| Summary: | The relative growth rate (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula>) is the standardized measurement of forest growth, whereby excluding the size differences between individuals allows their performance to be compared equally. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> model was developed using the National Forest Inventory (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NFI</mi></mrow></semantics></math></inline-formula>) data on the Daxing’an Mountains, in Northeast China, which contain Dahurian larch (<i>Larix gmelinii</i> Rupr.), white birch (<i>Betula platyphylla</i> Suk.), and mixed coniferous–broadleaf forests. Four predictor variables—i.e., quadratic mean diameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>D</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula>), stand basal area (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>G</mi></semantics></math></inline-formula>), average tree height (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>H</mi><mi>a</mi></msub></mrow></semantics></math></inline-formula>), and altitude (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>A</mi></semantics></math></inline-formula>)—and four different methods—i.e., the nonlinear mixed-effects models (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NLME</mi></mrow></semantics></math></inline-formula>), three nonlinear quantile regression (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>3</mn></mrow></semantics></math></inline-formula>), five nonlinear quantile regression (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>5</mn></mrow></semantics></math></inline-formula>), and nine nonlinear quantile regression (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>9</mn></mrow></semantics></math></inline-formula>) models—were used in this study. All the models were validated using the leave-one-out method. The results showed that (1) the mixed coniferous–broadleaf forest presented the highest <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula>; (2) the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> was negatively correlated with the four predictors, and the heteroscedasticity reduced significantly after the weighting function was integrated into the models; and (3) the quantile regression models performed better than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NLME</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>9</mn></mrow></semantics></math></inline-formula> outperformed both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>3</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>NQR</mi><mn>5</mn></mrow></semantics></math></inline-formula>. To make more accurate predictions, parameters of the adjusted mixed-effects and quantile regression models should be recalculated and localized using sampled <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> in each region and then applied to predict all the other <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>G</mi><msub><mi>R</mi><mrow><mi>n</mi><mi>v</mi></mrow></msub></mrow></semantics></math></inline-formula> of plots. <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mi>A</mi><mi>P</mi><mi>E</mi><mfenced><mo>%</mo></mfenced></mrow></semantics></math></inline-formula> indicates the mean absolute percentage error. The values were stable when the sample numbers were greater than or equal to six across the three forest types, which showed relatively accurate and lowest-cost prediction results.
|
|---|
