Individual-tree Diameter Growth Model Research Articles

Modelling Individual Tree Diameter Growth of Quercus mongolica Secondary Forest in the Northeast of China

Quercus mongolica secondary forest is widely distributed in the northeast of China, but it usually has low productivity, unstable structure, poor health, and low biodiversity. Diameter is a tree variable that is commonly used for forest growth measurement, to provide the basis for forest management decision. Two level generalized linear mixed effects individual tree diameter growth model were developed using data from two times surveys of 12 Q. mongolica secondary forest permanent plots that were distributed among Wangqing forest farms. Random effects of 14 tree species and 12 plots were introduced into the basic model consisting of three factors: tree size, competition of surrounding trees, and site quality. The results showed that initial diameter at breast height(DBH) was the most important variable affecting diameter growth, followed by competition, while the effect of site quality on diameter growth was not significant. Compared with the basic model, the prediction accuracy of the mixed effect model was improved by 17.69 %, where R2 reached to 0.6805, indicating that it is suitable for the individual-tree diameter growth prediction of the secondary forest of Q. mongolica.

Development of individual tree growth and yield model across multiple contrasting species using nonparametric and parametric methods in the Hyrcanian forests of northern Iran

The Hyrcanian forests of Iran contain many species-rich communities that can only be maintained through an understanding of the renewal and development of these forests. Located in the Jojadeh section of the Farim forest in northern Iran, individual tree growth of five distinct species [(Oriental beech (Fagus orientalis Lipsky), chestnut-leaved oak (Quercus castaneifolia Coss. ex J.Gay), Persian maple (Acer velutinum Boiss.), common hornbeam (Carpinus betulus L.) and Caucasian alder (Alnus subcordata C.A.Mey.)] were measured on 313 permanent sample plots (0.1 ha) over a 10-year period (2003–2013). In this analysis, various tree-level predictions were investigated using the available data with application of parametric models and two artificial neural networks [i.e., the multilayer perceptron (MLP) and radial basis function (RBF) networks]. Individual tree diameter growth models showed a robust negative relationship with basal area in larger trees, which was relatively consistent across species. A total height model indicated that the examined species did not differ for a given set of covariates. In the survival model, the survival probability of Oriental beech was lower than the other species, while the ingrowth model revealed sapling density of all species increased with greater basal area. The artificial neural network based on the MLP was superior for all models and predicted more accurately than the RBF. Furthermore, the models based on the MLP were also superior to the parametric individual tree models developed using mixed-effect regression. The use of these developed models in forest planning and management is imperative, particularly for uneven-aged stands, but assessment of long-term projection behavior across the contrasting statistical approaches used is warranted despite the general superiority of the nonparametric models.

Individual-tree diameter growth model for Korean pine plantations based on optimized interpolation of meteorological variables

To explore the influence of meteorological variables on the growth of Korean pine (Pinus koraiensis Sieb. et Zucc.) plantations and provide a scientific reference for the production and management of Korean pine, three approaches to interpolate meteorological variables during the growing season (i.e., May–September) were compared in Heilongjiang Province, China. Optimized meteorological variable interpolation results were then combined with stand and individual tree variables, based on data from 56 sample plots and 2886 sample trees from Korean pine plantations in two regions of the province to develop an individual-tree diameter growth model (Model I) and an individual-tree diameter growth model with meteorological variables (Model II) using a stepwise regression method. Moreover, an individual-tree diameter growth model with regional effects (Model III) was developed using dummy variables in the regression, and the significance of introducing these dummy variables was verified with an F-test statistical analysis. The models were validated using an independent data set, and the predictive performance of the three models was assessed via the adjusted coefficient of determination ( $${R}_{a}^{2}$$ ) and root mean square error (RMSE). The results suggest that the growth increment in tree diameter of Korean pine plantations was significantly correlated with the natural logarithm of initial diameter (ln D), stand basal area (BAS), logarithmic deformation of the stand density index (ln SDI), ratio of basal area of trees larger than the subject tree to their initial diameter at breast height (DBH) (BAL/D), and the maximum growing-season precipitation (Pgmax). The individual-tree diameter growth models of Korean pine plantations developed in this study will provide a good basis for estimating and predicting growth increments of Korean pine forests over larger areas.

