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Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce (Picea mariana (Mill) B.S.P.) and jack pine (Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH. [ABSTRACT FROM AUTHOR]

Taper models are used to estimate the diameter at any height along the bole of a tree. Individual tree volume can then be calculated based on these diameters and corresponding heights. As tree diameters are affected by stand density, inside- and outside-bark taper models that incorporate stand density information were developed for trees in red pine (Pinus resinosa Aiton) plantations. Data used in this study came from stem analysis on 150 red pine trees sampled from 30 even-aged, monospecific plantations across Ontario, Canada. A nonlinear mixed-effects approach was applied in fitting these taper models. Several forms of stand density were evaluated for both inside- and outside-bark diameters. A combination of stand densities expressed as --> BA / TPH --> (BA, basal area; TPH, trees per hectare) explained the most variation in stem taper of trees grown in red pine plantations in Ontario. This variable was highly significant in the regression and improved the predictive accuracies of both inside- and outside-bark taper models. The taper models presented here are dimensionally compatible. Therefore, these models are applicable for data using any system of units without adjusting parameter values. [ABSTRACT FROM AUTHOR]

Ninety-three dominant or co-dominant white pine (Pinus strobus L.) trees were sampled from 93 plots (one tree per plot) in even-aged monospecific plantations at 31 sites (three plots per site) across Ontario, Canada. Stem analysis data collected from these trees were used to develop and evaluate stand height models. The effects of site and climate on site productivity were examined by incorporating site and climate variables into a stand height model. Including climate variables improved the fit statistics of the stand height model for white pine. A covariance structure (AR(1)) was used to address autocorrelation in the data. Similarly, a variance function was used to account for heteroscedasticity. Stand heights were predicted for four areas (middle, easternmost, westernmost, and southernmost parts of Ontario where white pine were sampled) for the period 2021 to 2080 under two emissions trajectories known as representative concentration pathways (RCPs), with each reflecting different levels of heat at the end of the century (i.e., 2.6 and 8.5 W·m–2). At the end of the 2021 to 2080 growth period, projected heights were shorter by 7% for the southern parts and taller by 9.8% for the middle parts of Ontario under both climate change scenarios compared with those under a no change scenario. However, there was no pronounced difference in projected heights under both climate change scenarios and the no change scenario for the other two areas evaluated. The resulting height growth models can be used to estimate stand heights for white pine plantations in a changing climate. Using the same model, the site index of a plot or stand can be estimated by calculating height at a given base (index) age. In the absence of climatic data, the model fitted without climate variables can be used to estimate stand heights and site indices. [ABSTRACT FROM AUTHOR]

To predict the long-term effects of climate change - global warming and changes in precipitation - on the diameter (radial) growth of jack pine ( Pinus banksiana Lamb.) and black spruce ( Picea mariana [ Mill.] B.S.P.) trees in boreal Ontario, we modified an existing diameter growth model to include climate variables. Diameter chronologies of 927 jack pine and 1173 black spruce trees, growing in the area from 47°N to 50°N and 80°W to 92°W, were used to develop diameter growth models in a nonlinear mixed-effects approach. Our results showed that the variables long-term average of mean growing season temperature, precipitation during wettest quarter, and total precipitation during growing season were significant (alpha = 0.05) in explaining variation in diameter growth of the sample trees. Model results indicated that higher temperatures during the growing season would increase the diameter growth of jack pine trees, but decrease that of black spruce trees. More precipitation during the wettest quarter would favor the diameter growth of both species. On the other hand, a wetter growing season, which may decrease radiation inputs, increase nutrient leaching, and reduce the decomposition rate, would reduce the diameter growth of both species. Moreover, our results indicated that future (2041-2070) diameter growth rate may differ from current (1971-2000) growth rates for both species, with conditions being more favorable for jack pine than black spruce trees. Expected future changes in the growth rate of boreal trees need to be considered in forest management decisions. We recommend that knowledge of climate-growth relationships, as represented by models, be combined with learning from adaptive management to reduce the risks and uncertainties associated with forest management decisions. [ABSTRACT FROM AUTHOR]

Accuracy of a taper equation is affected by the quality of calibration data. We evaluated the effects of eight tree selection protocols, originating from two sample sizes and four tree selection criteria (randomly selected trees, trees with diameter at breast height (DBH) closest to quadratic mean diameter, dominant/ co-dominant trees, and trees randomly selected from each class of stratified basal area [BA]), on the accuracy of taper equations by Sharma and Zhang and Kozak by comparing resulting predictions of diameters inside bark and cumulative volumes of tree stems. Evaluations were performed using the data collected via stem analysis from 1098 jack pine (Pinus banksiana Lamb.), and 1122 black spruce (Picea mariana Mill. BSP) trees sampled across the boreal forest of Northern Ontario. About half of the trees were randomly selected for model calibration and the remainder was used for model evaluation. Prediction accuracy, here defined as bias, depended on the tree species, the tree selection protocol including sample size and tree selection criteria, and the model form of the taper equation. A protocol that involved selecting trees from five stratified BA classes (one randomly selected tree from each BA class) was more efficient than other protocols in representing the mean taper function of jack pine and black spruce trees for both taper equations for small sample sizes (five trees per plot). The minimum number of trees required to model taper equations without compromising model accuracy depended on tree species and the model form used to describe tree taper. [ABSTRACT FROM AUTHOR]

