Analysis of Heterogeneity in Complex Characters 241 



At the start two methods of recording for this part were used : (1) an exact 

 record of the type of pattern found and the extent and direction of the unions 

 between the component elements; (2) a record of the proportion of surface pig- 

 mented to that unpigmented, a purely quantitative statement of the " vari- 

 ation " in the amount of pigment present. This latter determination, esti- 

 mated on the scale of to 20, was abandoned at the close of 1906, the biometric 

 results being utterly meaningless and of no significance whatever. 



Each year, during the term of observation, the colony was visited at or near 

 the time when the first and second summer generations were at their maximum 

 in nupiber. The life-history, Chapter II, shows two annual generations of this 

 form; the second, passing the dry season in hibernation and emerging in late 

 May or early June, become the parents of the first summer generation, which in 

 turn breed at once, giving the second summer or hibernating generation. In 

 nature it is not always possible to be entirely sure that the population examined 

 is entirely of a given generation, because of the fact that a few of the overwin- 

 tering generation may live on and mix, and even breed with the first summer 

 generation. These can commonly be separated by the distinctly duller color and 

 generally aged appearance. Sonije, however, may have escaped detection, and 

 have been recorded as first-summer generation. So, too, the first generation 

 may mix with the second. As a rule these mixings can be detected easily in the 

 living specimens, but a few possibly have passed into the wrong records. 



Having established the general plan of investigation, the next step was to 

 determine what variations were present in the pronotum of this species over its 

 entire range. Accordingly, in 1903 a collection of over 8,000 specimens of this 

 species was made from all portions of its geographical range and these carefully 

 analyzed, and from this collection it was found that several distinct pattern-plans 

 were present, and upon these pattern-plans much, if not all, of the variations 

 found were based. In figure 34 is shown an array of these variations. In L. 

 decemlineata 1 had previously found that the variations could be arranged 

 around several central plans, which in turn could be arranged in a large 

 scheme covering the entire range of variations of the species. In L. multitceniata 

 12 such pattern-plans exist, as shown in figure 35, and these are in turn capable 

 of being arranged in a scheme of " variation " of the whole species as regards 

 the pronotal color-pattern, as shown in figure 36. It was further found that, 

 using figure 36 as a basis of plotting, a far more accurate expression of the char- 

 acter of the population as regards this feature was possible than by any 

 other means. It expressed well the direction, kind, and extent of the variations 

 presented by this part. In figure 36 are given all the variations found in the 

 species, and only rarely and in large populations are all of these ever present at 

 one time. It was found that the variations of this species could be accurately 

 separated by this method of plotting, precisely as had been previously used in 

 L. decemlineata. Blanks of this form (fig. 36) were prepared and taken into 

 the field, each individual being entered on the proper part of the blank and also 

 on the second record, indicating whether in the given pattern, the amount of 

 pigment was increased or decreased below the average for that pattern. In this 

 manner there was obtained by direct seriation a statement of the number of 

 individuals showing a given pattern and the variations of that pattern towards 

 others, and also in the quantity of pigment present. 



