Individual-tree Growth Models Research Articles

Individual Tree Growth Model of Larch Plantation based on Crown Competition Factors

Based on the re-measured data between 2007- 2009 from 14 permanent sample plots in larch plantations located in Mengjiagang Forest Farm,Jiamusi city of Heilongjiang province,the relationship between crown variables and increment of tree was analyzed and the distance-dependent individual tree growth model for larch plantation was developed by introducing two crown competition factors( CIaand CIb) as new competition index in this paper. The results showed that two crown competition factors( CIaand CIb) are better than the Hegyi competition index( CI). The correlation between various competition index with basal area increment of individual tree is CIb CIa CI for larch plantation. With enlargement of the competition influence zone of object tree,the competition index tends to be stable and the model fitting effect increases. Tee size is the main affecting factor for the individual tree growth for larch plantation. The basal area increment of individual tree increases as tree diameter at breast height increasing. The goodness of fit for individual tree growth model was improved 5. 6% by introducing new distance-dependent crown competition index. The distance-dependent individual tree growth model developed in this paper can be suitable for predicting basal area increment of individual tree for larch plantation.

Individual tree growth models for eucalyptus in northern Brazil

The diameter and height growth model is one of three submodels used for simulating individual tree growth. In Brazil, there are few studies on the dimensional growth of individual trees be they native or exotic species, despite their potential. This study aimed to evaluate diameter and height growth models for individual trees for eucalyptus stands and to validate the best fitting model. Tree diameter and height data were obtained from 48 permanent plots of unthinned stands of Eucalyptus grandis × Eucalyptus urophylla hybrid located in northern Brazil. The evaluation of the diameter and height growth models was based on adjusted coefficient of determination, standard error of estimate as a percentage, trend, root mean square error and Akaike Information Criterion. Analysis also included distribution of residual percentage, statistical significance and signs of the coefficients. The Lundqvist-Korf model provided the most accurate estimates for diameter and height growth, in comparison with the other models, providing better statistical values, greater proximity to observed values and better distribution of residual percentages. The use of this type of model is feasible and can result in significant improvements in the accuracy of yield estimates.

Predicting Risk of Long-Term Nitrogen Depletion Under Whole-Tree Harvesting in the Coastal Pacific Northwest

In many forest plantation ecosystems, concerns exist regarding nutrient removal rates associated with sustained whole-tree harvesting. In the coastal North American Pacific Northwest, we predicted the depletion risk of nitrogen (N), the region’s most growth-limiting nutrient, for 68 intensively managed Douglas-fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco) plantations varying widely in productivity. We projected stands to rotation age using the individual-tree growth model ORGANON and then calculated a stability ratio for each stand, defined as the ratio of N removed during harvest to total site N store (soil and forest floor). We assigned a risk rating to each site based on its stability ratio under whole-tree and stem-only harvest scenarios. Under whole-tree harvest, 49% of sites were classified as potentially at risk of long-term N depletion (i.e., 10% N store removed in harvest), whereas under stem-only harvest, only 24% of sites were at risk. Six percent and 1% of sites were classified as under high risk of N depletion (i.e., 30% N store removed in harvest) under whole-tree and stem-only harvest, respectively. The simulation suggested that sites with 9.0 and 4.0 Mg ha 1 site N store are potentially at risk for long-term N depletion and productivity loss under repeated whole-tree and stem-only harvest, respectively. Sites with 2.2 and 0.9 Mg ha 1 site N store are at high risk of N depletion under whole-tree and stem-only harvest, respectively. The areas with the highest concentrations of at-risk sites were those with young, glacially derived soils on Vancouver Island, Canada, and in the Puget Sound region of Washington.

Evaluation of different approaches to individual tree growth and survival modelling using data collected at irregular intervals ¿ a case study for

Evaluation of different approaches to individual tree growth and survival modelling using data collected at irregular intervals ¿ a case study for

Integrating pine honeydew honey production into forest management optimization

Pine honeydew honey is an economically important non-wood forest product from eastern Mediterranean Pinus brutia forests, which are also important for timber production. Pine honey is produced by bees that feed on the honeydew secretions of Marchalina hellenica, a scale insect that infests pine stands and feeds on pine sap. The aim of this study was to optimize the joint production of pine honeydew honey and timber by maximizing the soil expectation value of pine stands. The simulation of P. brutia stand dynamics and timber production in healthy and infested stands is based on individual-tree growth and yield models that account for the effect of M. hellenica on tree- and stand-level growth and mortality. The optimization procedure uses a direct search method based on nonlinear programming. The results suggest that pine stands growing on good sites should be managed using rather short rotations and mainly aiming at timber production. In contrast, forest management in medium- and poor-quality sites should aim at longer rotations by taking advantage of the joint production of pine honey and timber assortments. Honey-oriented forest management can be much more profitable than timber production in stands growing on medium and poor sites. Pine honey represents an opportunity to increase the value and economic profitability of P. brutia forests.

