NO. 573] CHROMOSOME HYPOTHESIS OF LINKAGE 525 



but here there is no direct parallelism between the 

 zygotic and gametic ratios. In determining what gametic 

 ratio underlies the F 2 results given by an experiment, the 

 practise has been to compare by the eye the given result 

 with a series of F 2 results calculated from selected gametic 

 ratios. Collins has shown 1 that this practise has led to 

 serious error. In F 2 coupling cases in which there has 

 been no crossing over in one sex (autosome genes in 

 Drosophila), there is a direct relation between the gametic 

 and zygotic series, but only in certain classes which com- 

 prise from one fourth to less than one half of the indi- 

 viduals of an experiment. While such data are more 

 accurate than the usual F 2 results, yet the percentage of 

 individuals which can be used directly is so low that we 

 avoid the use of such a method. In F 2 results involving 

 only sex-linked genes, the efficiency is at least 50 per cent., 

 for here there is always a direct relation between the 

 gametic and zygotic ratios in one half the flies (the males). 

 However, half the total number of flies (the females) are 

 useless unless the cross is made in such a way that F 2 

 becomes a back cross. These different kinds of F 2 results 

 (the two most advantageous of which are not generally 

 applicable) are separated in effectiveness by a wide gap 

 from the back cross which we use equally well in all cases, 

 which gives a zygotic ratio directly proportional to the 

 gametic ratio, and in which every individual occurs in the 

 most advantageous relations. 



Perhaps the least unsatisfactory method of dealing 

 with such F 2 series as are available in the case of the 

 sweet peas, is by means of the coefficient of association as 

 derived by Yule. Yule's coefficient of association is calcu- 

 lated from a zygotic series of the form AB:aB:Ab:ab by 

 the formula: 



Coefficient of association = {AB Xab) + {aB x Ah) • 

 To find the gametic ratio corresponding to this coeffi- 

 cient, use is made of a table which gives the coefficients 



