52 GENETICS 



8. Graduated, and Integral Variations 



It is comparatively simple to treat statistically 

 integral variations, illustrations of which have been 

 given in the case of beech-leaf ribs, starfish rays, and 

 daisy florets, all of which are characters that can be 

 readily counted. In the same way any measurable 

 character, such as the size of snail shells, may fall 

 into easily limited groups, as, for example, 10 to 

 11 mm., 11 to 12 mm., 12 to 13 mm., etc. It is 

 somewhat more difficult to classify variations when 

 color or pattern is the character in question, since it 

 then becomes necessary to define certain arbitrary 

 limits for each class of the series within which to 

 group the individual variants. 



Tower, in his famous researches on potato-beetles, 

 encountered variations in the pigmentation of the 

 pronotum all the way from entire absence of color 

 to complete pigmentation. By cutting up this 

 continuous series of variations into arbitrary groups 

 of equal extent, however, it was quite possible to 

 arrange the data so that they could be statistically 

 treated just as conveniently as the integral variations 

 mentioned above. Groups or classes of this kind 

 are termed graduated variations. 



9. The Causes of Variation 



With respect to the causes of variation authori- 

 tative biologists have taken different points of view. 



a. Darwin considered variations as axiomatic. 

 An axiom is self-evident, requiring no explanation. 



