Individual-tree Diameter Increment Research Articles

Development of Mixed-Effects Individual-Tree Diameter Increment Model for Casuarina Equisetifolia Considering the Effects of Tree-Size Diversity, Tree Density Reduction, and Climate

ABSTRACT Based on the data provided by the 6th (1998), 7th (2003), and 8th (2008) National Forest Inventory (NFI) in Hainan Province, southern China, we developed an individual-tree diameter increment model considering tree-size diversity, tree density reduction, and climate for Casuarina equisetifolia. Since the data was longitudinal and had a nested structure, we used a linear mixed-effects approach to construct the mixed-effects model based on sample plot effects. And we applied the method of 10-fold cross-validation to test the basic model without random effects and final mixed-effects model. The results indicate that natural logarithm of initial DBH (logDBH), sum of basal area of trees larger than objective tree (BAL), soil thickness (ST), Gini coefficient of DBH diversity for residual trees (GCres), and mean coolest month temperature (MCMT) had significant impact on the individual-tree diameter increment for Casuarina equisetifolia. Comparing with basic model, the final mixed-effects model performance was greatly improved. In the model validation, the mixed-effects model also showed a better fitting goodness. The individual-tree diameter increment models of Casuarina equisetifolia developed in this study will provide a good basis for estimating and predicting growth of Casuarina equisetifolia forests over larger areas.

Developing an individual tree diameter increment model of oaks using indicator variables and mixed effects in central China

ABSTRACT Developing an individual tree diameter increment (ΔDBH) model is the basis of near-natural management of mixed, uneven-aged oak forests. This analysis used remeasurement data (2009–2014) comprising 6154 observations from 112 permanent plots in central China to develop and compare an indicator variable model (IVM) and a mixed-effect model (MEM) to estimate ΔDBH. First, a basic model was estimated using 12 potential explanatory variables. Geographical regions (GR), competition intensities (CI) and species compositions (SC) were introduced into the basal model as indicator variables or mixed effects, step by step, and then the prediction accuracy of IVM and MEM was compared. The results showed that (1) the independent variables significantly affecting ΔDBH included the reciprocal of DBH, basal area, altitude, and mean annual rainfall; (2) the introducing GR could not improve the accuracy of estimating ΔDBH, but the CI and SC could. (3) Compared with the basic model and IVM, the percentage mean absolute deviation of MEM decreased by 2.07% and 1.11%, while the root mean square error decreased by 0.06 and 0.04, respectively. The MEM including CI and SC as a random effect showed the best predictive performance and can be applied to improve the prediction of individual oak trees ΔDBH.

Generalized Nonlinear Mixed-Effects Individual Tree Diameter Increment Models for Beech Forests in Slovakia

Individual tree growth and yield models precisely describe tree growth irrespective of stand complexity and are capable of simulating various silvicultural alternatives in the stands with diverse structure, species composition, and management history. We developed both age dependent and age independent diameter increment models using long-term research sample plot data collected from both monospecific and mixed stands of European beech (Fagus sylvatica L.) in the Slovak Republic. We used diameter at breast height (DBH) as a main predictor and other characteristics describing site quality (site index), stand development stage (dominant height and stand age), stand density or competition (ratio of individual tree DBH to quadratic mean diameter), species mixture (basal area proportion of a species of interest), and dummy variable describing stand management regimes as covariate predictors to develop the models. We evaluated eight versatile growth functions in the first stage using DBH as a single predictor and selected the most suitable one, i.e., Chapman-Richards function for further analysis through the inclusion of covariate predictors. We introduced the random components describing sample plot-level random effects and stochastic variations on the diameter increment, into the models through the mixed-effects modelling. The autocorrelation caused by hierarchical data-structure, which is assumed to be partially reduced by mixed-effects modelling, was removed through the inclusion of the parameter accounting for the autoregressive error-structures. The models described about two-third parts of a total variation in the diameter increment without significant trends in the residuals. Compared to the age independent mixed-effects model (conditional coefficient of determination, R c 2 = 0.6566; root mean square error, RMSE = 0.1196), the age dependent model described a significantly larger proportion of the variations in diameter increment ( R c 2 = 0.6796, RMSE = 0.1141). Diameter increment was significantly influenced differently by covariate predictors included into the models. Diameter increment decreased with the advancement of stand development stage (increased dominant height and stand age), increasing intraspecific competition (increased basal area proportion of European beech per sample plot), and diameter increment increased with increasing site quality (increased site index) and decreased competition (increased ratio of DBH to quadratic mean diameter). Our mixed-effects models, which can be easily localized with the random effects estimated from prior measurement of diameter increments of four randomly selected trees per sample plot, will provide high prediction accuracies. Our models may be used for simulating growth of European beech irrespective of its stand structural complexity, as these models have included various covariate variables describing both tree-and stand-level characteristics, thinning regimes, except the climate characteristics. Together with other forest models, our models will be used as inputs to the growth simulator to be developed in the future, which is important for decision-making in forestry.