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.

Modelling of tangential, radial, and longitudinal shrinkage after drying in jack pine and white spruce

The purpose of this study was to develop an understanding of the pattern of variation in longitudinal, radial, and tangential shrinkage in two commercially important Canadian wood species using multivariate nonlinear mixed-effects models. Shrinkage data were measured in each growth ring at different heights on trees harvested from a mixed-species Nelder tree-spacing plot located in New Brunswick, Canada. Live crown base was reconstructed based on stem analysis. Cambial age, sampling height, crown characteristics (crown length, crown ratio, and distance to live crown base), and ring width at time of wood formation were used as prediction variables. The results indicated that shrinkage magnitude and pattern were closely related to crown dimensions and stem position at time of wood formation. Trees from wider tree spacings with larger crown lengths and ratios tended to have smaller tangential and radial shrinkage. Longitudinal shrinkage decreased nonlinearly from pith outwards with slower rate changes near the bottom of the trees. The model fixed effects accounted for more variation in jack pine (Pinus banksiana Lamb.) than in white spruce (Picea glauca (Moench) Voss) for shrinkage in the same anatomical direction. After further validation, the model developed can be used to provide shrinkage predictions for lumber distortion models within the framework of an individual tree growth model.

Crescimento e produção de plantios comerciais de eucalipto estimados por duas categorias de modelos

O objetivo deste trabalho foi avaliar e comparar duas categorias de modelos de crescimento e produção em plantios comerciais de eucalipto. Para isso, foram ajustados um modelo de crescimento e produção para povoamento e outro para árvore individual, por meio de equações simultâneas e redes neurais artificiais, respectivamente. O volume de madeira por área foi estimado em diferentes idades e classes de produtividade. Foram avaliados dados de 63 parcelas permanentes de plantios clonais, não desbastados, do híbrido Eucalyptus grandis x E. urophylla, com os dados de 33 parcelas utilizados para o ajuste do modelo e o treinamento das redes neurais, e os das 30 parcelas restantes, para a validação dos modelos. As duas categorias de modelos ajustaram-se bem aos dados observados. No entanto, na validação dos modelos com dados independentes, o volume de madeira por área foi mais bem estimado com o modelo para árvore individual.

A comparison of fixed- and mixed-effects modeling in tree growth and yield prediction of an indigenous neotropical species (Centrolobium tomentosum) in a plantation system

Centrolobium tomentosum is a multipurpose pioneer tree species, indigenous in tropical South America and suitable for forest restoration, agroforestry and plantation systems. Despite its economic and ecological interest, no growth and yield models have been developed for this species so far. Fixed- and mixed-effects modeling can be used in model fitting, each technique having its pros and cons. Marginal predictions can be computed from fixed-effects models or randomized mixed-effects models. In forestry practice, models are seldom calibrated and mixed-effects models are mostly used to provide conditional predictions using only the fixed parameters, assuming that the random effects are zero. This study developed the first set of individual-tree growth and yield models for C. tomentosum and, by using the models, assessed the performance of three prediction approaches: fixed-effects models, conditional predictions of mixed-effects-models and marginal predictions of mixed-effects models. The fitted models predict maximum mean annual bole volume increments of 5.6–16.6m3/ha and optimal rotation lengths ranging from 11 to 21years, depending on site quality. Fixed-effects modeling was the best approach in growth and yield prediction, followed by conditional predictions of mixed-effects models, whereas marginal predictions based on mixed-effects models were in general the least accurate. Fixed-effects models should therefore be preferred in the absence of calibration data. However, since calibration is sometimes a feasible option, research articles should report both fixed- and mixed-effects models in order to enable the computation of the best predictions with and without the possibility of model calibration.

