LINKAGE RELATIONS IN MEN DELI SM 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 XXVII 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 z populations. When the two dominant 

 factors enter the cross from opposite sides it is practically impossible 

 to determine the linkage values by simply mating FI 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. 