Analyzing the impacts of forest disturbance on individual tree diameter increment across the US Lake States.

Disturbances play a critical role in forest ecosystem dynamics. Disturbances cause changes in forest structure which in turn influence the species composition of the site and alter landscape patterns over time. The impacts of disturbance are seen over a broad spectrum of spatial scales and varying intensities, ranging from biotic agents such as insect and leaf disease outbreaks to abiotic agents such as a windstorm (a stand-replacing disturbance). This study utilized Forest Inventory and Analysis (FIA) data collected between 1999 and 2014 in the US Lake States (Michigan, Minnesota, and Wisconsin) to examine the impacts that disturbances have on the growth of residual trees using species-specific diameter increment equations. Results showed that animal and weather damage were the most common disturbance agents and fires were the least common in the region. Results also indicated that while the diameter increment equations performed well on average (overprediction of 0.08 ± 1.98cm/10years in non-disturbed stands), when the data were analyzed by species and disturbance agent, the model equation was rarely validated using equivalence tests (underprediction of 0.30 ± 2.24cm/10years in non-disturbed stands). This study highlights the importance of monitoring forest disturbances for their impacts on forest growth and yield.

Comparing performance of contrasting distance-independent and distance-dependent competition metrics in predicting individual tree diameter increment and survival within structurally-heterogeneous, mixed-species forests of Northeastern United States

Most studies comparing the predictive performance of distance-independent and -dependent competition metrics have been conducted in even-aged, single species stands. In addition, past studies have generally not considered more sophisticated distance-dependent competition metrics such as open sky-view or light interception indices. Using data from fully stem mapped inventory plots (n = 260) established in structurally complex, mixed-species experimental forests (n = 5) in the Northeastern US, we evaluated prediction performance of one- and two-sided distance-dependent as well as more conventional distance-independent competition metrics in both annualized diameter increment (n = 1735) and probability of survival models (n = 1953) developed across 26 contrasting softwood and hardwood species. Prediction accuracy of non-spatial and spatial models was further assessed by classifying observations by species shade-tolerance, relative tree height, time since harvest, and tree clumping. Our analyses revealed no general superiority of distance-dependent competition metrics over their distance-independent counterparts for either diameter increment or survival, which was particularly true for the latter variable. Distance-dependent metrics tended to outperform distance-independent ones for observations from shade-tolerant species, trees of lower crown classes, and immediately after harvest. However, results on the comparative analysis of the predictive power of the different types of competition metrics under varying stand conditions and situations were often inconsistent and not always conclusive. In addition, model complexity, i.e. number of non-spatial explanatory variables in the base model, strongly affected the performance of distance-dependent competition metrics. Our findings thus appear to support the critical assumption that distance-independent competition metrics are sufficient for most operational growth and yield applications, even in managed, naturally-regenerated and species rich forests.

Evaluating the influence of stem form and damage on individual-tree diameter increment and survival in the Acadian Region: implications for predicting future value of northern commercial hardwood stands

Northern hardwood species display a variety of forms and defects that can reduce stem quality and complicate their timber management. However, for the most part, growth and yield models do not account for the influence of stem form and damage. This study determined the influence of stem form and damage on growth, survival, and projected future sawlog value among several northern commercial hardwood species. To accomplish this, hardwood trees on 112 permanent plots across three long-term research sites in Maine were assigned stem form and risk classes using a tree classification system developed in New Brunswick. A highly significant influence of stem form and risk on annualized individual-tree diameter increment and survival was found. Inclusion of these equations into a regional growth and yield model highlighted the importance of stem form and defects on long-term simulations as projected stand-level future value was significantly reduced by over 17%, on average (range of 13% to 28%), when compared with projections that did not include that tree-level information. The results highlight the importance of stem form and defects, as well as the need to account for them, in growth and yield applications that assess the forecasted value of commercially important hardwood stands.