Resource communication. Individual-tree growth model for radiata pine plantations in northwestern Spain

Individual-tree basal area and height increment models were developed with data from 130 permanent plots of Pinus radiata D. Don located in Galicia (northwestern Spain). Mixed-models techniques were used for model fitting. Covariates acting at tree and stand level were included as fixed effects. Estimated values of stand variables obtained from aggregation of individual-tree predictions were used in model evaluation. The developed models accounted for 54% of the variability in basal area increment and 36% of the variability in height increment, with mean errors of 16 cm2 and 0.36 m, respectively. These models, along with an existing individual-tree mortality model, constitute a whole individual-tree growth model that can be used to simulate forest management alternatives, helping in forest managers’ decision making.

Developing a computerized approach for optimizing individual tree removal to efficiently reduce crown fire potential

Thinning is a common silvicultural treatment being widely used to restore different types of overstocked forest stands in western U.S. because of its effect on changing fire behavior. Typically, thinning is applied at the stand level using prescriptions derived from sample plots that ignore variability in tree sizes and location within stands. Thinning prescriptions usually specify tree removal in terms of number of trees or basal area, resulting in a large number of cut-tree spatial patterns that meet the same prescription. However, the effect of each pattern on reducing crown fire potential can vary widely depending on the spatial distribution of leave-trees after treatment. Additionally, stand-level thinning prescriptions ignore cut-tree locations, which influence the economic efficiency of the thinning operations. Lastly, decisions on tree selection affect future competition levels of remaining trees, but the associated spatial and temporal effects on tree growth and crown fire potential over time are not considered in the development of thinning prescriptions. To address the limitations of current stand-level thinning practices, we designed a computerized approach to optimize individual tree removal and produce site specific thinning prescriptions that efficiently reduce crown fire potential. Based on stem map and tree attributes derived from light detection and ranging (LiDAR) technology and a distance-dependent individual tree growth model, current and future tree-level fuel connections between adjacent trees were predicted and used as measures of crown fire potential. The approach makes the spatial selection of cut- and leave-trees that most efficiently reduces crown fire initiation and propagation over time while ensuring cost efficiency of the thinning treatment. Application results on a forest stand in western Montana show that the optimal tree selection provided by the computerized approach can reduce crown fire potential more efficiently than current thinning practices represented by a manual selection of tree removal.

Abstracted models for assessing reforestation stocking in spruce-aspen mixedwoods

Individual tree growth models are often constructed with much more complexity than is required for many of the tasks to which they might be applied. In many cases, they also have detailed requirements for describing initial conditions, which may necessitate costly data collection. In cases where a large number of model pre- dictions are required for which there is a mismatch between available data and model requirements, an abstracted low-dimension predictive model (LDPM) that uses alternate input variables and that accurately mimics the outcomes of the more complex model for the specified problem may be an attractive option. In this simulation study, several sets of LDPMs are developed as possible replacements for individual tree models in assessing regeneration stocking implications for mixtures of white spruce (Picea glauca) and trem- bling aspen (Populus tremuloides). These models can accurately mimic a selected set of outcomes of the parent model, but add a small degree of uncertainty in the process. Limitations introduced by the abstraction process include an overall loss of information and a large reduction in the variability of conditions to which the model can be applied. Benefits introduced by the process include a much better efficiency of data collection and model application efforts towards a specific management problem.

A model for predicting the growth of Eucalyptus globulus seedling stands in Bolivia

Eucalyptus globulus is one of the most planted species in the Inter-Andean Valleys of Bolivia, where growing conditions are different from most places where eucalypts have been studied. This prevents a straightforward utilization of models fitted elsewhere. In this study a distance-independent individual-tree growth model for E. globulus plantations in Bolivia was developed based on data from 67 permanent sample plots. The model consists of sub-models for dominant height, tree diameter increment, height-diameter relationship and survival. According to model-based simulations, the mean annual increment with the optimal rotation length is about 13 m3 ha–1 yr–1 on medium-quality sites and 18 m3 ha–1 yr–1on the best sites. A suitable rotation length for maximizing wood production is approximately 30 years on medium sites and 20 years on the most productive sites. The developed models provide valuable information for further studies on optimizing the management and evaluating alternative management regimes for the species.

