688 



THE AMERICAN NATURALIST [Vol. XL Y 



II. The Problem of Differentiation in Koemer's 

 Pure Lines 



The method of Roemer's study was very simple. In 

 1908 a population of pea plants was grown from a sample 

 of ordinary seed. In 1909 the offspring of each of a num- 

 ber of these plants was studied separately, and the means 

 of several characters calculated. By a comparison of 

 selected pairs of these means Roemer concludes that the 

 several lines differ from each other, and by a seriation of 

 all the line means he obtains the Quetelet 's curve. 



Such evidence as this can not be accepted. Every 

 mean calculated on a sample of individuals is more or less 

 untrustworthy as a measure of the character in individ- 

 uals in general, because of the errors of random sam- 

 pling, and in attaching significance to a series of averages 

 this fact must be fully taken into account. It can not 

 adequately be allowed for by a comparison of selected 

 cases with their probable errors. 



First Test. A Comparison of the Variability within the 

 "Pure Line" with that of the "Population" 



One of the tests of the presence of differentiated 

 "biotypes," " genotypes'' or "pure lines" within a 

 ' ' population ' ' is the comparison of the intra-line with the 

 population variability. If both be the same there is no 

 justification in the assumption that the population is 

 composed of a number of differentiated pure lines. 4 If 

 the variability of the population is greater than that of 

 the individual lines it may (or may not) comprise a series 

 of "genotypes." 



The reason for this is obvious. The standard devia- 

 tion within the pure line, <r, describes only the differences 

 occurring among the individuals of the group, while 2, 

 the standard deviation of the group, includes also the 

 amounts by which the several lines are differentiated. 



