GENETICS: H. S. JENNINGS 
47 
(11) Assortative mating; parental population is the result of the 
random mating of rAA+/aa. After n assortative matings the popula- 
tion is r{r-\-nt)AA-{-2rtA2i-{-{n-\-l)t'^2i2i. 
(12) Assortative mating; parental population all Aa. After n assor- 
tative matings the population is nAA+lAsi+nsLSi. 
(13) Assortative mating; parental population A A and Aa in equal 
numbers. After n matings the population is (3n+6)AA+6Aa+/zaa. 
(14) Selection of dominants; parental population AA+2Aa-faa. 
After n generations the population is (n + lyAA + 2 (# -f 1) Aa + aa. 
(15) Self-fertiHzation; parents all Aa. After n self-fertiHzations 
the population is (2^- 1) AA + 2Aa + (2^-l)aa. 
(16) Self-fertilization; population at the beginning, rAA + ^Aa -j- /aa. 
After n generations the population is [r(2''+^)-{-s{2^—l)]AA + 2sA2i + 
[/(2-+i)+5(2^-l)]aa. 
D. In most cases the constitution of the population changes from gen- 
eration to generation, giving a series of values not readily expressed in 
terms of n (the number of generations) alone. In these cases diverse 
systems or diverse parents give different series of values, almost all of 
which are examples of certain simply derived mathematical series, or 
of their combinations. The results are therefore best presented by 
giving first these fundamental series, each with its designation. Then 
the results of any number of generations of any system of breeding can 
be given by designation of the series which it forms. The main series, 
with their first 10 terms, are given in the following table: 
Table of the Fundamental Series in Mendelian Breeding 
SERIES 
HOW FORMED 
n 
x + 1 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
B 
2x 
1 
2 
4 
8 
16 
32 
64 
128 
256 
512 
1024 
( = 2") 
c 
2x+l 
0 
1 
3 
7 
15 
31 
63 
127 
255 
511 
1023 
( = 2"-l) 
D 
2x-l 
2 
3 
5 
9 
17 
33 
65 
129 
257 
513 
( = 2"-i-M) 
E 
2x-f-l 
2 
5 
11 
23 
47 
95 
191 
383 
767 
( = 2"-2^-2-l) 
F 
Sum of two 
preceding 
0 
1 
1 
2 
3 
5 
8 
13 
21 
34 
55 
G 
2x+l, then 
2x-l 
0 
1 
1 
3 
5 
11 
21 
43 
85 
171 
341 
( = Bn-l — Gn-l) 
H 
G-F 
0 
0 
0 
1 
2 
6 
13 
30 
64 
137 
286 
I 
B-G-F 
1 
0 
2 
3 
8 
16 
35 
72 
150 
307 
628 
(=Gn+l — Fn) 
J 
Bn — Fn+l 
0 
1 
2 
5 
11 
24 
51 
107 
222 
457 
935 
K 
Bn — Fn-|.2 
0 
0 
1 
3 
8 
19 
43 
94 
201 
423 
880 
L 
Bn — Fn_i 
— Gn_i 
2 
2 
6 
11 
24 
48 
99 
200 
406 
819 
M 
2x+Fn_i 
2 
4 
9 
19 
40 
83 
171 
350 
713 
1447 
2952 
( = 3Bn-Fn+2) 
