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Diameter at breast height (DBH) is a unique attribute used to characterize forest growth and development for forest management planning and to understand forest ecology. Forest managers require an array of DBHs of forest stands, which can be reconstructed using selected probability distribution functions (PDFs). However, there is a lack of practices that fit PDFs of sub-dominating species grown in natural mixed forests. This study aimed to fit PDFs and develop predictive models for PDF parameters, so that the predicted distribution would represent dynamic forest structures and compositions in mixed forest stands. We fitted three of the simplest forms of PDFs, log-normal, gamma, and Weibull, for the DBH of eight tree species, namely balsam fir (Abies balsamea [L.] Mill.), eastern white pine (Pinus strobus L.), paper birch (Betula papyrifera Marshall), red maple (Acer rubrum L.), red pine (Pinus resinosa Aiton), sugar maple (Acer saccharum Marshall), trembling aspen (Populus tremuloides Michx), and white spruce (Picea glauca [Moench] Voss), all grown in natural-origin mixed forests in Ontario province, Canada. We estimated the parameters of the PDFs as a function of DBH mean and standard deviation for these species. Our results showed that log-normal fit the best among the three PDFs. We demonstrated that the predictive model could estimate the recovered parameters unbiasedly for all species, which can be used to reconstruct the DBH distributions of these tree species. In addition to prediction, the cross-validated R2 for the DBH mean ranged between 0.76 for red maple and 0.92 for red pine. However, the R2 for the regression of the standard deviation ranged between 0.00 for red pine and 0.69 for sugar maple, although it produced unbiased predictions and a small mean absolute bias. As these mean and standard deviations are regressed with dynamic covariates (such as stem density and stand basal area), in addition to climate and static geographic variables, the predicted DBH distribution can reflect change over time in response to management or any type of disturbance in the regime of the given geography. The predictive model-based DBH distributions can be applied to the design of appropriate silviculture systems for forest management planning. [ABSTRACT FROM AUTHOR]

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]

Global change in the climate is affecting tree/forest growth. There have been many studies that analyzed climate effects on tree growth. Results presented in these studies showed that the climate had both positive and negative effects on tree growth. The nature (positive/negative) and magnitude of the effects and the climate variables affecting growth depended on tree species. Climate-sensitive diameter growth models are not available for white pine (Pinus strobus L.) and white spruce (Picea glauca (Moench) Voss) plantations. These models are needed to project forest growth and yield and develop forest management plans. Therefore, diameter growth models were developed for white pine and white spruce plantations by incorporating climate variables. Four hundred white pine and white spruce trees (200 per species) were sampled from 80 (40 per species) even-aged monospecific plantations (five trees per plantation) across Ontario, Canada. Diameter–age pairs were obtained from these trees using stem analysis. A nonlinear mixed-effects modeling approach was used to develop diameter growth models. To make the models climate sensitive, model parameters were expressed in term of climate variables. Inclusion of climate variables significantly improved model fit statistics and predictive accuracy. For evaluation, diameters (inside bark) at breast height were estimated for three geographic locations (east, west, and south) across Ontario for an 80-year growth period (2021–2100) under three climate change (emissions) scenarios (representative concentration pathway or RCP 2.6, 4.5, and 8.5 watts m−2). For both species, the overall climate effects were negative. For white spruce, the maximum pronounced difference in projected diameters after the 80-year growth period was in the west. At this location, compared to the no climate change scenario, projected spruce diameters under RCPs 2.6 and 8.5 were thinner by 4.64 (15.99%) and 3.72 (12.80%) cm, respectively. For white pine, the maximum difference was in the south. Compared to the no climate change scenario, projected pine diameters at age 80 under RCPs 2.6 and 8.5 at this location were narrower by 4.54 (13.99%) and 7.60 (23.43%) cm, respectively. For both species, climate effects on diameter growth were less evident at other locations. If the values of climate variables are unavailable, models fitted without climate variables can be used to estimate these diameters for both species. [ABSTRACT FROM AUTHOR]

Site index (SI) is a commonly used measure of forest site productivity and is affected by climate change. Therefore, climate effects on site productivity were analyzed and modeled for jack pine (Pinus banksiana Lamb.), black spruce (Picea mariana (Mill.) B.S.P.), red pine (Pinus resinosa Ait.), and white spruce (Picea glauca (Moench) Voss) plantations using annual/seasonal values of climate variables. Jack pine and black spruce trees were each sampled from 25 plantations (sites), and red pine and white spruce trees were sampled from 30 and 31 plantations, respectively, from across Ontario, Canada. Stem analysis data collected from 201 jack pine, 211 black spruce, 90 red pine, and 93 white spruce trees were used in this study. To analyze and model climatic effects on site productivity, parameters of the stand height models were expressed in terms of climate variables. A nonlinear mixed-effects modelling approach was applied to fit the stand height models. Climate effects on site productivity was evaluated by predicting stand heights in three areas (the central, eastern/southeastern, and western parts of Ontario) for the period 2021 to 2080 under three emissions trajectories (representative concentration pathways (RCP) 2.6, 4.5, and 8.5 watts m−2). Climate effects on site productivity depended on tree species and location. For jack pine, climate effects were positive and pronounced only in western Ontario under all emissions scenarios. The effects were negative and mild after breast height age (BHA) 50 in central Ontario for black spruce. Similarly, the effects were negative and more pronounced at all areas after BHA 35 for red pine. On the other hand, for white spruce the effects were negative and highly pronounced from a young age under all scenarios, mainly in the southeast. For all species except for jack pine, climate effects were more pronounced under RCP 8.5 than the other two scenarios. [ABSTRACT FROM AUTHOR]