Modelling individual tree basal area growth of Blue pine (Pinus wallichiana) for Mustang district in Nepal

Individual tree growth models are important decision-making tools for forest management. We developed individual tree basal area growth models with Blue pine (Pinus wallichiana) data from Lete and Kunjo areas of Mustang district in Nepal. The sample trees were identified from all applicable ages, sizes, site qualities, and stand conditions and were cut. Diameters and ages were measured on the cut surface of stump (at 30 cm above ground). With the application of the auto-regressive error-structured modelling approach, we fitted Bertalanffy function to the data from 94 stumps by using basal area growth per year as dependent variable and stump age or stump diameter as independent variable. The age-independent individual tree basal area growth model showed better fits (R 2 adj = 0.8324) than its age-dependent counterpart (R 2 adj = 0.8174). Because of having better fits and being easier for application, the age-independent model is recommended for predicting basal area growth per year at an individual tree level for Blue pine across Lete and Kunjo areas of Mustang district.

Modelling dry matter allocation within Alnus nepalensis D. Don trees in Nepal

The models describing dry matter partitioning and allocation to various components within the individual trees would be important inputs for process-based individual tree growth models and simulation systems. This study presents the allometric and quadratic models fitted to the ratios of biomass data of various components (leaf, branch, stem, and root) of the individual tree against diameter at breast height (dbh). Data from twenty-seven Alnus nepalensis trees in mid-hill region of Nepal were used to develop the models. The most attractive fit statistics were found with the model of ratio of stem to leaf biomass (R2 = 0.95), and similarly the models with the ratios of leaf to branch, leaf to above-ground, and leaf to total-tree biomass explained more than 90% variations. The results also showed that leaf, branch, above-ground and tree-total biomass amounts rapidly increased with increasing dbh. The ratios of leaf to branch, leaf to above-ground, leaf to total-tree, crown to total-tree, and root to total-tree biomass rapidly decreased with increasing dbh in earlier stage and gradually levelled off in the later stage. The models can be used for estimation of biomass of components of the individual tree. These models may also be useful inputs for process-based individual tree growth models which have been gaining the popularity in forest science in recent years. Key words: Alnus nepalensis, biomass model, biomass ratio, dry matter allocation, Nepal.

Even-aged or uneven-aged modelling approach? A case for Pinus brutia

The past management of Pinus brutia forests in Lebanon has led to diverse stand structures that cannot be easily classified as even-aged (EA) or uneven-aged (UA). Most stands are between these stand types, and they may be called as “semi-even-aged”. This is a very common characteristic throughout the Mediterranean conifer forests and makes the choice between the EA and UA approaches problematic, in both management and modelling. However, previous research has devoted little attention to the performance of growth and yield models when applied to transitional stand structures. The aim of this study was to find the best modelling approach and to recommend equations for simulating the dynamics of the semi-even-aged P. brutia stands of Lebanon on an individual-tree basis. Fifty sample plots were measured in Lebanon. Individual-tree growth models were fitted to the whole dataset using either UA or EA modelling approach. Models were also fitted using two sub-samples containing the most EA and the most UA plots. The performance and accuracy of the two modelling approaches were evaluated in all three datasets. The article provides the first complete growth model for uneven-aged P. brutia stands. The EA sub-models presented better statistical fitting. However, the UA sub-models enabled more accurate predictions of wood production and were almost as good as the EA sub-models when predicting stand dynamics of the EA plots. The EA approach provided poor predictions, and the errors were high when it was applied to UA stands. In structurally complex stands, the UA modelling approach is to be preferred since it predicts the whole stand dynamics more accurately and enables simulations of a broader range of silvicultural treatments.

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.

A mathematical framework for modelling cambial surface evolution using a level set method

During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale. The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes. The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself. Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure.

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.

The evidence of stand development stages in simulations by an individual-tree growth simulator

Individual-tree growth models have often been evaluated at the stand level in terms of stand increment or the development of stand density, but rarely in conceptual terms of natural stand dynamics. This study addresses the stand development stage concept developed for natural forests and shows how individual-tree growth models can be evaluated in this respect. For this purpose, the individual-tree growth simulator PrognAus was used to simulate the development of three sites for 2500 years, and a statistical classification model and a rule-based classification scheme were used to identify development stages in the output of the simulator. A comparison of the simulated stages with stages observed in a natural forest in terms of the stand volume and a comparison of the simulated stages with hypotheses from the literature in terms of volume, change of volume, and stand density were performed to determine if the simulations are consistent with the theory.