Analysis of Heterogeneity in Some Simplest Chakacters 195 



The quantitative aspect of this spot is presented in figure 14, where is given in 

 the form of a curve the distribution of the areas found in the left spot (c) in 500 

 individuals. This statistical data presents simply the fact that in 500 individ- 

 uals from Tierra Blanca, State of Vera Cruz, Mexico, the area covered ranged 

 from to 3.7 sq. mm., with the modal condition 

 at 1.5 sq. mm. From these data I could, if 

 desired, calculate many mathematical values of 

 no significance. From the statistical aspect the 

 variations are in line mere plus and minus addi- 

 tions, made so by the method of study ; but ex- 

 amination of the areas shows that there are fea- 

 tures that are not and can not be stated statis- 

 tically; the character has spatial relations, and 

 these can not be analyzed by biometric methods. 



In figure 15 is given the condition of the spot 

 c found in L. multitceniata Stal, geographic 

 variety multitceniata Stal, at Puebla, Mexico. 

 In this location the spot is nearly always present 

 and usually of considerable area, but shows the 

 same direction of variation as in L. undecim- 

 lineata, pushing out from the center along the 

 same lines and in the same relative position on the pronotum. Statistically 

 it shows nothing more than in the first case, a distribution of the area of 



Fig. 14. — Statistical examina- 

 tion of area of 500 left c spots in 

 L. undecimlineata from Tierra 

 Blanca, Vera Cruz, Mexico. 



A 



/V Ai5/:*Ai5<V 



m 



Fig. 15. — Showing difference in size, shape, and directions of extension of spot 

 c. in L. multitwniata from Puebla. 



exposed pigment in a curve extending between different extremes with a different 

 mode, and hence with the possibility of deriving different mathematical coeffi- 

 cients if desired (fig. 16). 



The same character in the same species from Guadalupe, Mexico, when exam- 

 ined shows only differences in the end-results, but everywhere the same direc- 

 tions of variation movement. Biometrically considered, the data from 500 indi- 

 viduals show a different mode and distribution of areas (fig. 17). One might 

 go on in this manner without limit and in all it would be found that when the 

 areas were measured the variations would all fall into line, plus and minus. 



