886 
Journal of Agricultural Research voi.xxvii.no.xi 
Haldane states (5, p. 294) that the method gives the same value for p 
as Yule’s coefficient of association. This is, of course, true for a perfect 
distribution and it appears to hold also where the Mendelian ratio of only 
one of the characters is disturbed through a differential mortality of 
either gametes or zygotes, but where both characters are affected the two 
methods do not give identical results. Take for example a case with 
no linkage, that is p==. 5, in which Y / 2 the recessive gametes of both 
characters are not effective. The observed zygotic classes would be 
64: 8:8 : 1, n = 8i, 0 = o, giving/> = .5. 
Haldane’s formula gives ^> = .7111 as the first approximation. As a 
result of ten successive substitutions of T for 4 the value of p is reduced 
to 0.6626 the last substitution producing no change in the first four 
decimal places. It is clear that 0.5 is not the asymptote. 
COMPARISON OF METHODS 
In determining the per cent of crossingover from an F 2 population it 
is necessary to bear in mind that a value of p which gives a constructed 
population in closest agreement with the observed population may not 
be the correct value or the best that it is possible to find. 
Before any attempt can be made to evaluate p it is necessary to make 
some assumption regarding the factorial composition of the characters 
involved. If these assumptions are wrong any formula will lead, of 
course, to an erroneous value of p. It follows, further, that if there are 
departures from the expected Mendelian ratios, whether due to chance, 
selective fertilization, differential death rates or mistakes in classifica¬ 
tion, these departures may introduce errors into the calculation of p 
when populations with perfect Mendelian ratios are used as criteria. 
A method which would determine p by reference to a population with 
the observed instead of the theoretical Mendelian ratios should be free 
from this defect. 
Of the proposed methods the coefficient of association, Q, is the one 
that most nearly meets this requirement. Since Q is based on the rela¬ 
tion that exists between the product of the two crossover classes as 
compared with the product of the two noncrossover classes it is un¬ 
affected by zygotic changes in Mendelian ratios. 
Q is slightly affected by mistakes in classification, and by differential 
fertilization, but the most frequent cause of departures from Mendelian 
ratios is a differential death rate of zygotes and this has no effect on the 
value of Q. That Q has decided limitations as a measure of correlation 
should not affect its use as a measure of linkage. There is, however, one 
serious drawback to the use of Q. When any one of the classes is small, 
changes in this class produce a disproportionately large effect on the 
value of Q. When one class is o and Q equals 1, it may be open to argu¬ 
ment whether the correlation is or is not perfect, but certainly it does 
not follow that the linkage is complete. 
When dominant and recessive are linked and the population is small 
failure to recover the double recessive class may result' from errors of 
sampling. In such cases p may be calculated from the other three 
classes as follows: / -~ A „ - > - , —=r 
4 >= 2 (Ab + aB) 
\ 2 AB -j- (Ab FaB) 
Similarly, if there is difficulty in distinguishing any two classes as, for 
example, aB and ab p may be calculated from the ratio of AB to A b or 
AB to the total 
P 
AB -2 Ab 
AB -f -Ab 
or p 
~v 
4 AB — 2 
n 
n 
