Objective  This paper aims to explore the influencing factors and variation rules of wood density in the longitudinal stem of Populus nigra × P. simonii, so beta regression models with mixed effect of sapwood, heartwood, bark and stem density of the poplar were constructed, which was used as a reference for stem biomass prediction and wood timber properties.

  Method  Mixed effect beta regression models for sapwood, heartwood, bark and stem density of P. nigra × P. simonii were established, which based on the analytical data of 90 trees of P. nigrax × P. simonii plantation in Shangzhi City, Heilongjiang Province of northeastern China. Using correlation analysis and optimal subset methods to screen the variables of the beta regression base model, and the goodness of fit of the convergence model was evaluated by −2log-likehood value, akaike information criterion, bayesian information criterion, adjusted certainty coefficient (R_a ²) and likelihood ratio test. The leave-one-out-cross-validation was used to test the model, the indexes were mean absolute error (MAE) and mean absolute error percentage. Two sampling methods were combined (scheme Ⅰ: no relative height; scheme Ⅱ: limit relative height below 0.1) to correct the model.

  Result  The densities of sapwood, heartwood, bark and stem were not only affected by relative height, but also closely related to the average growth of DBH, age and DBH, respectively. R_a ² of the mixed-effect beta regression model based on tree factors was 0.53, 0.52, 0.52, 0.63, respectively, and the MAE < 0.05 g/cm³. Sapwood density and heartwood density decreased first and then increased from the base to the top of the stem, with an inflection point at a relative height of 0.2. Bark density first increased and then decreased from the base of the stem to the top of the tree, and there was an inflection point at the relative height of 0.6. The stem density increased gradually along the stem. When fixed relative height, the densities of sapwood and heartwood were both negatively correlated with the average growth of DBH. The densities of bark and stem were negatively correlated with age and DBH, respectively. Without limiting the relative height, the wood density value corresponding to the height of 4 discs randomly sampled along the stem was calibrated to obtain stable prediction accuracy. When the sampling height was limited to 0.1 (2.0 m) or less, there was little difference in the prediction accuracy between the optimal sampling combination and the density values (1.0, 1.3, 2.0, 1.0 m, respectively) of sapwood, heartwood, bark and stem at a disc height. Relative height, average growth of DBH, age and DBH were significant influencing factors of wood density of P. nigra × P. simonii.

  Conclusion   The beta regression model can directly simulate the stem density of P. nigra × P. simonii in the (0, 1) interval, and the random effect can improve the prediction accuracy of the model. The longitudinal variations of sapwood, heartwood, bark and stem density are different. The constructed mixed-effect beta regression model can lay a foundation for biomass estimation and wood property study of P. nigra × P. simonii.