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.

Productivity and optimal management of the uneven-aged hardwood forests of Hyrcania

Hyrcania is a productive region near the southern coast of Caspian Sea. Her forests are mostly uneven-aged beach-dominated hardwood mixtures. There is increasing willingness to treat these forests without clear-felling, following the ideas of continuous cover management. However, lack of growth and yield models have delayed this endeavor, and no instructions for uneven-aged management have been issued so far. This study developed a set of models that enable the simulation of stand development in alternative management schedules. The models were used to optimize stand structure and the way in which various initial stands should be converted to the optimal uneven-aged structure. The model set consists of individual-tree diameter increment model, individual-tree height model, survival model, and a model for ingrowth. The models indicate that the sustainable yield of the forests ranges from 2.2 to 7 m3 ha−1 a−1 in uneven-aged management, depending on species composition. Better ingrowth would substantially enhance productivity. The optimal stand structure for maximum sustained yield has a wide descending diameter distribution, the largest trees of the post-cutting stand being 80–100 cm in dbh. If cuttings are conducted at 30- or 40-year intervals, they should remove 20–40 largest trees per hectare. Despite moderate growth rate, uneven-aged management produces high incomes, 850–1,000 UDS ha−1a−1, because the timber assortments that are obtained from the removed large trees have very high selling prices. Optimal conversion to uneven-aged structure showed that the steady-state stand structure depends on initial stand condition and discount rate when the length of the conversion period is fixed. Discount rates higher than 1 % lead to reduced wood production, heavy cuttings, and low basal areas of the steady-state forest.

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.

Fitting Logistic Growth Curve with Nonlinear Mixed-effects Models

A nonlinear mixed-effects modeling approach was used to model individual tree diameter increment based on Logistic growth function for dahurian larch (Larix gmelinii Rupr.) plantations in northeastern China. The study involved the estimation of fixed and random parameters, as well as procedures for determining random effects variance-covariance matrices. Results showed that the mixed-effects model provided better model fitting than the fixed-effects model. The logistic model with three random parameters b₁, b₂, b₃ was considered the best mixed model. Time series correlation structures included Autoregressive correlation structure AR (1) and AR (2), Moving Average correlation structure MA (1) and MA (2) and Autoregressive-Moving Average correlation structure [ARMA (1, 1)] and ARMA (2, 2) were incorporated into the best mixed model. The mixed model with MA (2) correlation structure showed lower AIC and BIC values and significantly improved model performance (LRT = 545.6, p<0.0001). Techniques for calibrating the diameter growth model for a particular tree of interest were also explored. The results indicated that the mixed-effects model provided better diameter predictions than the models using only fixed-effects parameters.

Species Interactions in the Dynamics of Even- and Uneven-Aged Boreal Forests

Many boreal tree stands are neither clearly even-aged nor clearly uneven-aged. The stands may undergo a series of stages, during which an even-aged stand is transformed into two-storied mixed stand, and finally to multistoried or uneven-aged stand structure. The species composition often changes during the succession of stand stages. This study developed models for stand dynamics that can be used in different stand structures and species compositions. The model set consists of species-specific individual-tree diameter increment and survival models, and models for ingrowth. Separate models were developed for Scots pine, Norway spruce, and hardwood species. The models were used in a growth simulator, to give illustrative examples on species influences and stand dynamics. Methods to simulate residual variation around diameter increment and ingrowth models are also presented. The results suggest that mixed stands are more productive than one-species stands. Spruce in particular benefits from an admixture of other species. Mixed species improve diameter increment, decrease mortality, and increase ingrowth. Pine is a more beneficial admixture than birch. Simulations showed that uneven-aged management of spruce forests is sustainable and productive, and even-aged conifer stands growing on medium sites can be converted into uneven-aged mixed stands by a series of strong high thinnings.

