Analysis of Heterogeneity in Some Simplest Characters 219 



Much use has been made of the instances of improvement made in the domesti- 

 cated organisms by selection of " quantitative variations," and all are thoroughly 

 familiar by this time with the extensive use that has been made of these instances 

 by De Vries in the formulation of the mutation theory, and by Johannsen and 

 his followers in the development of the pure-line hypothesis. In all of these 

 instances it is assumed that there is " quantitative variation " ; but is it proven 

 that there is such ? Has it not been assumed that there are quantitative vari- 

 ations solely on the basis of the inaccurate findings of the statisticians ? In what 

 instance has a biometric worker really determined the nature and homogeneity 

 of his material before he began to investigate it through statistical methods? 

 Eecall, for example, the many determinations made by Pearson, Galton, and 

 others of the same school in the human species, with entire lack of homogeneity 

 of parentage, race, conditions of growth, present conditions of life, and other 

 factors that may enter into the production of the individual. It is results from 

 examinations of this sort that have led to the existence of " quantitative fluctuat- 

 ing variations " in the literature of the last two decades, and lead primarily to 

 the creation of the situation in this field that arose with the mutation theory. 



The history of the sugar beet has been again and again used as an example 

 of the existence of " quantitative " or " fluctuating variations " ; but is the deter- 

 mination of the saccharine content of the beet the character, and does it repre- 

 sent this group of substances as they exist in the beet ? In this instance a heter- 

 ogeneous group of compounds, the saccharine content, has been removed from 

 the organism, is determined in percentages of total weight of the body from 

 which it came, but the extracted product may have many mono- and di-saccha- 

 rides in it, but is rated as " one character," and no attention is paid to its diver- 

 sity in composition and the fact that it is an extracted product and not a charac- 

 ter in the organism. As to the materials in the organism, there is relatively little 

 information, but that available indicates complex relations, the product of 

 divers processes at work. For the practical purposes of the sugar industry the 

 amount of " sucrose " that can be extracted is important, and the development of 

 strains that produce large extractable quantities is commercially desirable, but 

 extractable amount measured quantitatively is hardly a determination of the 

 character as it exists in the organism. There is nothing in the work to indicate 

 whether the differences in the saccharine content in the sugar beets are fluctua- 

 tions in quantity or not. In the mono-saccharides and di-saccharides present 

 there is remarkable specificity of the different substances in composition, action^ 

 and relations in the organism, and differences of most numerous sorts may well 

 exist without being discovered or even considered by the statistical treatment of 

 the " character." 



In this instance saccharine content is not the only " character " that has been 

 considered; form of the root, woody content, leaf character, and others have 

 come under the observation and manipulation of the beet grower, have been puri- 

 fied, and races derived having the desired commercially valuable characteristics. 

 In this practical work the operators, misled by the selection idea and the com- 

 placent uncritical methods of the statisticians, applied " measures " to the char- 

 acters, which although fairly useful to a limited extent for the practical purposes 

 of industry, did not and can not express or indicate the real relations of these 

 " characters " in the plants. These are most complex, and differences of all 



