CUMULATIVE SEGREGATION THE RESULT. 109 



Solution reached by means of Table V. — Looking in Table V,* we find 

 that when c — ^, and M =10, 



{var. i) then with m= 2, half-breeds = pure-breeds x ~; 

 (var. 2) and with m= i, half-breeds = pure-breeds x j^; 

 that when c = J, and M = 10, 



{var. 3) then with m = 2, half-breeds = pure-breeds X 1; 

 {var. 4) and with m= 1, half-breeds = pure-breeds x i. 

 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 |^; 

 {var. 2) cross-breeds = pure-breeds x l; 

 {var. 3) cross-breeds = pure-breeds X 1 ; 

 {var. 4) cross-breeds = pure-breeds x i. 

 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 i . As in the previous 

 computation cross-breeds are multiplied by -1- 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? 

 In var. i, c = -|, M = i, m = A; {i. e., pure-breeding 500; crossing 



500), . . pure-breeds 500; half-breeds 100. 

 In var. 2, c = ^, M = 2, w = +; {i. e., pure-breeding 500; crossing 



500), .'. pure-breeds i,ooo; half-breeds 100. 

 In var. 3, c = -j, M = i, m = |; {i. e., pure-breeding 666; crossing 



333), .-. pure-breeds 666; half-breeds 66. 

 In var. 4, c=- I, M = 2, m= \; {i. e., pure-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. 



