Individual Tree Basal Area Growth Research Articles

Modelling individual tree maximum basal area growth rates of five tall eucalypt species growing in even-aged forests

Inventory plot data were available providing over 87,000 individual tree basal area growth rates from even-aged native forests of three ash eucalypts (Eucalyptus regnans, E. obliqua, and E. delegatensis), from temperate regions, and two other species from more sub-tropical climes (E. grandis and E. pilularis). Models were developed relating maximum observed growth rates for these species in relation to tree size when, presumably, trees were under ideal environmental conditions and without competition from neighbours for site growth resources. These maximum growth rates increased with increasing tree size to a maximum of their own and then declined as tree size (hence age) increased further. The tree sizes, at which these maximum growth rates reached their maxima, were much greater for the ash eucalypts than for the other two species. It is hypothesised that the ash eucalypts may have evolved physiological characteristics that make them more efficient in compensating for the well-known physiological constraints imposed on growth rates as trees grow to great heights and ages.

Neighborhood dissimilarity consistently attenuates competition stress on tree growth under altered water availability in a natural boreal forest

Tree growth regulates forest productivity and carbon sequestration. Although there has been evidence showing positive effects of neighborhood diversity on tree growth, few have experimentally demonstrated how tree growth may respond to neighborhood diversity in natural forests under altered water availability, which is anticipated to occur more frequently with ongoing global climate change. We examined three-year individual tree basal area growth under the water alteration treatments of reduced (-25% throughfall during the growing season), ambient and added (+25% throughfall during the growing season) rainfall in the broadleaf stands, conifer stands and their mixtures of a young natural boreal forest. We quantified neighborhood drought tolerance dissimilarity, phylogeny dissimilarity and neighborhood crowding based on individual tree sizes and the distance between them. We found that the tree growth on average did not change significantly with water alteration but decreased with neighborhood crowding, with the negative crowding effect being more pronounced in water reduction treatment than in ambient and water addition treatments. Higher neighborhood dissimilarity of drought tolerance and phylogeny promoted tree growth consistently across all water conditions. Moreover, the positive effects of neighborhood dissimilarity of drought tolerance and phylogeny became more pronounced with increasing neighborhood crowding. Our results suggest that promoting species mixtures in boreal forests may sustain higher boreal forest productivity under changing water availability.

Models Relating Individual Tree Basal Area Growth Rates to Tree Basal Areas in Even-Aged, Monoculture Forest Stands

As trees grow larger in even-aged, monoculture forests, stand density increases, taller trees shade smaller trees and a group of smaller, suppressed trees develops that may show little or no growth. Subsequent mortality is most common from this group. This work compares three models that may describe well the relationship between individual tree basal area growth rates and tree basal areas in a forest stand when a suppressed group of trees is present or not. The models are tested using a large collection of data from permanent sample plots in blackbutt (Eucalyptus pilularis Smith) forests in subtropical eastern Australia. An example is given for one stand showing how model parameter values may change as the stand ages; this illustrates how these models have potential for use in the first stage of model development to relate individual tree growth rates to tree sizes and stand characteristics. Such models may then be used widely across the forest population under consideration.

Tree-level differences in Norway spruce and Scots pine growth after extreme thinning treatments

ABSTRACT We studied tree-level dynamics (stem slenderness and growth) in spruce- and pine-dominated stands after intermediate commercial thinning of different type (low, crown normal, and crown strict) and intensity (standard and extreme), for two 5-years growth periods. Thinning treatments were included in modeling as numerical variables based on how they changed the stand- and tree-level conditions (in terms of mean diameter of remaining trees and basal area of larger trees removed). Stem slenderness significantly decreased with time for both species and all types only in the extreme intensity (excluding low thinning for pine). Regarding basal area growth, for both species it was slightly higher in low than crown thinning, and much higher in extreme intensity for all thinning types. Pine had a lower basal area growth in the second period after thinning compared with the first one. Height growth differences were not found across treatments. Concluding, extreme thinning increased individual tree basal area growth and decreased stem slenderness for both species compared with thinning carried out according to the standard guidelines. Across types, there were only small differences, hence crown thinning seems a viable option to the widely used low thinning in Fennoscandia.

