Growth models for six Eucalyptus species in Angola

This study developed growth models for Eucalyptus saligna Sm., E. camaldulensis Dehnh., E. macarthurii H.Deane & Maiden, E. resinifera Sm., E. siderophloia Benth. and E. grandis Hill ex. Maiden, for the central highlands of Angola, and used these models to simulate the development of stand characteristics. The obtained model set included dominant height, diameter increment, tree height and self-thinning models. The study was based on 10 499 radial increment observations measured on cores taken from about 700 trees growing in 22 plots located in seven sites in the Angolan highlands. The model set makes it possible to simulate stand development on an individual tree basis. Comparison of simulated stand development and measurements indicated good performance of the models. A non-linear fixed-effects diameter increment model performed best for most species, but a non-calibrated linear mixed-effects model used with the Snowdon correction was better for E. saligna and E. macarthurii. This study showed a similar dominant height development of young stands as found in most previous studies done for southern Africa. Some differences emerged at older ages.     

Do individual-tree growth models correctly represent height:diameter ratios of Norway spruce and Scots pine?

Height:diameter ratios are an important measure of stand stability. Because of the importance of height:diameter ratios for forest management, individual-tree growth models should correctly depict height:diameter ratios. In particular, (i) height:diameter ratios should not exceed that of very dense stands, (ii) height:diameter ratios should not fall below that of open-grown trees, (iii) height:diameter ratios should decrease with increasing spacing, (iv) height:diameter ratios for suppressed trees should be higher than ratios for dominant trees. We evaluated the prediction of height:diameter ratios by running four commonly used individual-tree growth models in central Europe: BWIN, Moses, Silva and Prognaus. They represent different subtypes of individual-tree growth models, namely models with and without an explicit growth potential and models that are either distance-dependent (spatial) or distance-independent (non-spatial). Note that none of these simulators predict height:diameter ratios directly. We began by building a generic simulator that contained the relevant equations for diameter increment, height increment, and crown size for each of the four simulators. The relevant measures of competition, site characteristics, and stand statistics were also coded. The advantage of this simulator was that it ensured that no additional constraint was being imposed on the growth equations, and that initial conditions were identical. We then simulated growth for a 15- and 30-year period for Austrian permanent research plots in Arnoldstein and in Litschau, which represent stands at different age-classes and densities. We also simulated growth of open-grown trees and compared the results to the literature. We found that the general pattern of height:diameter ratios was correctly predicted by all four individual-tree growth models, with height:diameter ratios above that of open-grown trees and below that of very dense stands. All models showed a decrease of height:diameter ratios with age and an increase with stand density. Also, the height:diameter ratios of dominant trees were always lower than that of mean trees. Although in some cases the observed and predicted height:diameter ratios matched well, there were cases where discrepancies between observed and predicted height:diameter ratios would be unacceptable for practical management predictions.     

Modelling annual individual-tree growth and mortality of Scots pine with data obtained at irregular measurement intervals and containing missing observations

An individual-tree growth model was developed with data from 54 permanent plots of Scots pine (Pinus sylvestris L.) located in Galicia (northwestern Spain). The study involved two model fitting approaches, one considering constant growth and mortality rates in the period between two consecutive inventories, and another considering variable growth and mortality rates in the same period. The individual-tree growth model was based on annual basal area growth, height growth and survival probability. The model included variables from groups pertaining to tree size, competition and age. Weighted regression was used as a tool for dealing with missing height observations in model fitting. Evaluation of the model via simulation of growth and mortality in the period between inventories showed that the variable growth rate approach provided slightly better results than the constant growth rate approach. The final model was consistent with expected diameter growth, height growth, dominant height growth, stand basal area growth and reduction in number of stems per hectare.     

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 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 m³ 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.     

A stand dynamic model for red pine plantations with different initial densities

A stand dynamic model was developed to predict the growth response in even-aged forest plantations of different initial planting densities. The model is based on the integration of three subcomponents: height growth, self-thinning, and diameter increment. The integrated model uses the height of dominant trees to simulate stand response to site quality and internal growth potential. An extended self-thinning submodel is used to simulate mortality in stands due to crowding and inter-tree competition. A diameter increment submodel is used to link the height growth and self-thinning submodels. The height growth submodel is based on an application of the “Pipe Model” theory. The three-parameter self-thinning submodel is developed from an extended self-thinning law that captures self-thinning in stands before they attain full stocking. The diameter increment model is based on the assumption that diameter increment is related to height growth and available growing space described by stand density. The integrated model is applied to data collected from a 45-year-old red pine (Pinus resinosa Ait.) plantation subsectioned with different initial planting densities. For the data used, only two parameters were required to capture 99% of measured variation in height growth. Additional data from sites with different planting intensities are required to formulate a more generalized height growth model. The slope of the linear self-thinning limit for red pine is approximately −1.5. Model predictions are consistent with field measurements.     

