A volume equation for predicting individual tree volume, and a taper function for describing a stem profile were developed for a little known species, Styrax tonkinensis (Siam benzoin) in northern Laos. The species has high potential commercial value and can make an important contribution to the local economy. It can provide two different types of products, a non-wood product (benzoin resin) and timber. In Laos, the most important product is currently resin, and the use of timber for commercial purposes is rare. One reason is that information about the timber is not available. In Vietnam, on the other hand, the species is an import pulpwood species. Data used in this study came from 73 trees. Trees were purposely selected to ensure coverage of a full range of tree sizes. Measurement was undertaken only on over-bark diameters due to some constraints, limitations and problems during the field data collection. However, due to the importance of under-bark volume for this species, a small available dataset was used to build a bark model as an interim guide to the errors associated with using over-bark models for estimating under-bark volumes. From this bark model, errors in estimating under-bark volumes of trees with diameters at breast height between 10cm and 17 cm were approximately 18%. Nineteen individual volume models, and 7 individual taper functions were compared for bias and precision. Collective names for the volume equations tested include single-entry, double-entry, logarithmic, combined variables. Most volume models had similar bias but a few were clearly biased. The models with similar bias were further evaluated by four common statistics including bias, standard error of estimates, standard deviation of residuals and mean absolute deviation. The results showed that a five parameter model was ranked first, and was the most precise model. However, the magnitudes of difference in prediction errors between this model and other models, particularly the three parameter model were not significant. For practical purposes, the simpler model was preferred. Seven taper functions tested here belong to three different groups including single taper equations, compatible taper equations and segmented taper equations. Evaluation of taper equations used the same residual analysis procedures and criteria as those applied with volume equations. Graphical residual analysis showed that most taper models had similar precision with their errors in diameter predictions being similar in range. However, some models showed obvious bias. The most highly ranked taper model was a compatible taper model of polynomial form. It was the least biased model. The second ranked model was a single, simple model. This latter model is relatively simple to apply, but it is not compatible with the volume model, yielding slightly different estimates of volume if it is integrated and rotated around the longitudinal axis of a tree. However, if the sole purpose is to describe tree taper, it is the best model to use.

<p>Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process.</p><p>A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model.</p><p>In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile.</p><p>Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model.</p>

Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process. A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data and compared several models with and without covariance structures. For simplicity and clarity of the nonlinear mixed effects modeling, four phases of modeling were introduced. The nonlinear mixed effects model for C. lustanica tree merchantable volume with the covariance structures for both the random effects and within group errors has shown a significant improvement over the model with simplified covariance matrix. However, this statistical significance has little to explain in the prediction performance of the model. In Paper III, using several performance indicator statistics, tree taper models were compared in an effort to propose the best model for the forest management and planning purpose of the C. lustanica plantations. Kozak's (1988) tree taper model was found to be the best for estimating C. lustanica taper profile. Based on the Kozak (1988) tree taper model, a Ds optimal experimental design study is carried out in Paper IV. In this study, a Ds-optimal (sub) replication free design is suggested for the Kozak (1988) tree taper model.