Statistical Studies on the Variation of Stac beetles. 89 



For this assertion, the results obtained from Luca/iiis afford still stronger 

 evidence. The variation is more striking also in the male than in the female; 

 but it is less pronounced, compared with Cladognathus, inasmuch as here the 

 dimorphic condition of tlie body length is not yet obvious enough, although a 

 tendency thereto cannot be denied. What concerns the female, the variation 

 is still simpler ; it represents a typical unimodal type. The female shows, a 

 striking characteristic which consists in the truncated posterior side margins of 

 the caput. This morphological characteristic is visible again in the low-typed 

 males (Fig. 5, b) and grows weaker towards the high-typed ones, until it is 

 totally lost in the highest (Fig. S, a). Notwithstanding the antlers which 

 differ widely from the claw-like mandibles of the female, the female has this 

 criterion referred to in common with the low-t)-ped male. This characteristic, 

 then, must once have been, I think, one of the conspicuous species characters. 

 Here we are, therefore, also forced to assume that the female represents the 

 primary type, whence the male type has been derived. 



The present results from the study of the two species of stagbeetles in- 

 terest us so far as they are concerned with variation, in the fact that they 

 parallel each other, and as to the degree of variation, in the fact that both 

 the forms are divergent from each other. It is obvious that Lncanns is in 

 this respect inferior to CladognatJnts ; hence the course of variation in the 

 latter can, to some extent, be deduced in that of the former. For instance, 

 the obtuse-angled curve in the females of Cladognathus must ha\'e been an 

 acute-angled one as in the case of the same sex of Ljicamis ; likewise the 

 zigzag-lined curve in the males of the latter shows, without doubt, a tendency 

 to pass over later into the dimorphic curve of the former. This multifarious 

 variety of forms, which both the species of stagbeetles exhibit, forces us to 

 assume that the beetles in question are in character quite variable. It is this 

 variability, I think, that caused the beetles to exhibit sexual dimorphism. 