Thinning responses of individual trees in mixed stands of Norway spruce and Scots pine

ABSTRACT Effects of species composition on the growth of Norway spruce – Scots pine mixtures had earlier only been studied in unthinned stands. Individual-tree thinning responses in mixed stands were studied to test for the presence of mixture effects in more open stands. Data were collected from 28 temporary sample plots with varying species proportions in 7 thinned spruce-pine stands on medium fertile sites in Eastern Norway. Effects of neighborhood species composition on the individual-tree basal area growth before and after thinning were tested for to detect mixture effects. Spatially-explicit competition indices were used to describe release during thinning in the growth models. Neighborhood species composition only had a minor effect on the thinning response of spruce. Growth before thinning of both species and the thinning response of pine were not affected by species composition. Release had a strong effect on the thinning response of both species. Low density of the studied stands and the more dominant position of pine compared to spruce in mixture, even after the thinning from below, explained some of the observed effects.

Predicting individual tree growth of high-value timber species in mixed conifer-broadleaf forests in northern Japan using long-term forest measurement data

ABSTRACT Quantifying individual tree growth of economically high-value timber species is important for the simulation and development of forest management options. Long-term permanent plot data provides crucial information of forest stand dynamics that can be used to predict individual tree growth. In this study, we developed individual tree basal area growth models of three high-value timber species: monarch birch (Betula maximowicziana), castor aralia (Kalopanax septemlobus), and Japanese oak (Quercus crispula) in a cool temperate mixed forest in northern Japan using long-term measurement data (1968–2016) collected in permanent plots. Data included species, diameter at breast height, and survival status, and stand management history. We applied linear mixed-effects modelling to predict the individual tree basal area growth as a function of individual tree size, competition, and forest management. Model prediction followed by leave-one-out cross validation revealed a correlation between predicted and observed basal area increments with r values of 0.62, 0.73, and 0.70 and root mean square errors values of 10.44, 7.91, and 11.62 cm2/year for monarch birch, castor aralia, and Japanese oak, respectively. The individual tree growth models developed in this study will provide valuable information for species-specific forest management of economically high-value timber species.

Distance-independent tree basal area growth models for Norway spruce, Douglas-fir and Japanese larch in Southern Belgium

This paper presents new harmonized distance-independent individual tree basal area growth models for Norway spruce, Douglas-fir and Japanese larch in pure even-aged stands in Southern Belgium. The selected model was originally developed for Norway spruce and Douglas-fir in neighboring France. New formulations are proposed for some of the model components in order to lower the number of fitted parameters and facilitate the fitting procedure. The resulting models integrate the most recent corresponding top-height growth models and use four simple and usually collected explanatory variables: stand age, top-height, total basal area and tree girth at breast height. The modified formulations maintain similar fitting performances and make it easier to interpret the influence of the explanatory variables on tree growth. Parameters estimates were fitted on thousands of growth measurements gathered from several monitoring plots, forest management inventories and silvicultural field experiments that represent the wide range of site conditions and of forest management scenarios applied to coniferous stands in Southern Belgium. Cross-validation of the models revealed no bias and highlighted their consistent behavior over the entire range of girth at breast height, age, top-height, site index and density represented in our dataset. Combining utility and robust performances, these models represent useful forest management tools, purposely ideal for forest simulation software development. Moreover, the flexibility and generic capabilities of the model formulation should make it easily adjustable for other species in even-aged stands.

Modelos de crecimiento de árbol individual: Aplicación del Simulador BWINPro7

Se describe el simulador de crecimiento y producción de rodales forestales BWINPro7 versión El Salto, Durango. Es una herramienta de sencillo manejo para ser utilizada por gestores y propietarios forestales como apoyo a la toma de decisiones en el manejo forestal. El programa incorpora modelos de crecimiento de árbol individual, desarrollados en los últimos años para las principales especies de pino y encino de los bosques mixtos e irregulares del noroeste de México. Específicamente, fueron incorporados al simulador de crecimiento BWINPro7: 1) modelos para estimar el diámetro de copa y la altura de fuste limpio, 2) modelos para la estimación del crecimiento en altura y área basal de árboles individuales y, 3) un modelo para la cuantificación de la mortalidad natural. Adicionalmente, el simulador puede ser usado con parcelas permanentes de inventario para describir la estructura espacial y prescribir cortas de aclareo y aprovechamientos forestales a escala industrial.

