New dynamic site equation that fits best the Schwappach data for Scots pine (Pinus sylvestris L.) in Central Europe

Using historical growth series data of Scots pine (Pinus sylvestris L.) in Central Europe we examine all the dynamic site equations previously used for modeling the height growth of this species as well as a new dynamic site equation that has not been used previously in the context of this forestry data. The tested models included two groups of anamorphic and polymorphic dynamic site equations (three-dimensional site–height–age models, such as Y = f(t,t₀,y₀)). One group of the models is based on the algebraic difference approach (ADA) implementation of different, preexisting base equations (two-dimensional equations, such as Y = f(t)). The other group of models is based on newer generalized algebraic difference approach (GADA) formulations of new site–height–age relationships that may use older models only as a part of their structure. The models were selected because they were relevant to Scots pine height growth modeling in other studies. We compared all the models with each other in terms of the sum of square deviations associated with fitting them simultaneously to all sites represented by the Scots pine data. All the fits were based on base-age invariant stochastic regressions, in which the global model parameters that are common to all growth series are estimated simultaneously with the site-specific effects that are different for each of the site productivity series. Cieszewski's model [Cieszewski, C.J., 2005. A new flexible GADA based dynamic site equation with polymorphism and variable asymptotes. PMRC Technical Report 2005-2] best described the data.     

A site index model for lodgepole pine (Pinus contorta Dougl. var. latifolia) in northern Sweden

A model was developed for predicting site index (SI) values and top height growth of lodgepole pine in northern Sweden. Data on 169 experimental plots from 61 experiments were used for model construction. Six dynamic site equations derived using the generalized algebraic difference approach (GADA) were tested. All of the equations estimate height and SI values on the basis of a known height and total age, and are base-age invariant. Unbiased parameter estimates were obtained by non-linear modelling without accounting for autocorrelation of residuals. The special formulation of the Hossfeld model and the GADA-transformed logistic function produced the most reliable SI curves. The Hossfeld model is recommended as it did not produce extreme outlying estimates for young stands. The developed model is polymorphic with variable asymptotes and can predict SI and dominant height growth for lodgepole pine between 20 and 50 years old.     

Development of a system to predict the evolution of individual tree mature cork caliber over time

The development of a model for the prediction of the evolution of individual tree cork caliber over time, from a measurement taken at a certain point in time, was the main objective of this work. The model includes three sub-models: a model to predict the thickness of complete rings from cork caliber at tc years; a cork growth model (for complete rings) and a model to predict cork caliber at age tc from the corresponding thickness of (tc − 1) complete rings. The algebraic difference approach (ADA) as well as the generalized algebraic difference approach (GADA) were used in modeling cork growth. Several base models with one or two site-tree-specific parameters were fitted to the data using the dummy variable approach. The selection of the cork growth model was based on several criteria: fitting ability, prediction performance evaluated through the PRESS residuals and behaviour screened with available knowledge on the cork growth process. The ADA model derived from the log-logistic function with the asymptote as free parameter was selected. The models developed to predict cork caliber and the corresponding thickness of complete rings were based in the linear relationship between the two variables. The two models were simultaneously fitted using two stage least squares approach. The predicted thickness of cork complete rings in a 9-year old cork is proposed as a cork growth index. The distribution of this index can be used to characterize the potential of a site for cork production.     

Modelling dominant height growth in plantations of Pseudotsuga menziesii (Mirb.) Franco in Spain

A model for predicting dominant height growth and site index of Pseudotsuga menziesii (Mirb.) Franco in Spain was constructed. Data from stem analysis of 117 site trees were used. Four dynamic equations using the algebraic difference approach (ADA) and its generalisation (GADA), which have provided good results in previous studies, were evaluated. The model parameters were estimated with the base?age?invariant method of dummy variables, which considers both global (common to all sites) and local parameters (specific to each site). A GADA equation based on the Bertalanffy–Richards base model yielded the best results. The model provides polymorphic curves with multiple asymptotes. A base age of 20 years is proposed to reference site index.     

An empirical comparison of two subject-specific approaches to dominant heights modeling: The dummy variable method and the mixed model method

The varying (local) parameter(s) in site index models can be treated as fixed or random. Two primary subject-specific approaches to height modeling, the dummy variable method (fixed individual effects) and the mixed model method (random individual effects), were compared using Chapman–Richards type models fitted to second-rotation loblolly pine (Pinus taeda L.) data from a designed experiment. For height prediction of new growth series, tested on our validation subset data, the mixed model provides a new (local) parameter prediction method (termed as mixed predictor), which generally performed better than the traditional method of recovering local parameters (the least squares (LS) predictor we used). However, using the LS predictor, both the dummy variable estimation method and mixed model estimation showed almost identical prediction results. With multiple pairs of height–age measurements, no big difference was found in empirical site index prediction between the LS and mixed predictor. Theoretically, one main advantage of the mixed model approach is the ability of its mixed predictor to predict several local parameters using a single height–age pair. However, our empirical results failed to support this point.     