Individual Tree Diameter Growth Models of Larch–Spruce–Fir Mixed Forests Based on Machine Learning Algorithms

Individual tree growth models are flexible and commonly used to represent growth dynamics for heterogeneous and structurally complex uneven-aged stands. Besides traditional statistical models, the rapid development of nonparametric and nonlinear machine learning methods, such as random forest (RF), boosted regression tree (BRT), cubist (Cubist) and multivariate adaptive regression splines (MARS), provides a new way for predicting individual tree growth. However, the application of these approaches to individual tree growth modelling is still limited and short of a comparison of their performance. The objectives of this study were to compare and evaluate the performance of the RF, BRT, Cubist and MARS models for modelling the individual tree diameter growth based on tree size, competition, site condition and climate factors for larch–spruce–fir mixed forests in northeast China. Totally, 16,619 observations from long-term sample plots were used. Based on tenfold cross-validation, we found that the RF, BRT and Cubist models had a distinct advantage over the MARS model in predicting individual tree diameter growth. The Cubist model ranked the highest in terms of model performance (RMSEcv [0.1351 cm], MAEcv [0.0972 cm] and R2cv [0.5734]), followed by BRT and RF models, whereas the MARS ranked the lowest (RMSEcv [0.1462 cm], MAEcv [0.1086 cm] and R2cv [0.4993]). Relative importance of predictors determined from the RF and BRT models demonstrated that the competition and tree size were the main drivers to diameter growth, and climate had limited capacity in explaining the variation in tree diameter growth at local scale. In general, the RF, BRT and Cubist models are effective and powerful modelling methods for predicting the individual tree diameter growth.

Models for diameter and height growth of Scots pine, Norway spruce and pubescent birch in drained peatland sites in Finland

The aim of this study was to develop individual-tree diameter and height growth models for Scots pine, Norway spruce, and pubescent birch growing in drained peatlands in Finland. Trees growing in peatland sites have growth patterns that deviate from that of trees growing in mineral soil sites. Five-year growth was explained by tree diameter, different tree and stand level competition measures, management operations and site characteristics. The drainage status of the site was influencing growth directly or in interaction with other variables. Site quality had a direct impact but was also commonly related to current site drainage status (need for ditch maintenance). Recent thinning increased growth of all species and former PK fertilization increased growth of pine and birch. Temperature sum was a significant predictor in all models and altitude for spruce and birch. The data were a subsample of the 7th National Forest Inventory (NFI) sample plots representing northern and southern Finland and followed by repeated measurements for 15–20 yrs. Growth levels predicted by the models were calibrated using NFI11 data to remove bias originating from the sample of the modelling data. The mixed linear models technique was used in model estimation. The models will be incorporated into the MOTTI stand simulator to replace the current peatlands growth models.

Individual-Tree Diameter Growth Models for Mixed Nothofagus Second Growth Forests in Southern Chile

Second growth forests of Nothofagus obliqua (roble), N. alpina (raulí), and N. dombeyi (coihue), known locally as RORACO, are among the most important native mixed forests in Chile. To improve the sustainable management of these forests, managers need adequate information and models regarding not only existing forest conditions, but their future states with varying alternative silvicultural activities. In this study, an individual-tree diameter growth model was developed for the full geographical distribution of the RORACO forest type. This was achieved by fitting a complete model by comparing two variable selection procedures: cross-validation (CV), and least absolute shrinkage and selection operator (LASSO) regression. A small set of predictors successfully explained a large portion of the annual increment in diameter at breast height (DBH) growth, particularly variables associated with competition at both the tree- and stand-level. Goodness-of-fit statistics for this final model showed an empirical coefficient of correlation (R2emp) of 0.56, relative root mean square error of 44.49% and relative bias of −1.96% for annual DBH growth predictions, and R2emp of 0.98 and 0.97 for DBH projection at 6 and 12 years, respectively. This model constitutes a simple and useful tool to support management plans for these forest ecosystems.

