, and that for 
the other half of the variety the average prepotence allows only one- 
third of the individuals to form cross-unions; and also that one-half of 
_ each of these variations is so adapted as to multiply by 2 in each 
generation, while the other half multiplies by 1. As in the previous 
computation cross-breeds are multiplied by 4 in each generation. 
Let us now assume that in a given generation there are 1,000 indi- 
viduals in each of these variations, and what will be the number of 
pure-breeds of each of the four variations that will come to maturity 
in the next generation, and what the number of cross-breeds? 
haart, 6 =, M1, m ==, G. ¢.,-piire-breeding ‘Seo, crossing 
500), .”. pure-breeds 500; half-breeds roo. 
nae 26 — 4, M2, m=; (1. ¢.,.pure-breeding, 5005 crossing 
Ab) 
(var. 3) cross-breeds = pure-breeds X 
500), .°. pure-breeds 1,000; half-breeds too. 
Petes i M1, 1 1; (. e., pure-breeding 666; crossing 
333), .'. pure-breeds 666; half-breeds 66. 
In var. 4, c— 1, M=2, m= ¢; (. e., pute-breeding 666; crossing 
333), -'. pure-breeds 1,332; half-breeds 66, 
The sum of the pure-breeds of all the variations 3,498. 
It will be observed that in one generation the pure-breeds have 
decreased from 4,000 to 3,498; that is, their numbers have dimin- 
* See my paper on Divergent Evolution, Appendix I. 