A growth and yield model for even-aged <Emphasis Type="Italic">Pinus brutia</Emphasis> Ten. stands in Syria

Pinus brutia Ten. subspecies brutia, which occurs in the Eastern Mediterranean region, is the main forest species in Syria and important for multi-purpose forestry. In this study, 6,631 10-year past growth diameter increment measurements were taken in 83 temporary sample plots. The current breast height diameter of all trees was measured and a sample of trees was measured for height and age. The plots were placed so as to capture the whole range of variation in site quality, stand age and stand density. The data were used to develop the following models:

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.     

The effects of species mixture on the growth and yield of mid-rotation mixed stands of Scots pine and silver birch

The effect of tree species mixture on stand volume yield and on tree-species-specific diameter and height growth rates were analysed in managed mixed stands of Scots pine (Pinus sylvestris L.) and silver birch (Betula pendula Ehrn.).Data were obtained from 14 repeatedly measured stands located in Southern Finland on mineral soil sites with varying admixture of Scots pine and silver birch. Statistical analysis was carried out for studying the effect of species mixture on the development of stand characteristics. For the analysis, the plots were categorised into three groups (plot types) according to the species dominance. In order to analyse species-specific growth rates, individual-tree mixed linear growth models for tree diameter and height growth were developed for both tree species.The results clearly show that the yield of the managed mid-rotation, mixed stands was greater for stands dominated by Scots pine than for stands dominated by birch, and the stand volume increment decreased with an increasing proportion of silver birch. Analysis of diameter and height growth by tree species revealed that the main reason for this pattern is the negative impact of birch competition on the growth of pine trees. The increase in diameter of pine was clearly hampered if the proportion of birch was high. An abundance of birch also slightly decreased the growth in height of Scots pine, although the effect was less than on diameter growth. Species mixture did not affect the diameter growth of birch but did have a significant effect on height development. Height growth of birch was considerably greater in pine-dominated stands than in birch-dominated stands. In pine-dominated mixed stands, the height growth of birch was quite close to that of dominant pine trees, and birches can endure in competition with pines for light.The results apply for even-aged and single-storey managed stands, where stocking density and structure are controlled with pre-commercial and commercial thinnings. The results are not applicable to unmanaged mixed stands undergoing self-thinning. This study provides new information on mixed stands from a silvicultural perspective, which can be applied in decisions involving the management of mixed stands.     

林分生长和收获模型整体化思路探讨

介绍了林分生长和收获模型的概念、分类及模型整体化研究的内涵,以单木直径生长模型作为基础模型,提出了单木直径、树高、断面积、材积模型之间,林分平均直径、断面积、材积模型之间以及单木生长模型、全林分模型和径阶分布模型之间的耦合思路,对于解决不同水平模型之间的相容性、一致性及内部结构的统一具有一定意义.     

A mixed nonlinear height–diameter model for pyrenean oak (Quercus pyrenaica Willd.)

A nonlinear mixed-effects modelling approach was used to model the individual tree height–diameter relationship in pyrenean oak (Quercus pyrenaica Willd.). A set of 24,627 pairs of height–diameter measurements were used to fit the model. These were taken at 950 Spanish National Forest Inventory plots embracing six different biogeoclimatic strata. Eleven biparametric nonlinear height–diameter equations were evaluated to find a local model, which only includes the dimensions of the tree as explanatory variables. After selecting the local model, a regional or generalized model was studied. The following stand variables were tested for inclusion in the model as fixed effects: stand density, quadratic mean diameter, arithmetic mean diameter, dominant diameter, arithmetic mean height, dominant height and basal area. Dominant height and basal area of the stand were found to produce the most satisfactory fits in the stand model. Interregional variability was studied by including strata effects as dummy categorical variables and was analysed using the non-linear extra sum of squares method and the Lakkis–Jones test. Height–diameter models were found to be similar for the six biogeoclimatic strata. Finally, a mixed nonlinear model technique was applied to fit the definitive model. By calibrating the model it is possible to predict random components of definitive model from height measurements previously taken from a subsample of trees. The different alternatives tested reveal that only two or three trees are necessary to calibrate the model.     

A probability model for root and butt rot in Picea abies derived from Norwegian national forest inventory data

Root rot in Norway spruce (Picea abies (L.) Karst.) causes substantial economic losses to the forestry sector. In this study, we developed a probability model for decay at breast height utilizing 18,141 increment cores sampled on temporary plots of the Norwegian National Forest Inventory. The final model showed a good fit to the data and retained significant relationships between decay and a suite of tree, stand and site variables, including diameter at breast height, stand age, altitude, growing season temperature sum (threshold 5°C), and vegetation type. By comparing model predictions with recorded decay at stump height in an independent data set, we estimated a proportionality function to adjust for the inherent underestimation of total rot that will be obtained by applying a probability model derived from increment cores sampled at breast height. We conclude that the developed model is appropriate for national and regional scenario analyses in Norway, and could also be useful as a tool for operational forestry planning. This would however require further testing on independent data, to assess how well the new model predicts decay at local scales.     