Individual tree diameter increment model for natural Betula platyphylla forests based on meteorological factors

Based on the 212 re-measured permanent plots for natural Betula platyphylla fore-sts in Daxing'an Mountains and Xiaoxing'an Mountains and 30 meteorological stations data, an individual tree growth model based on meteorological factors was constructed. The differences of stand and meteorological factors between Daxing'an Mountains and Xiaoxing'an Mountains were analyzed and the diameter increment model including the regional effects was developed by dummy variable approach. The results showed that the minimum temperature (Tg min) and mean precipitation (Pg m) in growing season were the main meteorological factors which affected the diameter increment in the two study areas. Tg min and Pg m were positively correlated with the diameter increment, but the influence strength of Tg min was obviously different between the two research areas. The adjusted coefficient of determination (Ra2) of the diameter increment model with meteorological factors was 0.56 and had an 11% increase compared to the one without meteorological factors. It was concluded that meteorological factors could well explain the diameter increment of B. platyphylla. Ra2 of the model with regional effects was 0.59, and increased by 18% compared to the one without regional effects, and effectively solved the incompatible problem of parameters between the two research areas. The validation results showed that the individual tree diameter growth model with regional effect had the best prediction accuracy in estimating the diameter increment of B. platyphylla. The mean error, mean absolute error, mean error percent and mean prediction error percent were 0.0086, 0.4476, 5.8% and 20.0%, respectively. Overall, dummy variable model of individual tree diameter increment based on meteorological factors could well describe the diameter increment process of natural B. platyphylla in Daxing'an Mountains and Xiaoxing'an Mountains.

Modelling individual tree diameter growth for Norway spruce in the Czech Republic using a generalized algebraic difference approach

Individual tree-based growth models precisely describe the growth of individual trees irrespective of stand complexity. These models are more useful than the stand-based growth models for effective management of forests. We developed an individual tree diameter growth model for Norway spruce (Picea abies /Linnaeus/ H. Karsten) using permanent research plot data collected from Krkonoše National Park in the Czech Republic. The model was tested against a part of the Czech National Forest Inventory (NFI) data that originated from the western region of the country. Among various models derived by a generalized algebraic difference approach (GADA), the GADA model derived from the Chapman-Richards function best suited to our data. Tree-specific parameters unique to each growth series, which describe tree-specific growth conditions, were estimated simultaneously with global parameters common to all growth series using the iterative nested regressions. The model described most of the variations in diameter growth for model calibration data (R<sup>2</sup><sub>adj</sub> = 0.9901, RMSE = 0.5962), leaving no significant trends in the residuals. A test against NFI data also confirms that the model is precise enough for predictions of diameter growth for ranges of site quality, tree size, age, and growth condition. The model also possesses biologically desirable properties because it produces the curves with growth rates and asymptotes that increase with increasing site quality. The GADA model is path-invariant and therefore applicable for both forward and backward predictions, meaning that the model can precisely predict diameter growth at any past ages of the trees.

Examining growth relationships in Quercus stands: An application of individual-tree models developed from long-term thinning experiments

This manuscript seeks to further the understanding of growth patterns in Quercus forests, thereby informing the development of appropriate thinning practice. The author leveraged a network of thinning experiments established by the US Forest Service more than 50years ago. Individual-tree diameter growth and survival models were developed along with a simulation framework to evaluate the relationship between stand stocking and 20-year basal area and volume growth. Models predicting five-year diameter growth and survival of individual trees included variables representing tree size, competitive position, stand density, and/or site quality. Model evaluation focused on the collective accuracy and cumulative error propagation of the individual-tree models through four, five-year growth cycles. Through a series of stand density simulations in white oak (Quercus alba L.) dominated forest structures representing four mid-rotation age conditions, it was found that stand basal area and total volume growth followed a unimodal pattern culminating at 50–60% stocking. Sawtimber volume growth was more sensitive to initial stand age, and the stocking level where it peaked increased with increasing age. The study not only helps to define relationships for Quercus stands of the Central Hardwood Forest Region, USA, but it also adds to the limited body of research quantifying individual-tree and stand growth relationships within mixed species broadleaf forest types.

