MEASUREMENT OF LINKAGE VALUES 1 
By G. N. Collins 
Botanist in Charge, Biophysical Investigations, Bureau of Plant Industry, United States 
Department of Agriculture 
The demonstration that Mendelian characters are inherited in groups 
that correspond to the chromosomes has been followed by much in¬ 
tensive work directed to the determining of the relative position of the 
genes in the individual chromosomes. 
If two Mendelian characters are shown to be correlated in trans¬ 
mission their genes are assumed to lie in the same chromosome, and are 
said to be linked. The early idea that the linkage relations might exhibit 
a numerical regularity comparable to Mendelian ratios has been aban¬ 
doned. There is now much evidence to show that the degree of asso¬ 
ciation of genes assumed to lie in the same chromosome is profoundly 
influenced by environmental factors. 
Since closely related progenies frequently show widely divergent cross¬ 
over ratios for the same pair of characters, a high degree of accuracy in 
measuring the ratio may seem to be of little value. But in all work that 
aims to test or to extend knowledge of the interrelations of characters 
it is of the greatest importance to determine whether any two characters 
are inherited independently or show a low degree of linkage. 
When the linkage is loose a large number of individuals is required to 
establish the linkage. In all such cases it is necessary to be sure that 
the method used for demonstrating the relationship of two characters is 
accurate. If the method is such that a correlation is indicated where 
none exists, large numbers will only inspire confidence in a spurious 
linkage. 
The most generally used method of determining the linkage relations 
of two characters is to cross individuals of the F x with individuals that 
are homozygous for the recessive allelomorphs of both characters. The 
sum of the individuals representing the two crossover or nonparental 
combinations expressed as a percentage of the total population is then 
taken as representing the percentage of the gametes in which crossing- 
over has taken place. This is undoubtedly the most simple and direct 
method, for if dominance is complete each back-crossed individual indi¬ 
cates directly the nature of the F 1 gamete that entered into its compo- 
sition. 
With many plants this method of back-crossing can not be used. Often 
the technique is difficult and it is impossible to obtain back-crossed indi¬ 
viduals in sufficient numbers to afford reliable averages. In locating 
new recessive characters by the back-cross method there is the loss of a 
generation necessary to obtain a double recessive stock. In other in¬ 
stances double recessive individuals are weak and it is difficult to main¬ 
tain the stock. Because of these difficulties in determining linkage 
values by the direct method many investigators have come to use F 2 
populations. 
1 Received for publication Feb. i, 1924. 
Journal of Agricultural Research, 
Washington, D. C. 
(881) 
Vol. XXVIT, No. r 1 
Mar. i<;, 1924 
Key No G-386 
