No. 631] 



FACTORS OF HEREDITY 



in; 



way that their distances could never be represented as a 

 function of distances in a single line. The cause of this 

 discrepancy between Castle's figures and the relation- 

 ships observed by the DrosopJiila workers lies in the 

 nature of the data which Castle uses, or rather, in his 

 manner of using the data. For Castle constructs his 

 maps, or models, on all the data obtainable, indiscrim- 

 inately, and regardless of the fact that most of the data 

 for the linkage values involved have been secured in as 

 many different experiments. On the contrary, it is nec- 

 essary, in order to determine exactly the relationships 

 existing between interdependent linkage values, that all 

 the data be obtained from the same experiment. This is 

 because the precise value obtained for any given linkage 

 is not only subject to the ordinary error of random sam- 

 pling but may vary significantly in different experiments, 

 in response to different environmental conditions, the 

 age of parents, genetic factors, and the amount of dis- 

 crepancy due to differential viability. Piling up enor- 

 mous counts does not eliminate these sources of varia- 

 tion. Any slight aberration thus produced in the abso- 

 lute value of one of the linkages (say AC) will then alter 

 so materially its relative value, as compared with the 

 other linkages (AB and BC), obtained in two different 

 experiments, that the different values no longer fit into 

 the linear system; they will not be expressible as any 

 sort of function of the system. That is why Castle found 

 that the DrosophUa workers' own data gave the per 

 cent, of crossing over between y(yellow) and w(white) 

 as 1.1, between w and bi (bifid) as 5.3, and between y and 

 bi as 5.5, a relationship quite at odds with their claims 



say, one unit of distance), the results of different experi- 

 ments. In fact, had we been allowed to select the experi- 

 ments for him, we could have chosen values such as the 

 following: Sb (frequency between star and black) 39.3; 



