The number of larval instars is important from both theoretical and practical perspectives. Three previous studies based on head capsule widths (HCWs) have suggested that Dendrolimus pini larvae pass through seven instars, but the estimated HCW means differed greatly. Various methods are available for determining the number of instars; however, these methods have not been compared on the same dataset. Therefore, the main goal of this study was to compare three approaches for instar separation in D. pini larvae: visual approach followed by non-linear least squares (NLLS) estimation, kernel density estimation (KDE) followed by NLLS, and model-based clustering. Two criteria were used to assess whether the resulting instar separations adhered to Brooks-Dyar's rule: Crosby's growth rule and a coefficient of determination indicating the goodness of fit of a straight line to the ln-transformed mean HCW of the respective instars. Our results showing that D. pini larvae pass through eight instars differed greatly from reports in the literature. The best results were obtained by KDE followed by NLLS. For proper instar separation, both criteria of Brooks-Dyar's rule must be met.
Keywords: Brooks-Dyar’s rule; Crosby’s growth ratio; Dendrolimus pini; clustering; frequency distribution; head capsule width; instar; kernel density.