Species shade tolerance affects tree basal area growth behaviour in two eucalypt species in thinned and unthinned even-aged monoculture

ABSTRACTIndividual tree and stand basal area growth were studied in a thinning experiment established over two sites in subtropical eastern Australia. The experiment compared the less shade tolerant species Eucalyptus dunnii with the more shade tolerant Corymbia citriodora var. variegata, both grown in plantation monoculture. Growth was compared over a 2½−3 year period that immediately followed thinning at 5½−7½ years of age. Towards the end of the growth period, tree crown depths and leaf mass per unit area were measured at one site. Crown depth and leaf mass per area of C. citriodora were greater than of E. dunnii, characteristics consistent with a more shade tolerant species. Gross stand basal area growth of E. dunnii was faster than that of C. citriodora. Individual-tree basal area growth behaviour was consistent with inter-tree competition involving asymmetric competition for light. Opening the stand by thinning reduced inter-tree competition to near zero. In unthinned control stands, smaller, more shaded trees of C. citriodora were better able to retain their basal area growth rates than those of E. dunnii in the face of competition. In consequence, the more shade tolerant C. citriodora developed a more evenly spread frequency distribution of tree diameters than less shade tolerant E. dunnii. This would have consequences for the assortment of log sizes that would be available ultimately from monocultures of the two species.

Individual tree basal area growth models for Chir pine (Pinus roxberghii Sarg.) in western Nepal

The individual tree growth models are important decision-making tools in forestry. Age dependent and age independent individual tree basal area growth models were developed for Chir pine ( Pinus roxberghii Sarg.) in one of the western districts, Rukum district, in Nepal. Data from thirty-five destructively sampled trees, which were representative of all possible stand densities, site productivities, age classes, and size classes of Chir pine forests in the district, were used. Sample trees were felled and diameters and ages were measured on the cut surface of the stump (at 30 cm above the ground). Since measurements from the same stump of a tree were strongly correlated, the autoregressive error structure modelling approach was applied while specifying the model in order to reduce bias. All parameter estimates of the models were significant ( P 0.86). Residual graphs showed no serious systematic bias for all observed age classes and diameter classes. The age independent growth model showed relatively better fit statistics ( R 2 = 0.8751, RMSE = 4.8494) than

An Algorithm for Influence-Zone Overlap Competition Indices

Evaluating competition for individual tree growth simulation is significant to forest management. However, few existing software were developed for practical use. To analyze the competition of spruce-fir conifer and broadleaf mixed forests in Changbai Mountain, China, an algorithm for Influence-zone overlap competition indices was developed. Firstly, based on different positions of subjected tree crown and competition tree crown, the overlap area and length were calculated separately in their related equations. Subsequently, a drawing flow chart, the user interface and fields of sheet were produced to construct concept models. Finally, the contribution of competition indices to individual tree basal area growth were tested by non-linear extra sum of squares method. Keyword: Competition Indices, Competitor Selection, Excel VBA,

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.

On Relative Maxima of Diameter Growth, Basal Area Growth, Volume Growth, and Mean Annual Increment for Individual Trees

Abstract A mathematical demonstration for the fact that maximum individual tree diameter growth occurs at an earlier age than maximum individual tree basal area growth is reviewed. This demonstration assumes that the growth functions are continuous, are twice differentiable with respect to age, and increase monotonically to one maximum, thereafter to decline monotonically. The relationship of the age of maximum individual tree volume growth to the age of basal area growth is also discussed. Mathematical demonstrations are given for the fact that the culmination of mean annual increment occurs earlier for diameter than for basal area, and results on age of maximum growth and mean annual increment are also given for arbitrary power functions in diameter.

A distance-independent basal area growth model for oriental spruce (Picea orientalis (l.) Link) growing in mixture with oriental beech (Fagus orientalis Lipsky) in the Artvin region, North-East Turkey

In this study, we developed an individual tree basal area growth model for oriental spruce (Picea orientalis (L.) Link) growing in mixture with oriental beech (Fagus orientalis Lipsky) in the Artvin, Turkey. In our modeling approach, the basal area growth variables were divided into 4 main groups, which included size, competition, site and mixture. The parameters of these variables were biologically consistent with general growth trends of forest growth models and we found them each to be statistically significant at the probability level of 0.05. Our model explained 62.4% of the basal area growth variation of oriental spruce with a standard error of 0.836 cm2. Furthermore, we found that the absolute and relative (%) biases and the root mean square error (RMSE and RMSE%) of the 5 year basal area growth of oriental spruce were 0.00823 cm2, 0.1353%, 0.8234 cm2, 33.39% respectively. We evaluated this model by plotting the biases with respect to considerable regressor variables. These graphical analyses of the model biases showed no meaningful and evident trend of bias values along with these independent variables. Our model provides a clear frame of reference for understanding about the individual tree basal area growth patterns of for oriental spruce growing in mixture with oriental beech. This model further shows that the parameter of the mixture proportion (BP) for oriental beech trees in the mixture model component was positive, indicating that basal area growth of spruce increases as the proportion of beech in the forest mixture goes up if other variables remain constant. This positive effect of admixture may be due to the facilitation process occurring in oriental spruce stands mixed with beech trees. The facilitation pattern of beech trees in mixing spruce stands suggests that poor or degraded forest sites may be improved by mixing beech trees for forest areas in this region. Key words: Oriental spruce, oriental beech, Individual tree basal area growth model, mixed species stands.