Nonlinear Simultaneous Equations for Individual-Tree Diameter Growth and Mortality Model of Natural Mongolian Oak Forests in Northeast China

A nonlinear equation system for individual tree diameter growth and mortality of natural Mongolian oak forests was developed based on 13,360 observations from 195 permanent sample plots in Northeast China. Weighted regression was used in a distance-independent diameter growth equation for dealing with heterocedasticity. Since diameter growth and mortality models have common predictors including the diameter at breast height (DBH), stand basal area (BA), basal-area-in-larger trees (BAL), and site index (SI), parameters were estimated using nonlinear three-stage least squares (N3SLS) and seemingly unrelated regression (SUR) which accounts for correlations of errors across models. The system equation provided better projection than individual fitting of the equation based on maximum likelihood estimation. Compared with the separate tree growth model, the simultaneous equations using N3SLS and SUR produced more efficient parameter estimation and smaller bias. Furthermore, N3SLS had more accurate projection. Overall, the simultaneous model will facilitate the growth and yield projection for better management of Mongolian oak forests in the region.

Nonlinear mixed-effects (NLME) diameter growth models for individual China-Fir (Cunninghamia lanceolata) trees in Southeast China.

An individual-tree diameter growth model was developed for Cunninghamia lanceolata in Fujian province, southeast China. Data were obtained from 72 plantation-grown China-fir trees in 24 single-species plots. Ordinary non-linear least squares regression was used to choose the best base model from among 5 theoretical growth equations; selection criteria were the smallest absolute mean residual and root mean square error and the largest adjusted coefficient of determination. To account for autocorrelation in the repeated-measures data, we developed one-level and nested two-level nonlinear mixed-effects (NLME) models, constructed on the selected base model; the NLME models incorporated random effects of the tree and plot. The best random-effects combinations for the NLME models were identified by Akaike's information criterion, Bayesian information criterion and −2 logarithm likelihood. Heteroscedasticity was reduced with two residual variance functions, a power function and an exponential function. The autocorrelation was addressed with three residual autocorrelation structures: a first-order autoregressive structure [AR(1)], a combination of first-order autoregressive and moving average structures [ARMA(1,1)] and a compound symmetry structure (CS). The one-level (tree) NLME model performed best. Independent validation data were used to test the performance of the models and to demonstrate the advantage of calibrating the NLME models.

Individual-tree diameter growth model for fir plantations based on multi-level linear mixed effects models across southeast China

An individual-tree diameter increment model is developed for fir plantations using a multi-level linear mixed effect model approach. The dataset came from National Forest Inventory plots. Stochastic variability is broken down among sites, blocks, plots, and within-tree components to account for repeated measurements and the hierarchical structure imposed by the sampling scheme. In addition, within-tree heteroscedasticity and correlation were taken into account. The dataset consisted of 583 plots, 62,831 trees, and 251,324 observations. The dataset was randomly split into ten parts and 80 % was used for initial model development while 20 % was used for model validation. Statistically significant predictors were total number of stems per hectare, the natural logarithm of initial diameter, basal area of trees larger than the subject tree, elevation, and thinning intensity. Both the fitting model and the validation dataset showed a substantial improvement compared with the classical approach widely used in forest management. The model was developed using autoregressive moving average [ARMA(1,1)] and constpower function covariance structures, and it performed better than the model developed using only random-intercept effects.

Liana community ecology and interaction with Parapiptadenia rigida (Bentham) Brenan in a fragment of secondary forest

The development of effective silvicultural prescriptions for Atlantic forest secondary patches could offset the amount of exploitative logging in Amazonian forests. This study described the diameter growth response of Parapiptadenia rigida (Fabaceae), a dense wooded, fast-growing canopy tree, to liana competition in attempt to determine silvicultural prescriptions for this species in natural forests. Field procedures were carried out in one fragment of natural forest, in which one hundred 0.01ha plots and 50 individual trees of the target species were selected. We found 23 species in the liana community, which was strongly dominated by Senegalia tucumanensis (Fabaceae). P. rigida had more lianas infesting it compared to the overall forest and its presence increased the abundance of S. tucumanensis. Trees with more than 50% of the crown occupied by lianas had a lower height:diameter ratio. Liana below-ground competition, measured by liana basal area around target trees, reduced diameter increment in P. rigida. The studied species showed great potential for timber production due to fast growth, wood quality and carbon sequestration. The developed individual tree diameter growth model shows that silvicultural treatments could increase diameter growth to about 1.5cm/year.