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

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

Modeling non-catastrophic individual-tree mortality for Pinus radiata plantations in northwestern Spain

An individual-tree mortality model for radiata pine (Pinus radiata D. Don) plantations in northwestern Spain was developed. The model relies on data from three inventories of a network of 130 permanent plots. The equation that predicts the probability of complete survival is a logistic function, which depends on tree size and competition (diameter, mean-squared diameter, stand basal area, dominant height and BALMOD competition index). Several methods of implementing the mortality model were tested (deterministic versus stochastic threshold selection and the use of expansion factors). The best results were obtained when using a fixed cut-off value to decide which trees would survive to the next growing period. When a cut-off value of 0.55 was applied, the model correctly classified 99% of the live trees and 25% of the dead trees. A cut-off of 0.71 provided an estimated mortality rate that was closest to the observed rate. With this cut-off value, the model correctly classified 95% of the live trees and 47% of the dead trees. This cut-off value is recommended when using the model to predict radiata pine individual-tree mortality in the study area.     

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

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

Individual-tree height-, diameter- and crown-width increment equations for young Douglas-fir plantations

This work presents the results from the initial model development of a simulator to predict vegetation dynamics in young plantations growing in a Mediterranean environment. The simulator can predict growth dynamics for coniferous crop trees as well as competing hardwoods and shrubs. Model specification included conifer, shrub, and hardwood competition expressed at the plot-level. The system employs water-holding capacity as an indicator of productivity. Growth data were obtained from 109 plantations, ranging in age from 3 to 25, in southern Oregon and northern California. Douglas-fir (Pseudotsuga menziesii Mirb. Franco), the most common conifer species, was observed in 80 of the sampled stands. These observations were used for model development of the primary driving functions, which forecast 2-year basal diameter increment, height increment, and crown width increment. Parameters for all three dynamic expressions for growth were estimated using weighted, nonlinear three-stage least squares. This estimation method provided a predictive model with slight improvements in standard errors for two of the three equations (an average of 3% for height and diameter growth) and no improvement for crown width, when compared with two-stage least squares. The system includes competition from shrubs and hardwoods in predictions of height growth, diameter growth and crown width increment. This allows individual-tree/distance-independent simulator architecture to be extended to young plantations in southern Oregon and northern California.     

Predicting and calibrating diameter distributions of Eucalyptus grandis (Hill) Maiden plantations in Zimbabwe

Diameter distribution models for even-aged Eucalyptus grandis plantations in Zimbabwe were developed using the two-parameter Weibull function. The analysis was based on data from Correlated Curve Trend (CCT) experiments replicated on four different sites. Parameters of the Weibull distribution were predicted using stand characteristics as regressors. Two sets of parameter models were estimated: a set with and one without stand basal area as a predictor. Stand variables such as dominant height, age, site index and number of stems were used in both sets. The models were further calibrated to result in a given number of stems and stand basal area simultaneously. The usability of constructed models was tested both in prediction of yield in a stand inventory situation and in simulation of growth in connection with different growth models. The results indicated that models not including stand basal area produce considerably less precise stand volume estimates compared to models including also stand basal area. Calibration improved the accuracy of diameter distribution models. In growth simulation diameter distribution models can be connected both to single tree growth models and to stand projection models. The usability of calibration in growth simulation depends on the accuracy of the prediction of stand characteristics.     

GROWTH AND YIELD MODELS FOR DAHURIAN LARCH PLANTATIONS

Growth and yield models were developed for individual tress and stands based on336 temporary plots with 405 stem analysis trees of dahurian larch(Larix gmelinii(Rupr.)Rupr.)plantations throughout Daxing’anling mountains.Several equations were selected using nonlinearregression analysis.Results showed that the Richards equation was the best model for estimatingtree height,stand mean helght and stand dominant height from age; The Power equation was thebest model for prediction tree volume from DBH and tree height; The logarithmic stand volumeequation was good for predicting stand volume from age,mean height,basal area and other standvariables.These models can be used to construct the volume table, the site index table and other for-estry tables for dahurian larch plantations.     

Application of theoretical growth functions for Mongolian oak (Qurcus mongolica)

Four alternative functions are used for fitting tree height and diameter growth models for mongolian oak. (Quercus mongolica Fisch. et Turcz.). The data set includes 1250 random trees and 755 dominant trees coming from 510 temporary plots. The resultsshow that the Richards function is the best model for predicting height. diameter at breast height (DBH) and dominant height from age. The average growth curve of dominant height is used as a guide curve for the construction of a site index table which is partially validated using an independent data set. The Mitscherlich function is the best model for estimating height and dominant height from DBH. (Responsible Editor: Chai Ruihai)     

马尾松人工速生丰产林林分生长模拟与最适密度管理技术研究

以固定样地观测和临时样地调查相结合的办法收集林分现实生长与经间伐或间伐设计后所保留群体的生长资料;以固定样地观测资料为依据,以林分平均胸径连年生长量及胸径度离散度的指标,确定不同地位指数林分间伐的起始年龄;采用Ｒｉｃｈａｒｄｓ函数模拟合理密度与生长水平下的林分平均树高及胸径生长;并采用间伐或间伐设计前,后林分生长标准的调查资料,以地位级指数,林林分平均胸径及胸径离散度为自变量建立起人工速生丰产林的