Growth models based on radial increment observations for eight pine species in Angola

Growth models for the Central Highlands of Angola were developed in this study for Pinus pseudostrobus Lindl., P. kesiya Royle ex Gordon, P. devoniana Lindl., P. chiapensis (Martinez) Andresen, P. elliottii Engelm., P. greggii Engelm. ex Parl., P. montezumae Lamb. and P. oocarpa Schiede ex Schltdl. for simulating the development of stand characteristics. The model set included dominant height, individual-tree diameter increment, individual-tree height and self-thinning models. The study was based on radial increment observations obtained from increment cores from 16 plots located in the Tchianga research station in the Angolan Highlands. The model set enables the simulation of stand development on an individual tree basis. The developed models are among the first models for these species in Africa. They showed good accuracy when the simulated stand development was compared to the observed development. Therefore, they can be used as a management planning tool in tropical pine plantations in Angola.

Using optimization for fitting individual-tree growth models for uneven-aged stands

A convenient model type for simulating the dynamics of uneven-aged and uneven-sized stands of Finland is individual-tree model. This is because the stand structures are complex due to the presence of several tree species and irregular size distributions of trees. The required minimum set of models in this approach consists of species-specific individual-tree diameter increment models, individual-tree survival models, and ingrowth models. The development of these models needs data in which the diameter and survival of each tree of the sample plots is known for at least two time points. For this, the trees need to be numbered, which is tedious in uneven-aged forests due to the great number of small trees and the continuous ingrowth process. This study proposes a modelling approach that fits the above models but requires only the diameter distributions of the plots in the beginning and at the end of the measurement interval. The method uses non-linear optimization to derive such values for model parameters that, when the models are applied to the initial diameter distribution, the simulated stand development results in a diameter distribution which agrees with the measured ending distribution. The study showed that the method produces similar models and model parameters as regression analysis. Since the method is less demanding in terms of modelling data, it brings new data sets available for modelling the dynamics of uneven-aged stands and reduces the cost of collecting new data. The models fitted by the proposed optimization method were rather similar to the models developed earlier for Finnish uneven-aged forests.

Growth models for Pinus patula in Angola

This study developed growth models for Pinus patula Schiede ex Schltdl. et Cham. for the Central Highlands of Angola for simulating the development of stand characteristics. The model set included dominant height, individual-tree diameter increment, individual-tree height and self-thinning models. The study was based on 7 656 radial increment observations obtained from increment cores from eight plots located in five sites in the Angolan Highlands. The model set enables the simulation of stand development on an individual tree basis. Despite the fact that site variation among the plots was small, a traditional site category index based on slope catena correlated logically with the observed diameter growth rate of the plots. The developed models showed a high level of accuracy when the simulated stand development was compared to observed development. The shape of the dominant height model is similar to earlier models developed in southern Africa.

Growth and yield models for uneven-sized forest stands in Finland

Uneven-sized forestry is gradually gaining popularity and acceptability also in the Nordic countries. This is because of the willingness of the public and some forest owners to avoid clear-fellings and pursue more near-nature forest structures. It has also been realized that the profitability of uneven-sized forestry may be competitive with even-aged forestry. In Finland, management of uneven-sized stands is hampered by the lack of information about the dynamics of such stands, and about the yield and profitability of uneven-sized forestry. This study developed models which allow managers to simulate the growth and yield of uneven-sized stands in Finland, making it possible to predict the yield and analyze the sustainability of different management options. The model set consists of individual-tree diameter increment, height and survival models, and a model for ingrowth. The modeling data consisted of two long-term field experiments of uneven-sized forest management, a set of temporary sample plots measured earlier for growth modeling purposes, and the sample plots of the third National Forest Inventory of Finland. The application area of the models covers all growing sites, all main tree species, and the whole surface area of Finland. According to the models, the sustainable harvest of a fertile ( Oxalis-Myrtillus site) uneven-sized Norway spruce forest varies between 5.5 and 7 m 3 ha −1 a −1 in Central Finland, depending on the length of the cutting cycle, stand density, and shape of the diameter distribution. It is profitable to harvest large diameter classes more heavily than small ones. Due to the large amount of data the models for diameter increment are highly significant and reliably show the growth level of trees in uneven-sized stands. The weakest models are the ingrowth models, which are based on a clearly smaller data set than the other models.