杉木、落叶松断面积模型参数比较

断面积模型是全林模型系统中最重要的模型。本文应用南方５省（区）杉木、北方３省长白落叶松标准地，分别建立了１０组断面积模型，进行比较。结果表明，杉木按立地区建模时，虽然优势高生长过程相似，但断面积生长过程却不同，不能使用同一模型参数。杉木按产区建模时，虽属同区同带，断面积生长过程差异仍很大，因此杉木产区也不是建模的依据。东北３省长白落叶松建模结果表明，各省优势高和断面积生长过程接近，模型参数差异不大。     

A review of stand basal area growth models

Growth and yield modeling has a long history in forestry. The methods of measuring the growth of stand basal area have evolved from those developed in the U.S.A. and Germany during the last century. Stand basal area modeling has progressed rapidly since the first widely used model was published by the U.S. Forest Service. Over the years, a variety of models have been developed for predicting the growth and yield of uneven/even-aged stands using stand-level approaches. The modeling methodology has not only moved from an empirical approach to a more ecological process-based approach but also accommodated a variety of techniques such as: 1) simultaneous equation methods, 2) difference models, 3) artificial neural network techniques, 4) linear/nonlinear regres-sion models, and 5) matrix models. Empirical models using statistical methods were developed to reproduce accurately and precisely field observations. In contrast, process models have a shorter history, developed originally as research and education tools with the aim of increasing the understanding of cause and effect relationships. Empirical and process models can be married into hybrid mod-els in which the shortcomings of both component approaches can, to some extent, be overcome. Algebraic difference forms of stand basal area models which consist of stand age, stand density and site quality can fully describe stand growth dynamics. This paper reviews the current literature regarding stand basal area models, discusses the basic types of models and their merits and outlines recent progress in modeling growth and dynamics of stand basal area. Future trends involving algebraic difference forms, good fitting variables and model types into stand basal area modeling strategies are discussed.     

A reduced growth model based on stand basal area. A case for hybrid poplar plantations in northeast Spain

Whole-stand models normally require data on initial stand basal area and dominant height. Dominant height measurements are time-consuming and often imprecise, compromising subsequent predictions. Poplar plantations provide a special case where basal area correlates with site index; a whole-stand model could thus be based on stand basal area. We report a static model constructed by the generalized algebraic difference approach (GADA) for poplar plantations for three different hybrid poplars (Populus × euramericana (Dode) Guinier “I-214”, “MC”, and “Luisa Avanzo”) in northeast Spain. The transition function was based on current stand basal area and was fitted with data from 158 permanent plots ranging from 1- to 17-year-old plantations. Merchantable stand volume was estimated by a volume equation where height was predicted by a height–basal area relationship based on 458 temporary plots. The model differences between clones were compared using the nonlinear extra sum of squares method. Significant differences were detected, while Luisa Avanzo presented the highest merchantable volume at the end of the rotation. Errors in basal area predictions were below 20% within 6 years in the case of Luisa Avanzo and MC clones, and within 3 years in the case of I-214. Our research showed that satisfactory predictions can be obtained using GADA with a single transition function based on an easily measurable variable such as stand basal area.     

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.     

Representing site productivity in the basal area increment model for FVS-Ontario

The utility of site index as a predictor variable in models for complex, mixed species stands is limited because the site index concept is not well suited for these stand types. Additionally, there is no standard protocol of estimating site index for uneven-aged mixed species stands, which is evident in permanent sample plot (PSP) and co-operative (COOP) data sets available from the Province of Ontario, Canada. Under such circumstances, an alternative to site index in a basal area increment model was explored, using a combination of climate and Forest Ecosystem Classification (FEC) variables from the Ontario boreal region. Among the four candidate climate variables chosen, mean annual temperature (MAT) explained the most variability in basal area increment for the four selected tree species – trembling aspen (Populus tremuloides Michx.), balsam fir (Abies balsamea (L.) Mill.), jack pine (Pinus banksiana Lamb.), and black spruce (Picea mariana (Mill.) B.S.P.). Our results indicated that a combination of the climate variable, MAT, and FEC explained a substantially higher proportion of variation in the basal area increment than site index alone. Thus, climate and FEC variables are superior substitutes in the basal area increment model even when error-free site index values are possible to obtain.     

