Determination of Larval Instars of Ips hauseri (Coleoptera: Curculionidae: Scolytinae), Using Kernel Density Estimation and Mixture Modeling of Head Capsule Widths

Ips hauseri (Coleoptera: Curculionidae: Scolytinae) is a destructive stem pest of Picea schrenkiana var. tianshanica, and determining its larval instars is essential for monitoring population development and timing control. Healthy spruce logs were deployed to attract ovipositing adults, and 553 larvae were collected through sequential destructive sampling of previously unsampled logs from June to July 2025. Head capsule widths were measured and analysed using kernel density estimation (KDE) and a Gaussian mixture model (GMM), and the classification was biologically validated against the theoretical growth expectation of the Brooks–Dyar rule, together with the Crosby growth-ratio test and linear regression. Head capsule widths showed a clear trimodal distribution corresponding to three instars, with mean widths of 515.82 ± 21.50, 676.01 ± 27.22, and 885.96 ± 38.27 μm for instars I–III. The mean Brooks–Dyar ratio was 1.311, and the natural logarithm of head capsule width was almost perfectly linear with instar number (R2 > 0.999; p < 0.001). This study provides the first quantitative evidence that I. hauseri has three larval instars, offering a basis for studying its developmental biology and improving population forecasting and precise management.