320 DIVERGENT EVOLUTION THROUGH SEGREGATION. 
TABLE I.—Arithmetical computation, showing the number of half-breeds as contrasted 
with the pure-breeds, when) of each variety form unions among themselves and double 
with cach gencration, while the offspring of the 4'y that form mixed unions simply equal 
the number of the parents by which they are produced, in other words when ¢ = 15, M= 
m= 1 (see Table I1). 
—— as 
Three-quarter . 
= Ree BF tak i Of what genera- | Half of the as Variety No. 2, 
Variety No. 1, pure-breeds. tion. half-breeds. pone pure-breeds. 
1, 000 = A ==) || Join ells Ae) hoe lo coms snoscoladaodosndsscie 1, 000 
1:8 | 
1, 800 — A (1°8) = | 1st generation .--. 100: |s2 soe eenceese 1, 800 
1:8 | 
| 
3, 240 = A (18)? — | 2nd generation. ... 260 20 3, 240 
18 | 
| 
5, 832 = A (1°8)3 = | 3rd generation -... 532 72 5, 832 
357°05= (1°8)'" computed by log. 
rae Oia) rs A. (1°8) 10 = /} 10th generation -.. 3D O88. = 5 2 eee cme | 357, 050 
39, 347-272 — (1°8)38 | 
Soo Otol) A (1°8) 8 = | 18th generation. - - BAU BY Bede ome ori ciaes 39, 347, 272 
EXPLANATION OF TABLE I.—The second generation of the half-breeds is found by 
taking +5 of the previous half-breeds, i. e. 100 x 7%5=90, and +; of the previous pure- 
breeds (the 4); that form mixed unions), minus 4/5 of the previous half-breeds (because 
;\; of the half-breeds consort with an equal number of pure-breeds, and so produce 
not half-breeds but three-quarter-breeds), 7. e. 130—10=170. Adding these two sums 
together we have 90 + 170260 =the second generation of half-breeds. 
As inthis table the computation commences without any half-breeds. the follow- 
ing generations of half-breeds are all a little less than {5 as large as the correspond- 
ing generations of pure-breeds. When, however, we come to the eighteenth genera- 
tion 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 m1. 
The three-quarter-breeds are obtained by multiplying >; of the previous genera- 
tion of half-breeds by 2, and adding to the result the sum of the previous genera- 
tions of three-quarter-breeds. This of course gives a number too large; for some of 
the three-quarter-breeds will fail to breed with three-quarter-breeds. A closer 
expression of the proportion between pure-breeds and three-quarter-breeds is given 
in Tables vi and vii. 