Nonlinear mixed modeling of basal area growth for shortleaf pine

Mixed model estimation methods were used to fit individual-tree basal area growth models to tree and stand-level measurements available from permanent plots established in naturally regenerated shortleaf pine ( Pinus echinata Mill.) even-aged stands in western Arkansas and eastern Oklahoma in the USA. As a part of the development of a comprehensive distance-independent individual-tree shortleaf pine growth and yield model, several individual-tree annual basal area growth models were fitted to the data with the objective of selecting the model that has superior fit to the data as well as attributes suitable for practical application in shortleaf pine stand simulator useful as an aid in forest management decision-making. The distance-independent individual-tree model of Lynch et al. [Lynch, T.B., Hitch, K.L., Huebschmann, M.M., Murphy, P.A., 1999. An individual-tree growth and yield prediction system for even-aged natural shortleaf pine forests. South. J. Appl. For. 23, 203–211] for annual basal area growth was improved to incorporate random-effects for plots in a potential-modifier framework with stand-level and tree-level explanatory variables. The fitted mixed-effects models were found to fit the data and to predict annual basal area growth better than the previous model forms fitted using ordinary least-squares. There was also some evidence of heterogeneous errors, the effects of which could be corrected by using a variance function in the estimation process. The revised parameter estimates from the selected mixed model could be utilized in a growth and yield simulator that also takes appropriate dbh–height and mortality functions into account.

Analysis of intraspecific competition in two subalpine Norway spruce ( Picea abies (L.) Karst.) stands in Paneveggio (Trento, Italy)

As a consequence of the recent change in human land-use intensity in mountain territories in the Italian Alps, many Norway spruce ( Picea abies (L.) Karst.) subalpine forests have recently developed without significant anthropogenic disturbance. Even so, their structure and dynamics are still influenced by past human activity. In order to analyze the interactions between past management and current stand dynamics, competition among trees was studied in two 1-ha permanent plots in the Valbona Forest Reserve, located within the Paneveggio-Pale di San Martino Natural Park (eastern Italian Alps). The plots were established in 1993 in two stands with similar age, density and structure but different management history. Tree measurement was repeated in 2005. We carried out the analysis both on the stand- and on the individual tree scale. We computed maximum Stand Density Index (SDI) for Norway spruce in Paneveggio Park (SDI max 1380) based on an ancillary sample plot network. The intensity of stand-level competition and its course through time was assessed in each study area computing percent relative SDI (SDI%) for the two inventory years. Competition at individual level was studied using known individual-based competition indices (CIs) as well as a new set of Crown Area Indices (CAI), all of them based on tree variables such as dbh, height, crown area and inter-tree distance. We assessed the performance of each index by evaluating its explanatory power in forecasting individual tree basal area growth (Δ g) in a 10-year period. In the more recently thinned plot, competition did not induce mortality rates comparable to the second plot, that has been unmanaged for the last 60 years. We expect the intensity of competition-induced mortality of the two stands to increase its similarity in the next future. Individual CIs based solely on tree diameter produced the best performance in plot 1 (e.g., Daniels’ CI, R adj 2 = 0.580 ). In plot 2 different CIs, including tree height, crown area and inter-tree distance as base variables also, proved the most explanatory ones, including CAI 6 ( R adj 2 = 0.553 ), which not consider dbh. We attributed the differential role of tree spatial location and dominance-related descriptors in predicting growth to the time when the stand experienced the last anthropogenic disturbance. The competition relationships still experience the effect of the artificial alteration of forest structure: after human disturbance, mature Norway spruce subalpine forests need several decades to approach more natural dynamics.