Subsidy or stress? Tree structure and growth in wetland forests along a hydrological gradient in Southern Europe

In forested wetlands, hydrology exerts complex and sometimes compensatory influences on tree growth. This is particularly true in semi-arid ecosystems, where water can be both a limiting resource and a stressor. To better understand these relationships, we studied hydrologic and edaphic controls on the density, growth, tree architecture and overall productivity of forested wetlands dominated by the tree species Alnus glutinosa and Salix atrocinerea in Southern Europe. We sampled 49 plots set within 21 stands in the Atlantic coastal zone of the Iberian Peninsula, and quantified woody composition, size structure (diameter and height), and radial growth using dendrochronology. Plots were grouped into three saturation classes to compare tree growth characteristics (tree density, degree of sprouting, live basal area and productivity) across levels of saturation. We used Principal Component Analysis (PCA) to create integrated explanatory factors of hydrology, soil nutrient status and soil texture for use in linear mixed models to predict stand characteristics. Increased site saturation favoured a shift in species dominance from Alnus to Salix and resulted in a higher degree of multi-stemmed tree architecture (‘shrubbiness’), particularly for Alnus. Radial growth was negatively correlated with long-term soil saturation; however, annual productivity on a per-tree basis varied by species. Alnus growth and tree density were negatively correlated with waterlogging and fine-textured soils, possibly due to anaerobiosis in the rooting zone. In contrast, Salix growth was more influenced by nutrient limitation. Overall site productivity as measured by annual basal area increment decreased with prolonged saturation. In summary, soil saturation appears to act as a chronic stressor for tree species in this ecosystem. However, these species persist and maintain a dominant canopy position in the most permanently flooded patches through increased sprouting, albeit at a reduced rate of overall biomass accumulation relative to well-drained sites. The diversity in functional responses among wetland forest species has important implications for the conservation and management of these ecosystems. The sustainable management of these ecosystems is directly tied to their vulnerability to changing hydrological conditions. Non-equilibrium modifications to the hydrologic regime from land use and climate change, which are particularly severe in semi-arid regions, may further decrease productivity, integrity and resilience in these stress-adapted communities.     

An empirical model of crown shyness for lodgepole pine (Pinus contorta var. latifolia [Engl.] Critch.) in British Columbia

Crown shyness or canopy disengagement, the phenomenon wherein gaps around trees develop from swaying, whipping and shading, has been identified in the literature since the 1920s. Recent results by researchers at the University of Alberta have clearly described many of the processes involved for lodgepole pine [e.g. Rudnicki, M., Silins, U., Lieffers, V.J., Josi, G., 2001. Measure of simultaneous tree sways and estimation of crown interactions among a group of trees. Trees 15, 83–90; Rudnicki, M., Lieffers, V.J., Silins, U., 2003. Stand structure governs the crown collisions of lodgepole pine, Canadian Journal of Forestry Research 33, 1238–1244; Rudnicki, M., Silins, U., Lieffers, V.J., 2004. Crown cover is correlated with relative density, tree slenderness, and tree height in lodgepole pine. Forest Science 50, 356–363; Fish, H., Lieffers, V.J., Silins, U., Hall, R.J., 2006. Crown shyness in lodgepole pine stands of varying stand height, density, and site index in the upper foothills of Alberta. Canadian Journal of Forestry Research 9, 2104–2111]. However, explicit models of crown shyness are sparse in the literature. This paper describes the development of empirical models of crown shyness in lodgepole pine for British Columbia (BC). We measured crown area and neighbour locations on 60 trees growing in 13 stands in central BC. We estimated potential crown area (A_V) using stem maps and Voronoi polygons constrained by estimates of maximum crown width, and then related observed crown area (A_C) to A_V and additional individual tree variables. One of the nine prediction equations was coded into a spatially explicit tree growth model modified to evaluate the effects of crown shyness at the stand level. Crown shyness models validated well against two independent sources and when linked with a light model tRAYci [Brunner, A., 1998. A light model for spatially explicit forest stand models. Forest Ecology and Management 107, 19–46], increased the below-canopy light by 0.07–0.11.     

