Analysis of Heterogeneity in Some Simplest Chaeactees 203 



Statistically, the problem must be answered from four aspects: (1) in the 

 species as a whole, regardless of where or when the specimens lived, it is 

 necessary to determine the entire range presented; (2) comparisons of one local- 

 ity with another are necessary to discover possible local influence; (3) successive 

 generations in the same location must be compared to determine the constancy of 

 relation between local causes and effects; (4) comparison of series of genera- 

 tions in the same and different localities to determine the existence of continued 

 or permanent local influences. These four examinations will give all the infor- 

 mation possible from this source, and when combined, will give some basis for the 

 determination of the nature of diversity in these simplest characters, and provide 

 the proper data for initiating experimental analysis of problems not touched by 

 the methods used. In this study I have examined these characters in many thou- 

 sands of specimens, and in living material and museum specimens have looked 

 constantly for new or unusual " variations." In figure 22 I have shown outline 

 drawings of the main types of variations found in L. undecimlineata. 



Fig. 22. — Diagrammatic representation showing common types of variation In 

 spot o found in L. undecimlineata. 



Fig. 23. — Diagrammatic representation of outer portion of pronotum in L. 

 undecimlineata, sliowing relation of different directions of variation in spots c, e, 

 and relations of these to the element x. 



Examination of the variations shows clearly that the character in its variations 

 is delimited to a few directions of change. These are diagrammatically shown in 

 figure 23, which is a composite of the spot in outline to show the direction of 

 departure. As compared with other species, it is quite distinct in its variations, 

 which are few and rarely of any magnitude. Medianward fusions with & 

 have not been found, although c may extend towards I, but & does not move 

 towards c; hence there is no fusion. Caudalward unions with e are rare, and 

 result from combined action of c and e ant. towards each other; and still more 

 rare are fusions with d, which depend upon the presence of a rare element h. 

 Its absence is not infrequent and its presence never reaches an area of over 5 

 sq. mm., 4.89 sq. mm. being the largest seen, and that a product of selection plus 

 environmental stimulus. 



Parallel observations in nature were made near Tierra Blanca, 57 miles south 

 of the City of Vera Cruz, at El Hule, 39 miles south of Tierra Blanca, and at San 

 Marcos, 68 miles south of El Hule, all upon the savannahs of Vera Cruz, Mexico. 



The location at Tierra Blanca was on the edge of a small stream 3 miles from 

 the town on the trail of Estanzeula. The immediate location was typical trop- 

 ical savannah with thorn forest, well watered, good drainage, and about 225 feet 

 above sea-level. The El Hule location was on the southern edge of the flood- 

 plain of the Eio Papalaopan, west of the station buildings about 1 mile, on the 



