Individual Tree Height Increment Model for Quercus mongolica Secondary Forest in the Northeastern China Using Generalized Nonlinear Two-Level Mixed-Effects Model

(1) Background: Mongolian oak secondary forest is widely distributed in the northeast of China, and most of these forests are formed after the overcutting of broad-leaved Pinus koraiensis mixed forest. Most of the forest productivity is low and the ecological function is degraded, due to insufficient understanding of Mongolian oak and lack of scientific management. Deepening the research on exploring reasonable management measures of Mongolian oak secondary forest to an improved stand status is the basis for improving its quality and promoting its forward succession process. (2) Methods: Twelve permanent plots with an area of 1 ha were established in the Mongolian oak secondary forest on Tazigou forest farm in Wangqing, Jilin Province of northeastern China. The response of tree height increment of Mongolian oak secondary forest is studied based on the survey data of 2013 and 2018. Two-level nonlinear mixed-effects models were constructed to predict the height of a single tree using sample plots and tree species as random effects, combined with a variety of tree size factors, site factors, and competitive factors as independent variables. (3) Results: The significant factors related to the height increment of Mongolian oak secondary forest are the initial diameter at breast height as the size of the tree itself (DBH), height (H), crown height ratio (CR), and site productivity index reflecting site quality (SPI). The distance-dependent and distance-independent competition indexes have no significant effect on tree height increment. The fitting accuracy of the two-level mixed-effects model that introduces plots and tree species as random effects has been greatly improved (coefficient of determination R-2 increased by 51.8%). The prediction results show that the two trees with the largest DBH have the strongest prediction ability. (4) Conclusions: The generalized nonlinear two-level mixed-effects model constructed in this study can describe the height increment of an individual tree in the Mongolian oak secondary forest. Two sample trees, namely the two largest trees in each sub-plot, were applied for estimating the random effects when both measurement cost and potential errors of prediction were balanced.