Prediction of annual tree growth and survival for thinned and unthinned even-aged maritime pine stands in Portugal from data with different time measurement intervals

An annual individual tree survival and growth model was developed for pure even-aged stands of maritime pine in Portugal, using a large data set containing irregularly time-spaced measurements and considering thinning effects. The model is distance-independent and is based on a function for diameter growth, a function for height growth and a survival function. Two approaches are compared for modeling annual tree growth. The first approach directly estimates a future diameter or height using well-known growth functions formulated in difference form. The second approach estimates diameter or height using a function in differential form estimating the increment over a year period. In both approaches, the function parameters were related to tree and stand variables reflecting the competition status of the tree as well as of a thinning response factor. Variable growth and survival rates were assumed in the modeling approaches. An iterative method was used to continuously update tree and stand attributes using a cut-off to convert the survival probability for a living or a dead tree. The individual tree diameter growth model and the survival probability model were fitted simultaneously using seemingly unrelated regression (SUR). Parameters of the height function were obtained separately as the number of observations for height was much lower than the number of observations for diameter, which may affect the statistical inference and the estimation of contemporaneous cross-equation error correlation inherent to the system of equations. PRESS residuals were used to evaluate the predictive performance of the diameter and the height growth functions. Additional statistics based in the log likelihood function and also in the survival probability were computed to evaluate the survival function. The second modeling approach, which integrates components of growth expansion and decline, performed slightly better than the first approach. A variable accounting for the thinning response that was tested proved to be significant for predicting diameter growth, even if the model already included competition-related explanatory variables, namely the basal area of trees larger than the subject tree. However, this thinning response factor was not significant for predicting height growth.

Individual-tree diameter growth models for black spruce and jack pine plantations in northern Ontario

Individual-tree distance independent diameter growth models were developed for black spruce and jack pine plantations. Data used in this study came via stem analysis on 1170 black spruce ( Picea mariana [Mill.] B.S.P.) and 800 jack pine ( Pinus banksiana Lamb.) trees sampled from 75 stands of 25 even-aged monospecific plantations for each species in the Canadian boreal forest region of northern Ontario. Of the 75 stands, 50 were randomly selected for each species and all trees from these stands were used for model development. Trees from the remaining stands were used for model evaluation. A nonlinear mixed-effects approach was applied in fitting the diameter growth models. The predictive accuracy of the models was improved by including random effects coefficients. Four selection criteria – random, dominant or codominant, tree size close to quadratic mean diameter, and small sized – were evaluated for accuracy in predicting random effects for a new stand using the developed models. Random effects predicted based on trees selected using the random selection criterion provided more accurate diameter predictions than those using trees obtained via other selection criteria for both species. The models developed here are very important to forest managers as the diameters predicted by these models or, their stand-level summaries (i.e., basal area, average diameter), are used as inputs in any forest growth and yield models. In addition, individual-tree diameter growth models can be used to directly forecast changes in diameter distribution of stands.

An individual-tree diameter growth model for managed uneven-aged oak-shortleaf pine stands in the Ozark Highlands of Missouri, USA

The Pioneer Forest encompasses more than 60,000ha in the Ozark Highlands of Missouri, USA and has been managed using single-tree selection since the early 1950s. This paper quantifies the influence of tree size and competitive position, stand density, species composition, and site quality on ten-year (1992–2002) diameter increment within oak (Quercus spp.) and shortleaf pine (Pinus echinata Mill.) stands on the Pioneer Forest. An individual-tree model was developed for each species using mixed-effects regression and 290 inventory plots. Model efficiency (R2) ranged from 0.26 to 0.57 and fit was generally better for oak species. Basal area in larger trees (BAL) and tree diameter were significant predictors for all species and crown competition factor improved prediction for shortleaf pine and hickory (Carya spp.). Effect of species composition and site quality on diameter growth was not consistent across species. Models were evaluated using a subset of data not included in model fitting and the effect of single tree and standwise (1, 3, or 5 sample trees) calibration on model predictions were evaluated. Inclusion of random effects through calibration improved model prediction for all species and fit was best following single tree and 3 tree calibration.

