89 ° 
Journal of Agricultural Research voi. xxvn, No. n 
Table) III.— Comparison of methods for measuring linkage in Ft. 2 5 per cent crossing - 
over 
Nature of 
Zygotic classes. 
Value of p. 
linkage. 
AB. 
Ab. 
aB. 
ab. 
Total. 
Q. 
P. 
T. 
Perfect population. . . 
2 5 per cent a gametes 
not effective. 
2 5 percent a and 6 gam¬ 
etes not effective. 
25 per cent a and B 
gametes not effective. 
25 per cent a zygotes 
die. 
25 per cent a and b zy¬ 
gotes die. 
2 5 per cent a and B zy¬ 
gotes die. 
25 per cent a called A . 
Double recessive not 
recovered. 
f .D and R . 
{D and D ... 
fD and R... 
\D and D. 
{D and R ... 
\D and D ... 
(D and R ... 
\D and D ... 
f D and R ... 
\D and D ... 
f D and R ... 
{D and D ... 
f D and R ... 
\D and D ... 
ID and R ... 
\D and D ... 
D and R ... 
33 
4 i 
424 
552 
5 ; 440 
7,488 
4, 824 
5 > 976 
132 
164 
528 
656 
396 
49 2 
147 
171 
33 
15 
7 
216 
88 
1 ,944 
792 
3.456 
1,408 
60 
28 
180 
84 
240 
112 
61 
37 
15 
15 
7 
I 3 S 
63 
i ,944 
792 
i ,377 
729 
45 
21 
180 
84 
135 
63 
45 
21 
15 
I 
9 
9 
81 
81 
729 
144 
1,296 
3 
27 
9 
81 
12 
108 
3 
27 
0 
64 
784 
784 
9.409 
9,8°i 
9. Sox 
9.409 
240 
240 
897 
9°5 
783 
775 
256 
256 
63 
0. 2500 
. 2500 
•2377 
. 2432 
. 2263 
•2359 
. 2496 
. 2498 
. 2500 
. 2500 
.2500 
. 2500 
. 2500 
. 2500 
. 2600 
. 2742 
. OOOO 
0. 2 500 
. 2500 
• 5997 
.2159 
. 4166 
• 1773 
.1174 
. 2612 
•3536 
.2308 
.4442 
. 2071 
•2053 
• 2595 
.4146 
. 2605 
. 2182 
0. 2500 
. 2500 
• 2336 
. 2417 
.2349 
. 2188 
. 2288 
. 2605 
. 2500 
. 2500 
. 2619 
. 2416 
.2415 
. 2582 
.2644 
. 2808 
. OOOO 
SUMMARY 
Some measure of linkage is necessary in all studies of the association 
between characters and chromosomes. 
Back-crossing the Fj on double recessives affords the most direct 
measure but with many plants this method can not be used. There is 
also a slight though usually unimportant error in the use of this method 
when the Mendelian ratios depart from the expected. 
Three methods have been proposed for measuring linkage in the F 2 : 
(1) Yule's coefficient of association, Q. 
(2) Emerson’s method, P. 
(3) Haldane’s method, T. 
All of these give the correct result with a perfect population, but are 
variously affected by differential death rates of the gametes or zygotes, 
selective fertilization and mistakes in classification, which cause de¬ 
partures from expected Mendelian ratios. 
Departures from expected Mendelian ratios are grouped into three 
classes and the effects of these departures on the accuracy of the three 
methods of measuring linkage in F 2 are investigated empirically. 
No one method is found to be most accurate for all classes of departures. 
Yule’s coefficient of association, Q, most nearly meets the requirements 
of a general method and a formula is given for evaluating the degree of 
linkage from observed values of Q . 
a D and R=dominant and recessive linked, D and D=dominants linked. 
