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Multilevel Nonlinear Mixed-Effect Crown Ratio Models for Individual Trees of Mongolian Oak (Quercus mongolica) in Northeast China.

Fu L, Zhang H, Lu J, Zang H, Lou M, Wang G - PLoS ONE (2015)

Bottom Line: Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors.When random effects were modeled at block level alone, the correlations among the residuals remained significant.These correlations were successfully reduced when random effects were modeled at both block and plot levels.

View Article: PubMed Central - PubMed

Affiliation: Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing, 100091, P. R. of China.

ABSTRACT
In this study, an individual tree crown ratio (CR) model was developed with a data set from a total of 3134 Mongolian oak (Quercus mongolica) trees within 112 sample plots allocated in Wangqing Forest Bureau of northeast China. Because of high correlation among the observations taken from the same sampling plots, the random effects at levels of both blocks defined as stands that have different site conditions and plots were taken into account to develop a nested two-level nonlinear mixed-effect model. Various stand and tree characteristics were assessed to explore their contributions to improvement of model prediction. Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors. Exponential model with plot dominant tree height as a predictor had a stronger ability to account for the heteroskedasticity. When random effects were modeled at block level alone, the correlations among the residuals remained significant. These correlations were successfully reduced when random effects were modeled at both block and plot levels. The random effects from the interaction of blocks and sample plots on tree CR were substantially large. The model that took into account both the block effect and the interaction of blocks and sample plots had higher prediction accuracy than the one with the block effect and population average considered alone. Introducing stand density into the model through dummy variables could further improve its prediction. This implied that the developed method for developing tree CR models of Mongolian oak is promising and can be applied to similar studies for other tree species.

No MeSH data available.


Related in: MedlinePlus

Residuals of predicted crown ratio values from Eq (17) for each of five stand density classes graphed against the predicted values for Mongolian oak in Wangqing Forest Bureau of northeast China.
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pone.0133294.g004: Residuals of predicted crown ratio values from Eq (17) for each of five stand density classes graphed against the predicted values for Mongolian oak in Wangqing Forest Bureau of northeast China.

Mentions: The estimates of model parameters for Eq (17) were listed in Table 6 and its statistics of performance to predict tree CR were shown in Table 7. In both tables, Eq (17) was compared with Eqs (13)–(15) based on the values of the performance statistics. The results showed that compared to Eqs (15) and (17) decreased the value of AIC by 3.51% and increased the value of Loglik by 3.57% (Table 6). Eq (17) also increased the coefficient of determination by 167.31%, 7.36%, and 6.09% compared to those from Eqs (13), (14) and (15), respectively. Based on the results from the validation data, Eq (17) led to a root mean square error of 0.0653, decreasing by 61.99%, 42.92%, and 38.05% compared to those from Eqs (13), (14) and (15). The residuals from Eq (17) were graphed against the predicted values of tree CR for five stand density classes (Fig 4). The results implied that if the stand density of each sample plot was known, Eq (17) in which stand density class was introduced through dummy variables can result in further improvement of predictions.


Multilevel Nonlinear Mixed-Effect Crown Ratio Models for Individual Trees of Mongolian Oak (Quercus mongolica) in Northeast China.

Fu L, Zhang H, Lu J, Zang H, Lou M, Wang G - PLoS ONE (2015)

Residuals of predicted crown ratio values from Eq (17) for each of five stand density classes graphed against the predicted values for Mongolian oak in Wangqing Forest Bureau of northeast China.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4524704&req=5

pone.0133294.g004: Residuals of predicted crown ratio values from Eq (17) for each of five stand density classes graphed against the predicted values for Mongolian oak in Wangqing Forest Bureau of northeast China.
Mentions: The estimates of model parameters for Eq (17) were listed in Table 6 and its statistics of performance to predict tree CR were shown in Table 7. In both tables, Eq (17) was compared with Eqs (13)–(15) based on the values of the performance statistics. The results showed that compared to Eqs (15) and (17) decreased the value of AIC by 3.51% and increased the value of Loglik by 3.57% (Table 6). Eq (17) also increased the coefficient of determination by 167.31%, 7.36%, and 6.09% compared to those from Eqs (13), (14) and (15), respectively. Based on the results from the validation data, Eq (17) led to a root mean square error of 0.0653, decreasing by 61.99%, 42.92%, and 38.05% compared to those from Eqs (13), (14) and (15). The residuals from Eq (17) were graphed against the predicted values of tree CR for five stand density classes (Fig 4). The results implied that if the stand density of each sample plot was known, Eq (17) in which stand density class was introduced through dummy variables can result in further improvement of predictions.

Bottom Line: Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors.When random effects were modeled at block level alone, the correlations among the residuals remained significant.These correlations were successfully reduced when random effects were modeled at both block and plot levels.

View Article: PubMed Central - PubMed

Affiliation: Research Institute of Forest Resource Information Techniques, Chinese Academy of Forestry, Beijing, 100091, P. R. of China.

ABSTRACT
In this study, an individual tree crown ratio (CR) model was developed with a data set from a total of 3134 Mongolian oak (Quercus mongolica) trees within 112 sample plots allocated in Wangqing Forest Bureau of northeast China. Because of high correlation among the observations taken from the same sampling plots, the random effects at levels of both blocks defined as stands that have different site conditions and plots were taken into account to develop a nested two-level nonlinear mixed-effect model. Various stand and tree characteristics were assessed to explore their contributions to improvement of model prediction. Diameter at breast height, plot dominant tree height and plot dominant tree diameter were found to be significant predictors. Exponential model with plot dominant tree height as a predictor had a stronger ability to account for the heteroskedasticity. When random effects were modeled at block level alone, the correlations among the residuals remained significant. These correlations were successfully reduced when random effects were modeled at both block and plot levels. The random effects from the interaction of blocks and sample plots on tree CR were substantially large. The model that took into account both the block effect and the interaction of blocks and sample plots had higher prediction accuracy than the one with the block effect and population average considered alone. Introducing stand density into the model through dummy variables could further improve its prediction. This implied that the developed method for developing tree CR models of Mongolian oak is promising and can be applied to similar studies for other tree species.

No MeSH data available.


Related in: MedlinePlus