Four variable-exponent taper equations and their modified forms were evaluated for lodgepole pine (Pinus contorta var. latifolia Engelm.) trees in Alberta, Canada. A nonlinear mixed-effects modeling approach was applied to account for within-and between-tree variations in stem form. Even though a direct modeling of within-tree autocorrelation by a variance-covariance structure failed to achieve convergence, most of the autocorrelation was accounted for when random-effects parameters were included in the models. Using an independent data set, the best taper equation with two random-effects parameters was chosen based on its ability to predict diameter inside bark, whole tree volume, and sectioned log volume. Diameter measurements from various stem locations were evaluated for tree-specific calibrations by predicting random-effects parameters using an approximate Bayesian estimator. It was found that an upper stem diameter at 5.3 m above ground was best suited for calibrating treespecific predictions of diameter inside bark, whole tree volume, and sectioned log volume.

A height-diameter mixed-effects model was developed for loblolly pine (Pinus taeda L.) plantations in the southeastern US. Data were obtained from a region-wide thinning study established by the Loblolly Pine Growth and Yield Research Cooperative at Virginia Tech. The height-diameter model was based on an allometric function, which was linearized to include both fixed-and random-effects parameters. A test of regionalspecific fixed-effects parameters indicated that separate equations were needed to estimate total tree heights in the Piedmont and Coastal Plain physiographic regions. The effect of sample size on the ability to estimate random-effects parameters in a new plot was analyzed. For both regions, an increase in the number of sample trees decreased the bias when the equation was applied to independent data. This investigation showed that the use of a calibrated response using one sample tree per plot makes the inclusion of additional predictor variables (e.g., stand density) unnecessary. A numerical example demonstrates the methodology used to predict random effects parameters, and thus, to estimate plot specific height-diameter relationships.

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Based on a multilevel nonlinear mixed model approach, a basal area increment model was developed for individual aspen ( Populus tremuloides Michx.) trees growing in boreal mixedwood stands in Alberta. Various stand and tree characteristics were evaluated for their contributions to model improvement. Total stand basal area, basal area of larger trees, and the ratio of target tree height to maximum stand height were found to be significant predictors. When random effects were modeled at the plot level alone, correlations among normalized residuals remained significant. These correlations were successfully removed when random effects were modeled at both plot and tree levels. The predictive abilities of two alternative models were evaluated at the population, plot, and tree levels. At the tree level, a tree measured at the first growth period was used for estimating random parameters, and basal area increments of that tree in future growth periods were subsequently predicted. At the plot level, one to five trees in each plot at each growth period were used to estimate random parameters. Basal area increments of the remaining trees in the same plot at the same growth period were subsequently predicted. The final model provided accurate predictions at all three levels.