No. 539] DISTRIBUTION OF PURE LINE MEANS 



carried out. Concerning "Svalofs Kapital Erbse" there 

 can be no doubt. The original plant was selected at 

 Svalof in 1896. Whether a further selection within the 

 offspring of this plant was made, Roemer was unable to 

 determine, but of the ancestry of his seed he felt quite 

 certain. 



Truly this is an anomalous state of affairs ! Analyzed 

 by the best available statistical methods, Roemer 's data 

 certainly indicate that the lines studied are significantly 

 differentiated. Pure-line specialists dispense with any 

 statistical analysis at all and accept the data as "a con- 

 firmation ... of Johannsen's epoch-making investigations 

 on beans." Yet if the differentiation in these lines be 

 due to anything other than faulty experimental condi- 

 tions, the observations described destroy entirely the 

 value of Johannsen's theory by showing that heritable 

 variations may occur in great numbers in the pure line. 



IV. Summary and Conclusions 



1. The statement that the means of the pure lines of a 

 population form a "Quetelet's Curve" is now being made 

 by genotypists. If it is true that an apparently homo- 

 geneous population is composed of a large number of 

 slightly differentiated genotypes, it seems a priori not 

 unlikely that their means will be arranged according to 

 "Quetelet's Law." The question which concerns the 

 biologist is whether this is, as a matter of fact, the condi- 

 tion found in nature. The object of the present rather 

 laborious study has been to test the validity of this asser- 

 tion on the basis of available facts. Roemer 's data for 

 pure lines in peas are the only passably satisfactory 

 published series available. 



2. Such a problem has two phases. It is first necessary 

 to determine by adequate statistical tests that the lines 

 in question may be reasonably regarded as differentiated 

 biologically — i. e., that the differences between them can- 

 not be explained as the errors of random sampling, such 



