Static allometry of the horn and pronotal depression in adult Oryctes rhinoceros supports continuous nonlinearity, sexual dimorphism, and size-independent covariation

Exaggerated insect traits often show positive allometry, yet nonlinear scaling can reflect either continuous curvature or discrete morphs. Distinguishing between these alternatives is important because they imply different developmental and evolutionary scenarios. Using cross-sectional data from 1,000 adult Oryctes rhinoceros , we analyzed the static allometry of nine traits with pronotum width as the primary body-size proxy and body length for sensitivity analyses. Cross-validated comparisons among linear, continuous nonlinear, and two-component mixture models showed that continuous nonlinear models improved predictive performance over linear models for horn length and pronotal depression width in both sexes. By contrast, mixture regression did not outperform the best continuous model in either sex, providing no positive support for discrete within-sex dimorphism under the tested model set. After accounting for body size, horn length remained positively associated with pronotal depression width, indicating size-independent covariation. These associations were retained when body length was used instead of pronotum width, supporting robustness to body-size proxy choice. Together, these results support continuous nonlinear adult scaling of the horn and pronotal depression in O. rhinoceros and indicate covariation not attributable solely to body size under the tested model set.