The impact of atmospheric deposition and climate on forest growth in European monitoring plots: An individual tree growth model

In the climate change discussion, the possibility of carbon sequestration of forests plays an important role. Therefore, research on the effects of environmental changes on net primary productivity is interesting. In this study we investigated the influence of changing temperature, precipitation and deposition of sulphur and nitrogen compounds on forest growth. The database consisted of 654 plots of the European intensive monitoring program (Level II plots) with 5-year growth data for the period 1994–1999. Among these 654 plots only 382 plots in 18 European countries met the requirements necessary to be used in our analysis. Our analysis was done for common beech (Fagus sylvatica), oak (Quercus petraea and Q. robur), Scots pine (Pinus sylvestris) and Norway spruce (Picea abies). We developed an individual tree growth model with measured basal area increment of each individual tree as responding growth factor and tree size (diameter at breast height), tree competition (basal area of larger trees and stand density index), site factors (soil C/N ratio, temperature), and environmental factors (temperature change compared to long-term average, nitrogen and sulphur deposition) as influencing parameters. Using a mixed model approach, all models for the tree species show a high goodness of fit with Pseudo-R² between 0.33 and 0.44. Diameter at breast height and basal area of larger trees were highly influential variables in all models. Increasing temperature shows a positive effect on growth for all species except Norway spruce. Nitrogen deposition shows a positive impact on growth for all four species. This influence was significant with p < 0.05 for all species except common beech. For beech the effect was nearly significant (p = 0.077). An increase of 1 kg N ha⁻¹ yr⁻¹ corresponds to an increase in basal area increment between 1.20% and 1.49% depending on species. Considering an average total carbon uptake for European forests near 1730 kg per hectare and year, this implies an estimated sequestration of approximately 21–26 kg carbon per kg nitrogen deposition.     

杉木人工林林分断面积生长模型的贝叶斯法估计

以江西杉木人工林为例,以Korf型、Richards型和Hossfeld型3种模型为基础,通过广义代数差分法(GADA)分别建立杉木林分断面积生长模型。结果表明:以Richards型为基础的杉木林分断面积预测精度最高,以Richards型模型为最优模型,分别基于贝叶斯法和传统法(非线性最小二乘法)估计杉木林分断面积生长模型。研究发现,利用贝叶斯法估计杉木林分断面积生长模型,预测精度相当且预测值的可靠性比传统法好。     

Increasing wood production through old age in tall trees

How long forest trees can sustain wood production with increasing age remains an open question, primarily because whole-crown structure and growth cannot be readily measured from the ground or on felled trees. We climbed and directly measured crown structures and growth rates of 43 un-suppressed individuals (site trees) of the two tallest species – Eucalyptus regnans and Sequoia sempervirens – representing a wide range of tree sizes and ages. In both species, ground-level measurements of annual growth, including height, ring width, and basal area increment, exhibited the oft-reported trend of decreasing growth (or no change in growth) with age, yet wood production of the entire main trunk and whole crown both increased with size and age up to and including the largest and oldest trees we measured. The balance between structural metrics of whole-crown respiratory demands (cambium area, inner bark volume, sapwood volume, and heartwood deposition area) and photosynthetic capacity (leaf area and green bark area) was statistically independent of size but not age. After accounting for the effect of size, trees with lower potential respiratory demands grew more than trees with higher potential respiratory demands per unit photosynthetic area. The strongest determinant of tree energy balance was the ratio of aboveground cambium area to leaf area. Among the site trees we examined, over 85% of the variation in annual wood production was explained by variation in size, and the proportion of total aboveground wood production in appendages (branches, limbs, and reiterated trunks) increased linearly with size. With increasing age in both species, the proportion of annual wood production converted to heartwood increased in main trunks and appendages. The oldest tree we measured produced more heartwood in its main trunk over 651 years (351 m³) than contained in any tree we measured <1500 years old. The two tallest tree species achieve similar stature despite divergent growth dynamics and ecologies. At one extreme, E. regnans attains great size quickly but dies relatively young because trees are susceptible to fire and fungi. At the other extreme, S. sempervirens attains great size more slowly but has a long lifespan because trees resist fire and prioritize investment in decay-resistant heartwood. Increasing wood production as trees age is a mechanism underlying the maintenance of biomass accumulation during forest development and the carbon-sink capacity of old-growth forests.     

利用线性混合模型和哑变量模型方法建立贵州省通用性生物量方程

以贵州省人工杉木和马尾松地上生物量数据为例,通过利用线性混合模型和哑变量模型方法,建立了适合不同树种和区域(中心区和一般区)的通用性立木生物量方程,为简化生物量建模工作提供了有效途径。结果表明,相同直径林木的地上生物量估计值随树种、区域的不同存在一定程度的差异,带随机参数的线性混合模型和带特定参数的哑变量模型比总体平均模型的精度高;线性混合模型和哑变量模型方法均同等有效,可推广应用于其它通用性模型(如材积方程)的建立。     

Quantifying height growth and monthly growing degree days relationship of plantation Taiwan spruce

