I analyzed male mandible and wing allometries in natural population samples of 76 species in 9 genera of the family Lucanidae. Positive allometry of mandible size to body size was highly significant in all the species, and negative allometry of wing size was significant in 72 species. Negative allometry of wing size was not related to phylogenetic background, suggesting developmental tradeoffs between resource allocations to mandible and wing structures. Wing allometry was correlated negatively with mandible allometry and with the proportion of mandible size to body size, suggesting that species with relatively large mandibles have proportionally smaller wings. There is an inherent negative correlation between mass of beetles and wing area per unit mass, and negative wing allometry further influences this linear relationship. Negative wing allometry may reflect a morphological cost to evolving oversized mandibles.
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Kazuo Kawano (1997) studied this question.