LINKAGE RELATIONS IN MENDELISM 127 
nor is it based on any known cytological phenomena. The series of 
ratios which lent original support to the theory appear to be no more fre- 
quent than should be the case on the basis of chance, and many which are 
supposed to fall into the series have been placed there on evidence which 
is entirely inadequate. The large series of linkage values which have been 
obtained in Drosophila demonstrate clearly that all intermediate ratios 
can be obtained, and since all other conditions are satisfied by the chro- 
mosome theory it seems unreasonable to give it up for an hypothesis which 
has no cytological support and an uncertain amount of experimental 
support. Moreover, it may be safely stated that all cases of linkage 
thus far reported may be explained according to the chromosome theory 
of linkage. 
The mathematical relations existing in linkage phenomena are 
of interest because they provide a method of determining the genetic 
relationships involved in certain cases of somatic correlations. If two 
factors are linked in inheritance it follows that a larger proportion of 
the population will display the corresponding two characters than would 
be the case, if the factors were inherited independently. Consequently 
character correlations of this type are an index to factor linkage. 
In Tables XXVITI and XXVIII the results of various strengths of 
factor linkage and the consequences with respect to the gametic and 
phenotypic ratios are given. These tables show clearly that the only 
satisfactory method of determining the presence of linkage and its value 
is to cross back the heterozygous individual to individuals recessive for 
both factors. In such crosses the phenotypic ratio corresponds exactly 
to the gametic ratio, and it is, therefore, possible to determine the per- 
centage of crossing-over by this method with a much greater degree of 
precision than from ordinary F, populations. When the two dominant 
factors enter the cross from opposite sides it is practically impossible 
to determine the linkage values by simply mating F; individuals together, 
for comparatively large differences in linkage value may affect the 
phenotypic ratio so slightly that the deviations, in small populations at 
least, might be ascribed merely to the operation of the laws of chance. 
The significant feature of such ratios is the small proportion of double 
recessives which appear. Thus with crossing-over values exceeding 20 
per cent., this class practically disappears in experiments involving the 
usual number of individuals in a population. Moreover, matings in 
species which display crossing-over only in the sex-homozygotes as shown 
in Table XXVIII give the ratio 2:1:1 for all percentages of crossing-over 
when one dominant factor enters the cross from one parent and the other 
dominant factor from the other parent. A careful consideration of these 
two tables will show clearly how difficult it is to determine linkage values 
precisely except by properly planned experiments, and in this difficulty 
lies the reason for many errors of interpretation. 
Digitized by Microsoft® 
