888 
Journal of Agricultural Research voi. xxvii, No.« 
Since the different methods of calculating crossover ratios are variously 
affected when the Mendelian ratios show departures from the expected, 
it may be of value to determine empirically* how Mendelian deviations 
of the various kinds affect the results obtained by the different methods. 
It would be of great interest to have the effects of Mendelian deviations 
on the various methods investigated by a competent mathematician, 
but until this is done a comparison of examples may be of some assistance. 
Deviations from expected Mendelian ratios fall into three groups: 
(1) Effective gametes of the recessive and dominant classes are not 
produced in equal numbers—Differential mortality of gametes. 
(2) Individuals showing the dominant or recessive character may 
not survive in equal percentages—Differential mortality of zygotes. 
(3) Individuals showing the dominant or recessive character may be 
wrongly classified as belonging to the opposite class. 
In each of the above the departure may affect one or both characters. 
Back-crosses and straight F 2 populations will be considered separately. 
In the case of a back-cross (1) and (2) produce the same result. 
It should be kept in mind that the differential death rates with 
which we are concerned and the effect of which we wish to eliminate 
are those in which one member of an allelomorphic pair, considered 
without respect of other Mendelian characters, has a higher death rate 
than its mate. Death rates due to incompatible gametic or zygotic 
combinations, may be distinguished from linkage by the method of 
balanced inviability proposed by Bridges. 
Table I shows the effect of the various forms of Mendelian aberrations 
on a back-crossed population. It will be noted that in many cases a 
formula gives the correct result when p = .5 and does not give the correct 
result when there is a linkage. 
Table II compares the accuracy of the three methods in F 2 populations 
where there is no linkage. 
It appears that Q gives the correct result except where one of the 
classes is not represented. 
T likewise gives the correct result with either gametic or zygotic 
disturbances provided only one of the characters is affected. Where 
both characters depart from the expected ratio, either gametically or 
zygotically, a linkage is indicated where none exists. 
With departures from the expected of any kind P indicates a linkage, 
but in cases where the double recessive class is not recovered, P indicates 
but a slight departure from no linkage while both Q and T indicate per¬ 
fect linkage. 
Table III makes similar comparisons where there is linkage with 25 
per cent crossingover. It appears that Q gives the correct result in all 
cases where the disturbance is zygotic except in mistaken classification 
and failure to recover the double recessive class. In the latter instance 
P is only slightly affected. P also has a slight advantage in the case 
where recessives are misclassified as dominant and the linkage is be¬ 
tween dominants. 
When the disturbance is gametic there is very little difference between 
Q and T though Q has a slight advantage in five of the six examples. 
