Individual-tree basal area growth models for jack pine and black spruce in northern Ontario - Zhang, Lianjun; Peng, Changhui; Dang, Qinglai (The Forestry Chronicle, 2004)
Individual-tree models of five-year basal area growth were developed for jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana (Mill.) BSP) in northern Ontario. Tree growth data were collected from long-term permanent plots of pure and mixed stands of the two species. The models were fitted using mixed model methods due to correlated remeasurements of tree growth over time. Since the data covered a wide range of stand ages, stand conditions and tree sizes, serious heterogeneous variances existed in the data. Therefore, the coefficients of the final models were obtained using weighted regression techniques. The models for the two species were evaluated across 4-cm diameter classes using independent data. The results indicated (1) the models of jack pine and black spruce produced similar prediction errors and biases for intermediate-sized trees (1228 cm in tree diameter), (2) both models yielded relatively large errors and biases for larger trees (> 28 cm) than those for smaller trees, and (3) the jack pine model produced much larger errors and biases for small-sized trees (< 12 cm) than did the black spruce model. Key words: mixed models, repeated measures, model validation

Developing and Validating Nonlinear Height–Diameter Models for Major Tree Species of Ontario's Boreal Forests - Peng, Changhui; Zhang, Lianjun; Liu, Jinxun (Northern Journal of Applied Forestry, 2001)
Abstract Six commonly used nonlinear growth functions were fitted to individual tree height-diameter data of nine major tree species in Ontario's boreal forests. A total of 22,571 trees was collected from new permanent sample plots across the northeast and northwest of Ontario.The available data for each species were split into two sets: the majority (90%) was used to estimate model parameters, and the remaining data (10%) were reserved to validate the models. The performance of the models was compared and evaluated by model, R2, mean difference, and mean absolute difference. The results showed that these six sigmoidal models were able to capture the height–diameter relationships and fit the data equally well, but produced different asymptote estimates. Sigmoidal models such as Chapman–Richards, Weibull, and Schnute functions provided the most satisfactory height predictions. The effect of model performance on tree volume estimation was also investigated. Tree volumes of different species were computed by Honer's volume equations using a range of diameters and the predicted tree total height from the six models. For trees with diameter less than 55 cm, the six height-diameter models produced very similar results for all species, while more differentiation among the models was observed for large-sized trees (e.g., diameters > 80 cm). North. J. Appl. For. 18:87–94.

Development and evaluation of ecoregion-based jack pine height-diameter models for Ontario - Zhang, Lianjun; Peng, Changhui; Huang, Shongming; Zhou, Xiaolu (The Forestry Chronicle, 2002)
The Chapman-Richards growth function is used to model jack pine (Pinus banksiana Lamb.) tree height-diameter relationships at provincial, regional, and ecoregional levels. The results suggest that the tree height-diameter relationships of jack pine are significantly different among the geographic regions of Ontario, depending on local climatic, soil, and ecological conditions. In light of this study, the provincial and regional height-diameter models are not appropriate for predicting tree heights at the ecoregional level. Further, applying a specific ecoregional model to other ecoregions will also result in significant biases for predicting local tree heights. The ecoregion-based height-diameter models developed in this study may provide more accurate information on tree growth and development to forest resource managers and planners. Key words: Chapman-Richards growth function, permanent sample plot, non-linear extra sum of square method, forest management

Developing and Evaluating Tree Height-Diameter Models at Three Geographic Scales for Black Spruce in Ontario - Peng, Changhui; Zhang, Lianjun; Zhou, Xiaolu; Dang, Qinglai; Huang, Shongming (Northern Journal of Applied Forestry, 2004)
Abstract A total of 11,612 black spruce trees were measured from permanent sample plots across the boreal and central regions of Ontario and were used to fit the well-known Chapman-Richards growth model at provincial, regional, and ecoregional scales. The results suggest that the height-diameter relationships of black spruce vary with different geographic regions and scales. There were significant variations in height-diameter relationships for black spruce between boreal and central regions as well as among some of the seven ecoregions. The ecoregion-based height-diameter models presented here will provide more accurate predictions for tree height and, consequently, tree volume than these models developed at both provincial and regional scales. Furthermore, the heterogeneity of tree species should be considered in developing and applying ecoregion-based height-diameter models for predicting local tree height.