Development of mixed-effects models for predicting early height growth and timber volume of forest tree species planted in Sarawak, Malaysia

Indigenous timber species are the most valuable tree in Malaysian tropical forest nowadays. Modeling of height growth and volume for indigenous timber species has been a challenge to foresters in recent years due to the rapid loss of forest biodiversity. The selection of species for afforestation and reforestation program is one of the most crucial tasks as it affects the growth of such forest and hence the financial viability of such program. The challenges in modeling of multi species stand in tropical forest are the large number of species, small number of individuals per species and almost impossible to develop models for every species in predicting height growth and timber volume. The objective of this study is to develop mixed effect models for predicting early height growth and timber volume of forest tree species planted in Sarawak. This investigation was conducted in the UPM-Mitsubishi Forest Rehabilitation Project area at Universiti Putra Malaysia, Bintulu, Sarawak, Malaysia. The joint research project started in July 1991 between Universiti Putra Malaysia (UPM) and Yokohama National University, Japan on a 47.5 ha forest site at UPM’s Bintulu campus, Sarawak. It is located about 600 kilometres northeast of Kuching and 50 meters above sea level. The joint project was financially sponsored by the Mitsubishi Corporation of Japan. The data used in this investigation were from a permanent growth plot within the project forest area. The project initiated is an excellent example of a highly successful forest rehabilitation project on degraded area. The data came from sapling trees planted in 50m x 5m plot that was established in June 1991. Open planting method was employed in the plot. The planted trees mimic a compact stand of natural forest, equivalent to a Kerangas forest. Several mixed-effects models were developed to represent the total height growth and volume of standing tree pattern of five Malaysian indigenous timber species planted in Sarawak. The result showed that the Linear Mixed-Effects Model (Model 1) with two random effect parameters is the best fitted model for predicting height growth of five indigenous timber species, and the Nonlinear Mixed-Effects Model (Model 2) with two random effect parameters is the best fitted model for predicting standing volume of the five indigenous timber species. Development of mixed-effects models based mainly on its early height and volume performance will help to overcome the species selection process for afforestation and reforestation in improving productive capacity of such forest. Statistical analysis were done using PROC MIXED and NLMIXED procedures in the SAS® 9.2 program. The number of trees used to develop models for each species is: Calophyllum sclerophyllum (73), Dryobalanops beccarii Dyer (84), Shorea mecistopteryx Ridt. (74), Shorea leprosula Miq. (60) and Shorea brunnescens Ashton (72). Based on model comparison and criteria for height models indicates that Linear Mixed-Effects Model (Model 1) has smaller value of AIC (3106.0) and BIC (3104.8) among the other models tested. The goodness-of-fit statistics also indicates Model 1 has the smallest value of RMSE (16.4806), MAE (11.2394) and a highest R2 (0.93396) compare to other models. Based on model comparison and criteria for volume models indicates that Nonlinear Mixed-Effects Model (Model 2) has smallest value of AIC (4165.7) and BIC (4163.3) among other model tested. The goodness-of-fit statistics also indicates Model 2 has the smallest value of RMSE (70.1363), and a highest R2 (0.99059) compare to other models. The models developed in this study can be implemented in prediction of sapling tree only. Based on prediction for height (Model 1), it can be concluded that the early height (cm) growth performance of the five species are in the following order: Shorea brunnescens Ashton (highest), followed by Calophyllum sclerophyllum, Dryobalanops beccarii Dyer, Shorea leprosula Miq., and Shorea mecistopteryx Ridt. (lowest). It indicat that Shorea brunnescens Ashton has the best early height growth among the five species compared. Based on prediction for volume (Model 2), it can be concluded that the volume (cm3) performance of the five species are in the following order: Shorea brunnescens Ashton (highest), follow by Dryobalanops beccarii Dyer, Calophyllum sclerophyllum, Shorea leprosula Miq. And Shorea mecistopteryx Ridt. (lowest). It indicated that Shorea brunnescens Ashton has the best early volume among the five species compared. The results of this study indicated that Shorea brunnescens Ashton has good early height growth and volume performance. Shorea brunnescens Ashton is thus a better species for afforestation and reforestation program. Other most potential species for rehabilitation in terms of early height growth, volume and survival performance is Dryobalanops beccarii Dyer. Based on the development of mixed-effects models in this study, there is also a limitation need to be considered here where the data came from early growth trees or sapling trees (31 months after planted). The models indicate a good result for predicting species performance based on height and volume as a method to select species for afforestation and reforestation program. However application of the models coefficient to predict (e.g. height and volume) other trees from this data need to be caution beyond the range of basal diameter. This model cannot represent trees beyond the range of basal diameter in this study. The models error variances in this study shown non-constant based on Breusch-Pagan test and it indicates that the heteroscedasticity presence in the mixed effect models (height and volume). The heterogeneity of error variance presence due to a different of basal diameter size class of trees. Model transformations were also carried out in this study in order to reduce the error variance heterogeneity for height and volume models using Log transformation. However, the model transformation method didn’t improving the mixed effect models where the models perform not very well with a reduction of R2 and highest value of MAE and RMSE compare to a real mixed effect models without transformation. The nature biological of the data in this study is a key factor affect for models development and efficiency. It indicates that development of models using sapling trees are not appropriate and need to be caution when using this model, especially for development of local height and volume table. Based on the results in this study indicate that there is no need for model transformation and the best fitted of mixed-effects models for height and volume are still adequate mostly for predicting timber species performance in this study based on highest R2 value. The models developed in this study should be used with caution, that is, they provide a good early height and volume prediction within the range of tree diameters and heights of the data to develop the models. Furthermore, verification models were not developed for all five species due to small number of trees within each species.

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