Modeling Individual Tree Growth For Dahurian Larch

This article take planted larch forest with different ages, densities and site conditions in Dailing Forest Bureau in Heilongjiang Province as the research object. Based on the stem analysis data of80sample trees from20plots.19growth models was selected to model the height/age, diameter/age and volume/age relationships using non-linear regression in SAS and S-PLUS software. According to fitting statistics, the Richards model was selected as the best growth model to model height/age and diameter/age relationship, the Logistic model was selected as the best growth model to model volume/age relationship.Based on the two modes, mixed-effects models were developed with consideration of individual tree effect and plot effect. We used the evaluation statistics such as AIC, BIC and Log Likelihood to test the prediction precisions of the models, the results showed that Richards model with parameters b1and b3as mixed effects showed the best performance for both height-age relationships and diameter-age relationships. Based on the Logistic model, the random effect models with parameters b1, b2and b3had the best performance when considering individual tree effect, while the models with parameter b1as random parameter had the best performance when considering plot effect. The random effects models provided better model fitting than original model whatever considering individual tree effects and plot effects, Correlation structures including first-order autoregressive correlation structure AR(1), moving averagecorrelation structure MA(1) and autoregressive-moving average correlation structure [ARMA(1,1)] were incorporated into the optimal height and diameter mixed models. AR(1) significantly improved the precision of mixed height model and MA(1) significantly improved the precision of mixed diameter model. The application of the mixed model showed not only the mean trends of height and diameter prediction, but also the individual difference by calibrating random parameters using variance-covariance structure and correlation structure. The volume/age model validation indicated that random effect models not only showed the mean variation trend of individual tree volume growth, but also showed the differences among the individuals. In addition, the prediction precision of the models could be further improved through the calibration of random parameters.