Ontogenetic progression of individual head size in the larvae of the beetle Trypoxylus dichotomus (Coleoptera: Scarabaeidae): catch-up growth within stages and per-stage growth rate changes across stages

The ontogenetic progression of insect larval head size has received much attention due to its fundamental and practical importance. However, although previous studies have analyzed the population mean head size, such an approach may not be appropriate for developmental studies of larval head sizes when the trajectory of individual head size growth is correlated with pre-molt head size and developmental stage. Additionally, there is covariation between the head and body sizes; however, few studies have compared the ontogenetic progression of individual head sizes with that of individual body sizes. In this investigation, the per-stage growth rates (PSGRs) for head width (HW) and cubic-rooted body mass at the beginning of each instar (body size, BS) were assessed in Trypoxylus dichotomus. Linear models were used to test the size- and instar-dependence of the ontogenetic progression of individual HW and BS. The individual PSGRs of the HW (iPSGR(H)) and BS (iPSGR(B)) were then compared. In addition, the allometric relationship between HW and BS was examined. The iPSGR(H) was negatively correlated with the pre-molt HW at every instar (i.e., head catch-up growth). Furthermore, the mean iPSGR(H) at L2 was relatively higher than that at L1 when the pre-molt HW was used as covariate in the analysis (i.e., instar-effect), whereas the mean iPSGR(H) decreased ontogenetically. The iPSGR(B) showed catch-up growth and instar-effects similar to those of iPSGR(H); however, iPSGR(H) was found to be lower than iPSGR(B). Due to the differences between the PSGRs for the larval head and body, the larval head size showed negative ontogenetic allometry against body size.