Is Allometric Variation in the Cephalic Horn on Male Rhinoceros Beetles Discontinuously Dimorphic?

摘要

I used linear and nonlinear regression to re-examine the allometric relationship between length of the cephalic horn and width of the pronotum (a measure of body size) for males of 28 species of rhinoceros beetle (Coleoptera, Scarabaeidae, Dynastinae). An earlier investigation reported that variation in relative size of the horn conforms in most of the 28 species to a pattern of discontinuous, loglinear allometry, which implies, in turn, that two different power equations are needed to describe the full range in untransformed data. My analyses indicate, however, that allometric variation is continuous in all 28 species and that pattern in each of the original bivariate distributions is well described by a single mathematical function. Allometric variation on the original, arithmetic scale is linear for some species; either linear or slightly sigmoidal for other species; and decidedly sigmoidal in still other species. So-called major and minor morphs merely represent the extremes in absolute and relative size for the horn on animals drawn from the same, continuous distribution. The different findings reported in the earlier investigation resulted from insidious problems introduced by logarithmic transformation of the original bivariate data coupled with an overly complex statistical protocol for classifying individual males as either "major" or "minor." Attempts at classification lead inevitably to oversimplification and misrepresentation of the pattern of allometric variation. Focus needs to return to describing and interpreting pattern in untransformed observations because the relationship between the original variables is the relationship of interest.