Individual tree diameter increment model for managed even-aged stands of ponderosa pine throughout the western United States using a multilevel linear mixed effects model

A diameter increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in the United States using a multilevel linear mixed model. Stochastic variability is broken down among period, locale, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, site index, and competition indices are included in the model as fixed effects in order to explain residual variability. The data set used in this study came from long-term permanent research plots in even-aged, pure stands both planted and of natural origin. The data base consists of six levels-of-growing stock studies supplemented by initial spacing and other permanent-plot thinning studies for a total of 310 plots, 34,263 trees and 153,854 observations. Regression analysis is the preferred technique used in growth and yield modeling in forestry. We choose the mixed effects models instead of the regression analysis approach because it allows for proper treatment of error terms in a repeated measures analysis framework. Regional growth and yield models exist for ponderosa pine. However, data collection and analysis procedures differ. As a result, comparisons of growth responses that may be due to geographic variation of the species are not possible. Our goal is to present a single distance-independent diameter increment model applicable throughout the geographic range of ponderosa pine in the United States and by using only data from long-term permanent plots on sites capable of the productivity estimated by Meyer [Meyer, W.H., 1938. Yield of Even-Aged Stands of Ponderosa Pine. US Department of Agriculture Technical Bulletin 630].

Bedrock type significantly affects individual tree mortality for various conifers in the inland Northwest, U.S.A.

Individual tree mortality models for western white pine (Pinus monticola Dougl. ex D. Don), Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco), grand fir (Abies grandis (Dougl. ex D. Don) Lindl.), western redcedar (Thuja plicata Donn ex. D. Don), western hemlock (Tsuga heterophylla (Raf.) Sarg.), and western larch (Larix occidentalis Nutt.) were developed using data from permanent research plots located throughout the inland Northwest. The proposed linear logistic models included the following independent variables: diameter at breast height, basal area in larger trees, basal area per hectare, individual tree diameter increment, and a set of dummy variables for the six bedrock types, which were granite, basalt, metasedimentary, sedimentary, mixed – glacial till, and deep deposit. The results show that rock type significantly affects individual tree mortality for western white pine, Douglas-fir, and western redcedar, while grand fir, western hemlock, and western larch were not affected. Western white pine and Douglas-fir growing on meta sedimentary rocks exhibited greater mortality probabilities than on other rocks. Mortality probabilities for western hemlock were low across all rock types, including "nutrient-poor" rocks like metasedimentary types.

Constraining Individual Tree Diameter Increment and Survival Models for Loblolly Pine Plantations

Abstract Among extant forest growth and yield models, individual tree growth models provide the most detailed information, which is useful for intensive forest management. However, individual tree growth models may be inaccurate for stand-level predictions because of the cumulative error resulting from individual tree predictions. This paper is aimed at developing a method to ensure that individual tree growth models not only provide precise individual tree predictions but also give precise stand-level estimation. Based on the conceptual relationships between basal area of each diameter class and the diameter increment of trees in the same diameter class, a constrained regression equation system is proposed. The same approach is also applied to modeling individual tree survival probability. An algorithm for estimating multiresponse regressions was developed. Results using data from unthinned loblolly pine (Pinus taeda L.) plantations show that the simultaneous equation system provides nearly the same individual tree diameter increment estimates as the unconstrained model but better estimates for basal area of each diameter class and for total stand basal area. The potential for improving stand mortality estimation with a constrained individual tree survival model where there is little mortality in the data is limited. For. Sci. 43(3):414-423.

An individual tree diameter increment model for white spruce in Alberta

Based on a data set from 164 permanent sample plots, an age-independent individual tree diameter increment model is presented for white spruce (Piceaglauca (Moench) Voss) grown in the boreal mixed-species stands in Alberta. The model is age independent in that it does not explicitly require tree or stand age as input variables. Periodic diameter increment is modelled as a function of tree diameter at breast height, total tree height, relative competitiveness of the tree in the stand, species composition, stand density, and site productivity. Because data from permanent sample plots are considered time series and cross sectional, diagnostic techniques were applied to identify the model's error structure. Appropriate fit based on the identified error structure was accomplished using weighted nonlinear least squares with a first-order autoregressive process. Results show that (1) all model parameters are significant at α = 0.05 level, and (2) the plot of studentized residuals against predicted diameter increment shows no consistent underestimate or overestimate for diameter increment. The model was also tested on an independent data set representing the population on which it is to be used. Results show that the average prediction biases are not significant at α = 0.05 level, indicating that the model appropriately describes the data and performs well when predictions are made.