The objective of this study was to determine empirically the optimum disk selection protocol when calibrating (1) the dimensional compatible variable-exponent taper equation, (2) the segmented polynomial taper equation, and (3) the modified variable-exponent taper equation, for plantation-grown jack pine (Pinus banksiana Lamb.) trees. Analytically, the full data set, consisting of 187 trees randomly selected within 21 jack pine plantations situated within the Canadian Boreal Forest Region, was randomly subdivided into calibration (parameterization) and validation (performance) subsets of approximately equal size. Based on prediction lack-of-fit indices (positional and tree-level absolute and relative mean biases in inside-bark diameter, cross-sectional area and total stem volume), the results indicated that the performance of the dimensional compatible and segmented equations was approximately equivalent among the 16 protocols evaluated (combinations of four above breast-height percentage-height sampling schemes with four below breast-height fixed-height sampling schemes). Conversely, the modified variable-exponent equation was strongly influenced by disk selection protocol, with the 10% sampling intensity combined with disks selected at 0.15, 0.5, 0.9 and 1.3 m being the most efficient. In summary, the results of this study suggest that the empirically derived modified variable-exponent equation was more data sensitive than the functionally derived dimensional compatible and segmented equations, when calibrated for plantation jack pine trees. [ABSTRACT FROM AUTHOR]

Height-diameter relationships based on stand characteristics (stand density, basal area and site index) were investigated for jack pine and black spruce trees using the data from permanent growth study plots in northern Ontario, Canada. Approximately half of the data was used to estimate model parameters and the rest was used for model evaluation. Multiple Chapman-Richards growth functions with parameters expressed in terms of various stand characteristics were fitted to determine the best models for predicting height. Models providing the most accurate predictors of height included basal area, trees ha -1 and diameter at breast height. The inclusion of site index did not increase predictive accuracy. [ABSTRACT FROM AUTHOR]

Data for modeling forest stand development require repeated, costly measurements over extended periods of time. The purpose of this study was to develop methods for generalizing short-term observations in juvenile stands to long-term trends in more mature stands. The concepts applied involve scale modeling techniques whereby small physical models (model system) provide insight into the nature of important phenomena (prototype system). Loblolly pine plantations in an operational spacing and in a scale that consisted of reducing the distance between plants to 1/16th that of the operational spacing were regarded as prototype and model systems, respectively. Stand development in these two forest systems was examined using principles from similarity theory.In order to apply similarity theory, the temporal development of two commonly measured variables, height and diameter, were standardized on a common scale using data from prototype and model systems. Then, nondimensional height and diameter ratios in the two systems were created using appropriate reference variables from each system. Analysis showed that the height and diameter growth relationships developed similarly for the two systems making growth results from the model system scalable to the prototype system. Scaling functions for forest systems established at small spatial scales could be useful tools for a host of research and developmental purposes. [Copyright &y& Elsevier]

Presents a study that suggested that forestry experimentation in miniature may be a viable tool once basic scaling relationships between operational and miniature scales have been developed. Background on miniature-scale modeling; Primary aspects of scaling problem; Materials and methods; Advantages of experimentation in miniature for evaluating sustainable forestry issues.

Evaluates the effect of spacing rectangularity on tree growth and stand development of loblolly pine plantations. Advantage of rectangular spacings over square spacings; Diameter distributions from the spacings; Calculation of skewness.

At present Nepal's demand for forest products exceeds its production. The Sagarnath Forest Development Project with its 10,000 hectares in sissoo and eucalyptus plantations may fulfill part of the country's requirement of firewood and timber products. To ensure the sustainable management of these plantations, a harvesting plan was developed. Linear programming was applied to obtain optimal harvesting levels. Models for both sissoo and eucalyptus were run with and without nondeclining, and even flow constraints separately. Linear Interactive and Discrete Optimizer (LINDO) was used to run these models. The plan with even flow constraints was found to be the best fulfilling the demands of both timber and fuelwood to some extent and making the harvest financially sustainable. [ABSTRACT FROM PUBLISHER]

Reports on a dimensional analysis approach that was applied to derive analytically consistent tree taper and volume equations. Parameters of the taper and the volume equations that were estimated simultaneously; Data from loblolly pine (Pinus taeda L.) trees grown in natural stands in the Coastal Plain of North Carolina and the Coastal Plain and Piedmont areas of Virginia that were used to estimate the parameters; Dimensionally compatible volume equation that is shown to be a better equation for estimation of the volume of loblolly pine trees grown in these sites and that can be applied for the estimation of total volume; Taper equation that accurately predicts tree diameters from butt to the tree tip.

Competition in forest stands has long been of interest to researchers. However, much of the knowledge originates from empirical studies that examined the effects of competition. For instance, many studies were focused on the effects of the presence of herbaceous species on the development of tree seedlings or the decrease in individual tree growth with increases in stand density. Several models that incorporate competitive effects have been developed to predict tree and stand growth, but with simplified representations of competitive interactions. While these studies provided guidance useful for forest management, they contributed only partially to furthering our understanding of competitive mechanisms. Also, most competition studies were conducted in single-species stands. As competitive interactions occurring in mixed stands are characterized by a higher degree of complexity than those in single-species stands, a better understanding of these mechanisms can contribute to developing optimal management scenarios. The dynamics of forest stands with at least two species may be affected not only by competition, but also by facilitation or complementarity mechanisms. Thus, knowledge of the mechanisms may provide insight into the relative importance of intra- versus inter-specific competition and whether competition is symmetric or asymmetric. Special attention to the implementation of field experimental designs is warranted for mixed stands. While traditional spacing trials are appropriate for single-species stands, the examination of competitive interactions in mixed stands requires more complex experimental designs to examine the relative importance of species combinations. Forest productivity models allow resource managers to test different management scenarios, but again most of these models were developed for single-species stands. As competitive interactions are more complex in mixed stands, models developed to predict their dynamics will need to include more mechanistic representations of competition. [ABSTRACT FROM AUTHOR]