The future of the endemic Taiwan spruce (Picea morrisonicola) under climate change is of great concern. It is the southernmost species of the genus and its current distribution is limited to high altitudes of Taiwan. As a first step toward assessing the impact of future temperature changes on the species, we quantified the effects of past monthly growing degree days (GDD) on the height growth of plantation Taiwan spruce based on nonlinear mixed-effects growth analysis. Our results showed that past GDD variations had both positive and negative effects on the height growth of the species. July of the preceding year had the greatest influence on current year height growth. An increase in the mean GDD level of the current May would also promote height growth. In contrast, a warmer previous November or current January had negative effects on height growth. If the established height growth–GDD relationship holds, the influences of climate change on Taiwan spruce height growth will depend on the timing of the temperature increases, as well as on the trees current growth stages. Our results suggested that a warmer climate would have a greater influence on trees that are still in the early stages along the height growth trajectory. The established height growth–GDD relationship will be a keystone for developing models assessing how Taiwan spruce responds to climate change.     

Estimating growth in beech forests: a study based on long term experiments in Switzerland

? This contribution presents a dynamic stand growth model for Beech (Fagus sylvatica L.) forests, based on a dataset provided by the Swiss Federal Institute for Forest, Snow and Landscape Research WSL, Birmensdorf. The dataset includes 143 research plots, covering a wide range of growing sites and providing up to 16 interval measurements per research plot.

? The objective of this research is to complement the range of existing beech growth models by bridging the gap between the historical yield tables and the single tree growth models. The specific aim is to develop transition functions which will project three state variables (dominant height, basal area and number of trees per hectare) at any particular time, in response to any arbitrary silvicultural treatment.

? Two of the transition functions were derived using the generalized algebraic difference approach (GADA), the third one was derived with the algebraic difference approach (ADA). All the functions were fitted simultaneously using iterative seemingly unrelated regression and a base-age-invariant method. The influence of thinnings on basal area growth was included by fitting different transition functions for thinned and unthinned stands.

? The overall model provides satisfactory predictions for time intervals up to 20 years. The new model is robust and its relatively simple structure makes it suitable for economic analysis and decision support.

     

Relationships between climate and tree radial growth in interior British Columbia,Canada

Climate is a main driving factor of the formation of annual tree-rings, but which climatic variables are the most influential on radial growth may vary among species and sites. To explore these interactions, tree-ring chronologies along a major elevation gradient were examined for three tree species in southern interior British Columbia (Canada): Pseudotsuga menziesii, Pinus contorta, and Picea glauca × engelmannii. We used correlations and linear and multiple regressions to explore the relationships between tree-ring radial growth and climate variables in the area from 1922 to 1997. All correlation coefficients between ring chronologies and monthly climatic variables were medium to low (from −0.3 to 0.4); nevertheless, moderate but significant trends could be identified. Multivariate models explained up to 53%, 43% and 32% of radial growth variability for P. contorta, P. menziesii and P. glauca × engelmannii, respectively. All three species showed similar radial growth–climate patterns across the elevational gradient, but they had different details that made ring width–climate relationships species-specific. Precipitation-related variables were more related to radial growth at low-elevations, changing into temperature-related variables at high-elevations. Tree-ring width for all three species was primarily and significantly affected by climate variables from the year previous to the growing season and only secondly by current year conditions, but the critical months varied for different species and altitudes. Winter precipitation also affected radial growth, either as a source of water or as a possible agent of physical damage. Although our work showed significant climate influences on breast height tree radial growth, our results also indicated that other site factors such as microclimate or stand dynamics can be as or more important than climate variability.     

Predicting Potential Density and Basal Area Development in the Social Forestry Plantations of Acacia nilotica in Gujarat State of India

ABSTRACT

Growth modelling is an important and effective tool for evaluating the effects of a particular management action on the future development of a forest ecosystem. However, such necessary growth models are not available for many indigenous tree species in India. Acacia nilotica is an important multipurpose tree species found in India and growth models are required for proper management of the species in the region. This paper presents equations for estimating potential stand density and predicting basal area in pure even-aged stands of A. nilotica in Gujarat State of India. Although no thinning was suggested, decrease in the number of trees in the stands was observed because of mortality due to overcrowding and some biotic factors. Relationships between quadratic mean diameter and stems per hectare were developed, which was used to establish the limiting density line. Eight different stand level models, belonging to the path invariant algebraic difference form of a non-linear growth function, were compared for projecting basal area. They can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are crucial for evaluating different silvicultural treatment options. The performance of the models was evaluated using different statistical criteria to recommend the suitable model for projecting the basal area in A. nilotica stands.