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TABLE VI.—Formula for Segregation, Segregate Fecundity, and Segregate Vigor, giving 
the proportion of Half-breeds to Pure-breeds (constructed from Table LIL, according to — 
rule 3). 
DIVERGENT EVOLUTION THROUGH SEGREGATION, 
Pure-breeds. Half-breeds. 
eA Initial number. 
A(MV—MVe). 
A(MV—MvVe)?. 
Amve. 
Amve(1—2c)mv-+ Amve(MV —MVe). 
1st generation ----- 
2nd generation... -- 
A(MV—M Ve). 
3rd generation. .- --- 
Amve((1—2c)mv)?2+- Amve(M V —M Ve) (1—2e)mv+Amae 
(MV—MVe)?. 
Amve((1—2e) mv)? + Amve(MV—M V e) ((1—2e) mv)? 4- Amve 
(MV—MVe)2(1—2c) mv + Amove(MV—M Ve)’. 
((1—2e)mv)? — ((1—2e) mv)? 
(MV—MvVe)3* (MV—MVe)? 
Cpe) 
(MV—MVe)3}~ 
A(MV—MVoe)4. 4th generation... - -- 
=Am ne(MV—MVe)3( 
((1—2e) mv) | 
(MV—MVe) * 
A(MV—MVe)n—! mn—Ilth generation. 
A(MV—MVe)n nth generation... -- 
MV—MVe 
1—-2¢e)1 =I 
Amoe(MV—MVe)n—1( ( c)mv Je hy 
+( Js 
( (1—2e) mo is (1—2e)mov ) 
MV—MvVc) *MV—Mvet?)- 
nth generation of Pure-breeds=A(MV—M Ve)»—1 x 
: Half-breeds move 
(MV—M Ve); and therefore Pure-brecds a MiV=AaNEWE >< 
(1 tM pees aE 
TMV—MVe'° 
In the above formula V=vigor of pure-breeds expressed by a fraction that gives 
the proportion of each generation that grow to maturity and propagate; v=the 
vigor of the half-breeds expressed in the same way. 
TABLE VII.—formula for Segregation, Segregate Fecundity, and Segregate Vigor, giving 
the proportion of the Three-quarter-breeds to the Pwre-breeds. 
T=the number of Three-quarter-breeds, m/=ratio of fertility for the same; v’, a 
fraction giving the proportion of the Three-quarter-breeds that come to maturity. 
H=the number of Half-breeds. P—the number of Pure-breeds. 
Turning to Table I, we find that the Three-quarter-breeds of each generation are 
the offspring of jy (or c) of the previous generation of Half-breeds who consort with 
an equal number of Pure-breeds, plus the descendants of previous generations of 
Three-quarter-breeds in as far as they breed with each other. Commencing our 
computation with the nth generation we know from Table VI, that the previous 
generation of Pure-breeds=A (MV—MVe)” ”, and the Half-breeds of the same gen- 
eration=A(MV—MVc)” e = 
breeds, which is obtained as shown in Tables IV, V, and VI; and ¢ of this number 
will consort with an equal number of Pure-breeds, making A(MV—MVe)" 1x3 2c 
parents in the n—1th generation, that will produce m/v’ times that number of Three- 
quarter-breed offspring of the nth generation that will grow to maturity. Starting 
being the ratio in which Half-breed stand to Pure- 
