Mar. 15, 1924 
Measurement of Linkage Values 
883 
MEASUREMENT OF LINKAGE BY THE BACK-CROSS METHOD 
The back-cross method, sometimes called the direct method, may be 
used when the cross is of the nature A a Bb X aa bb. The formula is: 
, A b -f ~aB 
The probable error of this determination is usually given as: 
E P =.6 745 ^/tlll±. 
Even this approved method of determining the degree of linkage may 
not be entirely free from error when the Mendelian ratios do not agree 
with the expected. 
Haldane states (5, 2 p. 292) that by the method of back-crossing “we 
automatically eliminate the effects of differential mortality due to one 
factor, or to both if they affect the mortality independently.” This ap¬ 
pears to be an error. Take a simple example with no linkage, if there is 
no differential mortality the four zygotic classes will be equal. If now 
in such a population 50 per cent of the recessive class of each character 
fails to survive, the observed classes will be in the proportion 4 AB , 2 
Ab, 2 aB, 1 ab , indicating a linkage between dominants with 44 per cent 
crossing-over, 4/9 = .44 +. 
If the Mendelian ratios are aberrant in only one character the linkage 
relations are not affected, but where there are departures in both, the 
per cent of crossover individuals will fail to indicate the true ratio of 
crossover to noncrossover gametes. If the extent of the error or the 
spurious linkage be designated e y then its value is .5 —r—s + 2 rs 
where r= the number of individuals recessive with respect to one char¬ 
acter divided by the total number of individuals and s=the correspond¬ 
ing determination with respect to the other character. 
If either r or ^ = 0.5, e will equal 0.0—that is, there is no spurious link¬ 
age. If both r and s depart from 0.5 in the same direction there will be 
a spurious linkage between dominants. If r and ^ depart from 0.5 in 
opposite directions the spurious linkage will be between dominant and 
recessive. 
To eliminate the effects of differential mortality on the measurements 
of linkage in back-crosses, Bridges (2, p. 3) proposed the method of 
balanced viability. The procedure is to average the results obtained 
from two original crosses in which the parental combinations are reversed, 
that is, AABB Xaabb and AAbbXaaBB. This method practically 
eliminates the effects of differential mortality, either in gametes or 
zygotes and undoubtedly is the most desirable method to use whenever 
material for making the two crosses can be made available. 
METHODS FOR DETERMINING LINKAGE VALUES FROM AN F 2 
POPULATION 
Three general methods have been proposed for measuring linkage 
values in an F 2 population. These are, Yule’s coefficient of association, 
“Q,” Emerson’s method, “P,” and Haldane’s method “T.” 
2 Reference is made by number (italic) to “Literature cited,” p. 891. 
