Analysis of Heterogeneity in Some Simplest Chaeacteks 199 



It would be rash, with present knowledge, to attempt further separation which 

 would be purely anticipatory as to the nature and constitution of organisms. I 

 believe the conclusion valid that there is no sharp demarcation in nature. 

 Aspects of any character that are measured in units of some measure will be 

 arrayed in line and expressed in terms of measure ; those that are not or can not 

 be measured must be expressed in terms of position and relationship ; and there 

 the matter rests for the present. It is not possible to express in quantitative 

 terms, plus and minus, the facts of the fluctuations of these single characters. 



(2) Are the differences of the simplest characters, spots c, h, and d, continuous 

 or discontinuous, or both, and what is the relation between the two? In recent 

 years many authors have drawn sharp distinction between continuous and dis- 

 continuous " variations " and their supposed role in evolution. That variations 

 do arise suddenly is undeniable, at a single step, and stand much apart from 

 their fellows without intergrading conditions; and from changes of this kind 

 stable races unquestionably have arisen. As a protest against the complacent 

 assertions regarding the omnipotent efficiency of minute, constantly accumulat- 

 ing, utilitarian variations as the sole cause of evolution, and in the hope that a 

 new viewpoint and mode of investigation might be the outcome, many have 

 enthusiastically advocated the idea that sudden transformations in the attributes 

 of animals and plants accounts better for the rise of stable races and species than 

 slow accumulation of utilitarian variations. Discontinuities, or sudden jumps 

 with gaps wherein there are no intergrades, must of necessity follow in De Yries's 

 system, from the very nature of the initial concept as to the nature of organic 

 bodies. Eegardless of the assumed underlying entities, actual investigations of 

 the origin and behavior of these sudden variations have been organized and com- 

 pleted with marked success, in striking contrast to the masterly inactivity of the 

 neo-Darwinians. These variations in most instances are the same as the 

 " sports " or " spontaneous variations " of Darwin and Wallace, the " saltations " 

 of other writers ; but in De Vries's Oenotheras a different phenomenon is clearly 

 present. 



It is necessary to keep constantly in mind the possible differences in these 

 changes ; one arising as " variations " in the sense of a departure ; the other as 

 due to rearrangements of characters following crossings. De Vries's Oenotheras, 

 in their recurrent production of the same types, clearly suggest this origin for 

 their " mutations," and the recent studies of Davis, Herbert-Nilsson, Gates on 

 Oenothera, and mine on Leptinotarsa, show clearly the fact and a method of 

 producing these mutating races. 



It is shown that the fluctuations of simple characters were not linear, but in 

 several directions, and that there were also variations in amount, extent of area, 

 and other measurable features ; in other words, that there was a complex varia- 

 tion of the simplest character. 



In the study of the variations of the simplest characters many conditions have 

 been found which might be described as discontinuous, where in the population 

 there were no intergrades. One of the most common discontinuities is that 

 found in statistical study, of which one illustration is presented in figure 31, 

 where in 1000 left c spots of L. undecimlineata Stal, from Tierra Blanca, 

 Mexico, there were a few individuals that stood some distance from the rest of 

 the variates of the lot and without intergrades. These latter were all collected 



