THE DISTRIBUTION OF PURE LINE MEANS 



DR. J. ARTHUR HARRIS 



Carnegie Institution of Washington 



Several times recently we have been told that the 

 means of a character in a series of pure lines form a 

 * ' Quetelet 's Curve. ' n Some of those responsible for this 

 assertion seem to attribute a particular virtue to ' ' Que- 

 telet 's Law," and to feel that the statement that the 

 means of a series of pure lines form a chance curve fur- 

 nishes uncontrovertible evidence for the genotype theory 

 of heredity. The questions which interest the biologist 

 are, first, whether the statement is true in the sense that 

 it is made on a sufficient body of actual observations, and 

 second, what is the general biological significance to be 

 attached to it, if true. 



But among these biologists the interpretation of the 

 facts has apparently preceded the demonstration of the 

 existence of the facts themselves. Now while it is not at 

 all unlikely that the means of genotypes — if such entities 

 in Johannsen's sense of the term do exist in nature — 

 form a chance curve, it by no means follows that con- 

 versely a series of averages which can be arranged in a 

 symmetrical variation polygon proves or even suggests 

 the existence of differentiated pure lines or biotypes. 

 Yet just such differences in means are being accepted 

 and cited without criticism as valid evidence in support 

 of Johannsen's sweeping generalizations. 



A case in point is a paper by Roemer 2 on pure lines in 

 peas. It is with regret that one criticizes Roemer 's 



Compare, for example, in this connection: Nilsson-Ehle, Bot. Not., 1907, 

 pp. 113-140; Lang, Zeitschr. /. Ind. Abst.- u. Vererbungsl., Vol. 4, pp. 15- 

 16, 1910; Spillman, Amer. Nat., Vol. 44, p. 761, 1910; Pearl, Amer. Nat., 

 Vol. 45, p. 423, 1911. 



2 Roemer, T., " Variabilitatsstudien, " Arch. f. Eassen- u. Gesellsch.- 

 Biologie, Vol. 7, pp. 397-469, 1910. 



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