Ten-year responses of ponderosa pine growth, vigor, and recruitment to restoration treatments in the Bitterroot Mountains, Montana, USA

Little is known about ponderosa pine forest ecosystem responses to restoration practices in the Northern Rocky Mountains, USA. In this study, restoration treatments aimed at approximating historical forest structure and disturbances included modified single-tree selection cutting, with and without prescribed burning. We compared the effectiveness of restoration treatments on growth, vigor, and composition of recruitment responses with untreated controls. We used a randomized block design to detect treatment differences in mean individual tree basal area increment (BAInc10), growth efficiency (GE), and recruitment abundance between two restoration treatments (Cut-only and Cut-burn) and a Control. We further examined treatment effects by tree age-class (Young, Mature, Presettlement) using a spatial ANOVA model that incorporates the spatial autocorrelation among trees within experimental units. Ten years after implementing restoration treatments, mean individual tree BAInc10 and GE were significantly higher for treated units relative to Control units; all three age-classes benefited similarly from restoration treatments relative to the Control, with the greatest response in the Cut-only and moderate response in the Cut-burn. When treated units were compared, Cut-burn negatively affected BAInc10 and GE relative to Cut-only. Presettlement trees responded positively to treatment relative to the Control, particularly for BAInc10, demonstrating the potential of these old trees to respond to reduced competition. The Cut-burn treatment, in contrast, negatively affected the BAInc10 and GE response of postsettlement trees when compared to Cut-only. Restoration treatments did not reduce the amount of Douglas-fir recruits. In addition, the recruitment of both ponderosa pine and Douglas-fir species was associated with the proximate cover of woody debris in Cut-only and Control treatments. Finally, special consideration needs to be taken for spring Cut-burn treatments, which appeared to dampen growth and vigor, relative to Cut-only, particularly for Young and Mature trees, and increased recruitment of ponderosa pine and particularly Douglas-fir.

The effect of competition on individual tree basal area growth in mature stands of Pinus cooperi Blanco in Durango (Mexico)

In this paper, we evaluated how well-selected distance-dependent and distance-independent competition indices explain individual tree basal area growth of trees, growing in mature and even-aged stands of Pinus cooperi Blanco. A total of 18 competition measures were analyzed of which six do not need tree location (distance-independent) and 12 that utilize tree location (distance-dependent). The competition situation of a stand and/or an individual tree was studied using 11 different competitor selection methods. The mean square error reduction relative to no-competition was used to judge the performance of each competition index. It was found that the best distance-independent competition indices performed as well as the best distance-dependent competition indices. It was concluded that the BALMOD-index would be a good competition index to be incorporated into further individual tree basal area growth models for the study area.

Individual-tree basal area growth models for jack pine and black spruce in northern Ontario

Individual-tree models of five-year basal area growth were developed for jack pine (Pinus banksiana Lamb.) and black spruce (Picea mariana (Mill.) BSP) in northern Ontario. Tree growth data were collected from long-term permanent plots of pure and mixed stands of the two species. The models were fitted using mixed model methods due to correlated remeasurements of tree growth over time. Since the data covered a wide range of stand ages, stand conditions and tree sizes, serious heterogeneous variances existed in the data. Therefore, the coefficients of the final models were obtained using weighted regression techniques. The models for the two species were evaluated across 4-cm diameter classes using independent data. The results indicated (1) the models of jack pine and black spruce produced similar prediction errors and biases for intermediate-sized trees (12–28 cm in tree diameter), (2) both models yielded relatively large errors and biases for larger trees (> 28 cm) than those for smaller trees, and (3) the jack pine model produced much larger errors and biases for small-sized trees (< 12 cm) than did the black spruce model. Key words: mixed models, repeated measures, model validation

Estimating parameters for tree basal area growth with a system of equations and seemingly unrelated regressions

A method was developed for estimating parameters in an individual tree basal area growth model using a system of equations based on dbh rank classes. The estimation method developed is a compromise between an individual tree and a stand level basal area growth model that accounts for the correlation between trees within a plot by using seemingly unrelated regression (SUR) to estimate the restricted parameters. Previously, basal area growth has been modeled on either the stand or the individual tree level. Individual tree models have usually disregarded the regression assumption of independent error terms. Violation of the regression independence assumption may lead to serious underestimation of the mean square error (MSE) and standard error(s) of the parameter estimate(s). The SUR parameter estimation technique has been shown to provide a gain in efficiency for parameter estimation when the error terms for a system of equations are correlated. The data are from an ongoing natural even-aged shortleaf pine growth and yield study being conducted by the USDA Forest Service and Oklahoma State University Department of Forestry for the Ouachita and Ozark National Forests. The basal area growth model based on SUR estimation using a system of four equations (Model 2) corresponding to four dbh rank classes within a plot was compared with a basal area growth model (Model 1) using ordinary least squares (OLS) parameter estimation. The calibration, validation, and complete data set results reveal that Model 2 has a better fit index (FI) and MSE, but that Model 1 has a smaller absolute average error. Model 2 accounts for partial tree interdependency within a plot and consequently should more accurately estimate the parameter standard errors.