882 
Journal of Agricultural Research voi. xxvn, no. h 
A number of methods have been proposed for determining the cross¬ 
over ratio from an F 2 population, any of which will give accurate results 
for a theoretically perfect population. In practice, however, disturbing 
factors, such as differential death rates or indistinct classes frequently 
cause significant departures from a theoretically perfect population. 
Disturbing factors are made manifest by departures from the expected 
Mendelian ratios for each character. Deviations from expected Mende- 
lian ratios may be due to a variety of causes any of which may be without 
effect on the percentage of gametes in which crossingover has taken 
place, but which may influence the apparent percentage of crossingover 
as determined from zygotic ratios. 
The results obtained by the different formulae are variously affected 
by departures from expected Mendelian ratio depending on the cause of 
the deviation, and there seems to be no single method that will give the 
most accurate results in all cases. 
Although it may not be possible to determine with certainty the 
cause of any given departure from an expected Mendelian ratio, fre¬ 
quently there will be strong presumptive evidence in favor of some one 
cause, and when such is the case it should be of value to be able to choose 
a method that is not seriously affected by the disturbing factor. In the 
following pages the methods in most general use have been brought 
together and compared empirically as to their accuracy. 
NATURE OF ABERRANT MENDEEIAN RATIOS 
Departures from expected Mendelian ratios may be due to irregu¬ 
larities in the behavior of the gametes or of the zygotes. Several types of 
gametic disturbances have been recognized, such as the formation of 
dominant and recessive gametes in unequal numbers, differential mor¬ 
tality, and selective fertilization. The effect on linkage relations is the 
same in all cases—that is, effective gametes bearing the dominant and 
recessive members of an allelomorphic pair are unequal in number. 
Similarly, there may be a variety of ways in which one zygotic class 
is influenced adversely, but the general result is a differential mortality 
or a difference in the survival value of dominant and recessive individuals. 
In addition to these two main causes of aberrations there is the slightly 
different case that results from mistakes in the classification of zygotes. 
The deviation is, of course, zygotic, but while the numbers representing 
one member of the character pair are increased at the expense of the 
other, it is not the same as a differential mortality, for if there is a linkage 
between the two character pairs a differential death rate in one character 
must necessarily affect the ratio of dominant to recessive in the other 
character, whereas mistakes in the classification of one character do not 
affect the ratio of dominant to recessive in the second character. 
In discussing the various measures of linkage the following terminol¬ 
ogy will be used: 
AB , Ab, aB , a& = the number of individuals in each of the four zygotic 
classes in a hybrid involving two character pairs A a and Bb. 
n= total number of individuals. 
p=that part of the total number of gametes in which crossingover 
has taken place expressed as a decimal fraction. 
i — p — noncrossover gametes. 
The percentage of crossingover is then p X ioo and the crossover 
. . p i — p 
ratio is ~: ——^ • 
p p 
