Analysis of Heterogeneity in Some Simplest Characters 231 



In 1906 I gave the results obtained in the study of the size of L. decemlineata 

 as determined statistically in two locations. In these determinations more than 

 the usual care was taken to have the materials of uniform composition, as regards 

 location, generation, and the possible presence of material of other generations. 

 The result expressed at that time in quantity showed only the customary array 

 in a polygon of distribution without significance. This I followed in the popula- 

 tion at West Bridgewater, Massachusetts, through 16 generations, and at Chicago 

 I followed the same investigation through 8 generations, with the same results at 

 both places. I was interested in doing this because of its bearing upon many 

 problems of evolution and transmutation. The net result of this and similar 

 examinations made in the same way was to show that the biometric method was 

 seriously invalidated by the failure to consider the action of place variation, and 

 the further false assumption that the materials collected in nature are homoge- 

 neous, even when collected in one location of the same generation and at the same 

 time. It was early evident in my determinations that the material was heteroge- 

 neous, and hopelessly so, as far as any eifort to simplify it by biometric means 

 was concerned. I kept up the effort, using all of the precautions possible with 

 the collections made in nature, both with our native species and those of the 

 tropics, with the idea of giving this " quantitative variation idea " the fullest and 

 fairest test that I could, and for this express purpose I kept in the background 

 other ideas and methods of investigation. 



" Graduated variates," as determined by measurement of stature or other 

 dimensions, have been the basis of much " quantitative variation " literature 

 and arguments, and the stature, or longest diameter of the mass of the system, 

 is often assumed to be a unit. Neo-Mendelian investigations have shown beyond 

 doubt that in many instances " stature " is a specific property of a mass and does 

 not blend into intermediate masses in fixed combinations, but segregates out of 

 any mixtures into which it enters. The experiences with plants of different 

 statures, of different sizes of animal forms that segregate out, and of which an 

 ever-increasing array of instances is being discovered by enthusiastic workers, 

 leads one to be highly doubtful of the " blended " nature of these characteristics 

 in any organism and of the existence of a long series of " graduated variates " 

 therein. 



Without any exception, I believe, everyone has accepted the idea that at 

 some point in the series there was a certainty of there being " graduated vari- 

 ates " that were " quantitative fluctuations " in the " amount " of the character 

 present. The biometricians, starting with heterogeneous unknown material, 

 measured anything that was convenient and further complicated it with the 

 application of their treatment of the data, while the De Vriesians, starting with 

 refined material in pedigree cultures, attained an exactness of analysis and refine- 

 ment of results quite beyond the ken of the former school. The unit-character, 

 however, was not destined to long survive the searching analysis given " charac- 

 ters," and gave place to the conceptions of Johannsen and his followers. All 

 have retained the conception of the existence of quantitative fluctuations. In 

 reality the problem has not been analyzed ; rather with the recognition of more 

 and more refined units of operation in the investigation, and the establishment of 

 the reality of these, the fundamental propositions as regards the nature of the 

 diversity presented by the unit has been assumed and not investigated. 



