Estimating crown width in degraded forest: A two-level nonlinear mixed-effects crown width model for Dacrydium pierrei and Podocarpus imbricatus in tropical China

Tropical forest degradation makes a major contribution to greenhouse gas emission. Crown width (CW) is one of the important predictors in forest growth and yield models that provide basic data for assessment of forest degradation. Precise method of estimating tree crown for two tropical tree species (Dacrydium pierrei Hickel and Podocarpus imbricatus Bl), which are the major species in the degraded coniferous mixed forests in the tropical China, is necessary. These forests play a pivotal role in maintaining ecosystem functions, but are under the threat of severe degradation in recent years, and none of the studies has provided focus to these forests. We developed a nonlinear mixed-effects CW model using the permanent sample plot data acquired from D. pierrei and P. imbricatus forests. A number of tree- and stand-level variables were evaluated for their potential contribution to the CW variations, and included only highly significant ones in the model. The random effects at the levels of both sample plots and stands with different site quality class (blocks) were included in the CW model through mixed-effect modeling, and resulting model is therefore a two-level nonlinear mixed-effects model. Leave-one-out cross-validation was applied to evaluate the models. Among several predictor variables, diameter at breast height (DBH), height-to-DBH ratio (HDR), and height to crown base (HCB) contributed relatively highly to the CW variations. Dummy variable was introduced into the model to differentiate CW variations of two tree species. Correlations of CW and predictor variables significantly decreased when random effects at both the block and sample plot levels were included. We calibrated the nonlinear mixed effects CW model following the empirical best linear unbiased prediction theory, using four strategies of selecting CW trees per sample plot (largest, medium-sized, smallest trees and randomly selected trees) and fifteen sample sizes (one to fifteen trees). The prediction accuracy increased with increasing number of trees per sample plot, except the smallest trees, but the largest increase occurred with three largest trees used in calibration. This article emphasized more on modeling methodology, which can be applied to construct CW models for any forest elsewhere including degraded forest in the tropics.