Forest managers need site productivity estimates for tree species growing in mixed stands. Models developed in the past are generally for pure stands and don't factor in the effects of climate change on site productivity. Therefore, site index (SI) models were developed for black spruce (Picea mariana Mill. B.S.P.) and trembling aspen (Populus tremuloides Michx.) trees grown in natural origin mixed stands. For this, 186 trees (93 black spruce and trembling aspen each) were sampled from 31 even-aged natural mixed stands (sites) (3 trees/species/site) across Ontario, Canada. Stand height growth models were developed by incorporating climate variables during growth for each species. Stem analysis data collected from sampled trees were used to develop these models. A mixed effects modelling approach was used to fit the models. The relationship between SIs of black spruce and trembling aspen grown in mixed stands was analyzed by calculating correlation coefficients and plotting black spruce SIs against those of trembling aspen. Climate effects on site productivity were evaluated by predicting stand heights for 4 geographic areas of Ontario for the period 2021 to 2080. Three emissions scenarios reflecting different amounts of heat at the end of the century (i.e., 2.6, 4.5, and 8.5 watts m−2) were used in the stand height growth models developed here for evaluation. Climate effects were more pronounced for trembling aspen than black spruce only in the far west. The relationship between SIs of black spruce and trembling aspen trees grown in natural origin mixed stands could not be described using a linear/nonlinear mathematical function. The models developed here can be used to estimate stand height and SI of black spruce and trembling aspen trees grown in natural origin mixed stands in a changing climate. In the absence of climate data, models fitted without climate variables can be used to estimate SI of both species. [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]

Six height-age determination methods (Graves, Lenhart, Carmean, Newberry, ratio, and ISSA) were evaluated for their accuracy and sensitivity to sample size in determining height-age pairs using stem analysis data from plantation-grown black spruce (Picea mariana [Mill.] B.S.P.) and jack pine (Pinus banksiana Lamb.) trees from Ontario, Canada. Twenty-three disks (sections) were used from 102 jack pine and 93 black spruce trees each for evaluation. The Graves, ratio, and Newberry methods were unbiased for determining height-age pairs for both black spruce and jack pine across the site productivity gradient and different crown classes. However, on the basis of the magnitude of height prediction bias, reconstructed tree profiles, and the amount of information required for height-age determination, the Graves method with at least 13 stem sections is recommended for height-age determination. [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]

We assessed 27 indicators of plant diversity, stand yield and individual crop tree responses 25 years post-treatment to determine long-term trade-offs among conifer release treatments in boreal and sub-boreal forests. This research addresses the lack of longer-term data needed by forest managers to implement more integrated vegetation management programs, supporting more informed decisions about release treatment choice. Four treatments (untreated control, motor-manual brushsaw, single aerial spray, and complete competition removal) were established at two jack pine (Pinus banksiana Lamb.) sites in Ontario, Canada. Our results suggest that plant diversity and productivity in boreal jack pine forests are significantly influenced by vegetation management treatments. Overall, release treatments did not cause a loss of diversity but benefitted stand-scale yield and individual crop tree growth, with maximum benefits occurring in more intensive release treatments. However, none of the treatments maximized all 27 indicators studied; thus, forest managers are faced with trade-offs when choosing treatments. Research on longer term effects, ideally through at least one rotation, is essential to fully understand outcomes of different vegetation management on forest diversity, stand yield, and individual crop tree responses. [ABSTRACT FROM AUTHOR]

Sustainable forest management requires accurate estimates of wood volume. At present, red pine (Pinus resinosa Sol. ex Aiton) is the most widely planted conifer tree species in southern Ontario, Canada. Therefore, inside and outside bark volume equations were developed for red pine trees grown in plantations. One hundred and fifty red pine trees were sampled from 30 even-aged plantations from across Ontario, Canada. Height-diameter pairs along the boles of sampled trees used to calculate stem volumes were obtained from stem analysis. Equations fitted to the data were a combined variable, modified combined variable, and modified form of dimensionally compatible volume equations. These equations were compared for their goodness-of-fit statistics, logical consistency, and predictive accuracy. The goodness-of-fit characteristics for all three equations were comparable for both inside and outside bark volumes. However, the estimated values for the intercept for the modified form of the dimensionally compatible and modified combined variable volume equations were negative and nonsignificant. The combined variable volume equation resulted in logically consistent parameter estimates in the presence of random effects parameters. Therefore, this equation was selected as the inside and outside bark volume equation for red pine trees grown in plantations. A nonlinear mixed-effects modeling approach was applied in fitting the final volume equation that included a weight (power function) to address heteroscedasticity. The equations developed here can be used to calculate inside and outside bark volumes of red pine plantations in boreal forests in Eastern Canada. These equations would require both diameter at breast height (DBH) and total height values in meters. [ABSTRACT FROM AUTHOR]