Per-stage growth rates of head and body sizes in scarab larvae (Coleoptera: Scarabaeidae) decrease across ontogeny following a species-specific pattern

It has been widely assumed that the stepwise increase in the exoskeleton size of larval insects approximately follows a geometric progression from instar to instar, known as Dyar's Rule. However, it is not clear whether the per-instar increase in body size follows this rule. In insects, Dyar's Rule has been identified either by regressing the log-scaled size on the instar number (log-linear regression analysis) or by comparing the postmolt/premolt size ratio between instars (growth rate analysis). A previous study on the body mass of caterpillars showed the methodological pitfall that Dyar's Rule was statistically supported by log-linear regression analysis, but not at all by growth rates analysis. I considered this concern here by examining the per-stage growth rates of head and body sizes for larvae of the beetle Trypoxylus dichotomus using both methods and compared the resulting growth rates for body size within and between taxonomic orders. Dyar's Rule was statistically supported by the log-linear regression analysis but not by growth rate analysis for both the head and body sizes in T. dichotomus. The body size growth rate in T. dichotomus decreased as the instar progressed. This developmental pattern was also found in reported data for the other six scarabs, but not in data for Lepidoptera or Hymenoptera. These findings confirm that the per-stage growth rate of body size does not follow Dyar's Rule in a wide range of insects, and suggest that developmental change in the body size growth rate varies among insect groups.