198 The Mechanism of Evolution in Leptinotarsa 



If the changes in different directions producing unlike shapes of spots are 

 mutations, there ought to be visible or demonstrable discontinuity, but there is 

 nowhere the slightest trace of breaks to be discovered. The " variations " which 

 these spots show are not of the same kind, or at least have different directions and 

 hence differing consequences in the composition of the color-pattern of the part. 

 Movement medianward is different and is productive of different pattern-results 

 from one that moves caudalward. The departures shown by these spots in sev- 

 eral directions can be found in many if not in all simplest characters, showing 

 first one, then another, or one or more of its potential possibilities at the same 

 time. I see no escape from the conclusion that the biometric definition of 

 fluctuations is not only not true as a general proposition concerning variation in 

 simplest characters, but must be regarded as an anticipatory definition framed 

 in the interest of a particular hypothesis, and in no wise a carefully derived con- 

 clusion directly deduced from data carefully considered. 



It is possible that supporters of the biometric proposition may maintain that 

 the different directions of variation found are in reality the basal " unit-char- 

 acters," and that variations along the different lines are the variations to be con- 

 sidered, and statistically analyzed. Experience has not shown these spots ever 

 to break up into lesser units in nature, and I have not been able to accomplish 

 it by experimental means. Further than this I can not go at present ; as it repre- 

 sents the limit of experience and the conclusions to be logically derived there- 

 from. Any further statement would, therefore, be anticipatory, dogmatic, to 

 support some one or other theory, but any other similar statement has just the 

 same chances of being true or false. It must be shown that the simplest char- 

 acters in nature and in experiment can be broken up into lesser units, and until 

 this is done it is fairest to consider that spots c, h, and d really represent simplest 

 characters, indivisible, and that they clearly do not conform to the requirements 

 of the De Vriesian hypothesis as regards their common or fluctuating variations. 



The question whether the pigment as a substance which should be measured in 

 terms of quantity or area colored and the pattern or distribution of it considered 

 as another character, and that the two are necessary for visibility can hardly be 

 answered with any exactness. Neo-Mendelian hybridology has shown clearly 

 that pigment and pattern can be shifted independently of one another in crossing. 

 If this proposition be admitted as true and as applicable to these simplest char- 

 acters, the problem is not solved. Pigment then becomes a character that fluc- 

 tuates in quantity as statistically measured ; pattern, its companion, shows noth- 

 ing that can be called fluctuation, nor that can be called mutation. The decision 

 would largely depend upon definition in the absence of experimental evidence. 



Each of these characters presents, therefore, heterogeneity; and depending 

 upon what is considered the correct point of view hangs the kind of statements 

 that will be made. If the character is calibrated only in units of area, diameters, 

 length of perimeter, and angles between the directions of variation, the state- 

 ments will all of necessity be in terms of more or less ; the determinations are 

 forced to become quantitative. What is actually present are differences existing 

 between the same character in different individuals, and these are neither entirely 

 quantitative nor entirely qualitative, hut are differences in the quantity of mate- 

 rial, in composition, and in the physical position, arrangement, and relations to 

 surrounding parts. From a descriptive standpoint it is impossible to go further. 



