Nonlinear mixed-effects crown width models for individual trees of Chinese fir (Cunninghamia lanceolata) in south-central China

Abstract An individual-tree crown width model was developed with data from 2461 Cunninghamia lanceolata trees in 103 sample plots located on a Huangfengqiao state-owned forest farm in south-central China. To prevent correlations between observations from the same sample plot but different classes of site index, we developed a nested two-level nonlinear mixed-effects (NLME) model that accounts for the random effects of site index classes and sample plots on tree crown width. Various stand and tree characteristics were evaluated for their contribution to model improvement. The best random-effects combination for the two-level NLME model was determined by Akaike’s information criterion and logarithm likelihood. Heteroskedasticity was reduced by three residual variance functions: exponential function, power function and constant plus function. The prediction abilities of the model were tested at the levels of population average, site index class, and combined site index class/plot. Significant predictors of tree crown width were diameter at breast height, dominant height, height to crown base and height. Heteroskedasticity was most successfully removed by the power function. The interaction between site index class and plot played a more important role than site index class alone. The prediction accuracy of the final model with nested two levels of site index class and plot was higher than the model only at site index class level or at population average level. Additional stand and tree variables (such as canopy density) further improve the prediction efficacy of the model. This article focuses on the research methods, which could be adopted in similar studies of other tree species.

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