Liana infestation impacts tree growth in a lowland tropical moist forest

Abstract. Ecosystem-level estimates of the effect of lianas on tree growth in mature tropical forests are needed to evaluate the functional impact of lianas and their potential to affect the ability of tropical forests to sequester carbon, but these are currently lacking. Using data collected on tree growth rates, local growing conditions and liana competition in five permanent sampling plots in Amazonian Peru, we present the first ecosystem-level estimates of the effect of lianas on above-ground productivity of trees. By first constructing a multi-level linear mixed effect model to predict individual-tree diameter growth model using individual-tree growth conditions, we were able to then estimate stand-level above-ground biomass (AGB) increment in the absence of lianas. We show that lianas, mainly by competing above-ground with trees, reduce tree annual above-ground stand-level biomass increment by ~10%, equivalent to 0.51 Mg dry weight ha−1 yr−1 or 0.25 Mg C ha−1 yr−1. AGB increment of lianas themselves was estimated to be 0.15 Mg dry weight ha−1 yr−1 or 0.07 Mg C ha−1 yr−1, thus only compensating ~29% of the liana-induced reduction in ecosystem AGB increment. Increasing liana pressure on tropical forests will therefore not only tend to reduce their carbon storage capacity, by indirectly promoting tree species with low-density wood, but also their rate of carbon uptake, with potential consequences for the rate of increase in atmospheric carbon dioxide.

Individual-tree diameter growth model for sugar maple trees in uneven-aged northern hardwood stands under selection system

An individual-tree diameter model was developed for sugar maple ( Acer saccharum Marsh.) in northern hardwood stands managed under selection system. We fitted long-term remeasurement data to a linear mixed model to account for the temporal autocorrelation of the remeasurements. The model was evaluated using independent data from two physiographic regions and representing a range of tree diameter classes, residual basal areas and years since cut. We compared our model to several individual-tree models based on data from stands with varied management histories. Several competition indices were also tested for an improvement in model fitting and prediction. Our model had lower bias and prediction error when compared to two previous models, as it better accounted for the increased diameter growth that occurred in trees from appropriately managed stands. The addition of a tree-specific competition index failed to improve model fit and predictive ability over stand-level basal area.

Stability of the large tree component in treated and untreated late-seral interior ponderosa pine standsThis article is one of a selection of papers from the Special Forum on Ecological Studies in Interior Ponderosa Pine — First Findings from Blacks Mountain Interdisciplinary Research.

Ponderosa pine ( Pinus ponderosa Dougl. ex P. & C. Laws.) stands with late-seral features are found infrequently, owing to past management activities throughout western North America. Thus, management objectives often focus on maintaining existing late-seral stands. Observations over a 65 year period of stands with no past history of harvest showed substantial ingrowth in the smaller diameter classes and elevated rates of mortality among the largest mature trees in the stand. Adjacent stands, with combinations of thinning and prescribed fire, had far fewer high-risk mature trees and generally lower rates of mortality after treatment. Forecasts using individual-tree diameter growth and mortality models suggest that observed declines in these stands with remaining old trees and a dense understory will continue in the absence of any treatment. Increased vigor in thinned stands appeared to be offset by an increase in mortality of large trees when thinning was followed by prescribed fire.

Modeling Individual-Tree Growth from Data with Highly Irregular Measurement Intervals

Abstract Fitting annual tree growth and survival models to data with irregular measurement intervals requires special consideration to the interpolation of the independent variables. This study presents an iterative method for continuously updating individual-tree and stand attributes, using the hypothesized functional form of a system of forward difference equations. Based on data from permanent sample plots, parameter estimates were obtained for three first-order difference equations of diameter and height growth and mortality for European beech in Denmark. One parameter of the individual-tree diameter and height growth models was estimated locally and expresses apparent site quality. The plot-specific parameters of the individual-tree growth models were highly correlated with site index and plot-specific estimates of rate constants from a dominant height growth model. Parameter estimates of individual-tree models based on either of those indicators of site quality allow for a flexible use of the models. The study failed to establish any relation between plot-specific rate constants and soil texture variables. The resulting system of individual-tree models is consistent with tree growth and mortality expected for beech in Denmark.