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.     

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.     

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.     

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.     

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.     

Sugar maple (Acer saccharum Marsh.) growth is influenced by close conspecifics and skid trail proximity following selection harvest

In this study, we quantified the effects of local neighbourhood competition, light availability, and proximity to skid trails on the growth of sugar maple (Acer saccharum Marsh.) trees following selection harvest. We hypothesized that growth would increase with decreasing competition and increasing light availability, but that proximity to skid trails would negatively affect growth. A total of 300 sugar maples were sampled ∼10 years after selection harvesting in 18 stands in Témiscamingue (Québec, Canada). Detailed tree and skid trail maps were obtained in one 0.4 ha plot per stand. Square-root transformed radial growth data were fitted to a linear mixed model that included tree diameter, crown position, a neighbourhood competition index, light availability (estimated using the SORTIE light model), and distance to the nearest skid trail as explanatory variables. We considered various distance-dependent or -independent indices based on neighbourhood radii ranging from 6 to 12 m. The competition index that provided the best fit to the data was a distance-dependent index computed in a 6 m search radius, but a distance-independent version of the competition index provided an almost equivalent fit to data. Models corresponding to all combinations of main effects were fit to data using maximum likelihood, and weighted averages of parameter estimates were obtained using multimodel inference. All predictors had an influence on growth, with the exception of light. Radial growth decreased with increasing tree diameter, level of competition and proximity to skid trails, and varied among crown positions with trees in suppressed and intermediate positions having lower growth rates than codominants and dominants. Our results indicate that in selection managed stands, the radial growth of sugar maple trees depends on competition from close (≤6 m) conspecific neighbours, and is still affected by proximity to skid trails ∼10 years after harvesting. Such results underscore the importance of minimizing the extent of skid trail networks by careful pre-harvest planning of trail layout. We also conclude that the impact of heterogeneity among individual-tree neighbourhoods, such as those resulting from alternative spatial patterns of harvest, can usefully be integrated into models of post-harvest tree growth.     

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.     

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.     

A tree distance-dependent growth and yield model for naturally regenerated pure uneven-aged maritime pine stands in central inland of Portugal

? Context

Maritime pine (Pinus pinaster Aiton) is one of the most important Portuguese species, growing in pure stands ranging from even-aged to multi-aged structures. Current growth and yield models were developed only for even-aged, managed stands and/or for very specific regions of Portugal.

? Aims

This paper focuses on the validation of the existing size-class model PBRAVO, adapted to even-aged stands, and on the subsequent development of a single tree distance-dependent growth and yield model (PBIRROL), both in distance-independent and distance-dependent versions, for uneven-aged stands.

? Methods

The new model is composed of four modules, each with a set of sub-models for: tree variable prediction, tree volume prediction, future tree list prediction and growth projection.

? Results

The evaluation of the PBRAVO and PBIRROL models showed that the new model gives more accurate predictions. Moreover, medium-term simulations provided consistent and logical predictions.

? Conclusion

It was verified that individual tree models are more suited to simulate poorly managed uneven-aged stands than diameter distribution models. No clear superiority of distance-dependent models was found over models using just distance-independent measures of inter-tree competition.     

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.     

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.     

Growth models for Pinus patula in Angola

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

Growth responses of West-Mediterranean Pinus nigra to climate change are modulated by competition and productivity: Past trends and future perspectives

Positive and negative effects of climate change on forest growth have been observed in different parts of the world. However, much is still unknown about how forest structure and productivity might affect climate-growth relationships in the future. We examined the effects of climate, site quality, and competition on tree basal area growth of black pine (Pinus nigra Arn.) between 1964 and 2005 in 21 sites in the Iberian Peninsula. We used a new approach to simultaneously account for climate-growth relationships, inter-annual growth variability, and stand structural changes, by fitting a linear mixed effects model (LMEM) for basal area increments (BAI) using climate data, tree-ring chronologies, and repeated forest inventory data. This approach showed the potential to improve our understanding of climate effects on tree growth and to include climate in empirical forest growth models. We used the LMEM to make projections of BAI growth under two CO₂ emission scenarios and two global circulation models (GCM). The main climate drivers for growth were precipitation from previous autumn to summer and winter temperature with a positive effect, and temperature in spring-summer which had a negative effect. Tree response to climate was modulated by stand conditions, tree competition, and productivity. The more productive stands showed greater ability to either maintain or increase growth at warmer spring-summer temperatures under different levels of autumn-summer precipitation. Growth projections showed important regional differences. In general, growth under future climate is predicted to decrease although moderate growth increases might be expected in the northern region for highly and moderately productive stands.     

Spruce diameter growth in young mixed stands of Norway spruce (Picea abies (L.) Karst.) and birch (Betula pendula Roth B. pubescens Ehrh.)

A stand-based model for predicting basal-area mean diameter growth for Norway spruce (Picea abies (L.) Karst.) in young mixed stands of spruce and birch (Betula pendula Roth, B. pubescens Ehrh.) was developed and compared with two existing growth models developed for older stands. The main data were from experiments with four different pre-commercial thinning regimes. A multiplicative model with four independent variables was found suitable. The independent variables were total number of trees per hectare of all the species, site index, dominant height of spruce, and a measure of competition between birch and spruce, i.e. dominant height of spruce divided by the dominant height of birch multiplied by the proportion of spruce of total number of trees. The R² value was 0.59 and the coefficient of variation was 12%. A test with an independent data set from the National Forest Inventory (NFI) indicated that the function developed in this study is suitable for young stands at medium to highly productive areas. Large deviations between observed and predicted growth for the two existing functions were revealed in highly productive stands. The tests based on data from the NFI also indicated that the existing function developed for spruce in older mixed stands is suitable for practical purposes for young stands.     

Stand structure, competition and growth of Scots pine (Pinus sylvestris L.) in a Mediterranean mountainous environment

The relationship between competition and tree growth was studied in four stands of Pinus sylvestris L. occurring in a continental Mediterranean mountain area (in the Guadarrama range, Spain), i.e., an uneven-aged stand, a stand with oak (Quercus pyrenaica Willd.) understorey, a plantation, and a mature even-aged stand. Competition was measured by a simple size-ratio distance-independent index and was negatively associated with tree diameter. This negative association was stronger in the uneven-aged, plantation and mature even-aged stands than in the stand with oak understorey. Competition was also negatively associated with current diameter increment. This relationship was moderately strong in the mature even-aged stand and weak in the uneven-aged stand and the plantation. In the uneven-aged and the mature even-aged stands, a weakly significant relationship was found between diameter growth and tree size, whereas these parameters were not associated in the stand with oak understorey. The competition index provided a better prediction of growth rate than the alternative use of diameter. Both diameter and basal area growth were greater in the uneven-aged than in the even-aged 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.     

Modeling individual-tree growth in stands under forest conversion in East Germany

One major result of forest conversion in Saxony, East Germany, is the increasing importance of two-storied stands composed of a conifer canopy and a deciduous-tree understory. To enhance the applicability of the growth and yield simulator BWINPro under these conditions, three of its major sub-models were adapted to the regional growing conditions and to the relatively high level of diversity in spatial structure, mixture of species, and age variability typical for forests in conversion: (1) A new module for simulating single-tree juvenile growth was developed for European beech and Common oak under canopies of Norway spruce and Scots pine. Predictions in this sub-model are derived from individual height, diameter at breast height (dbh), and the influences of horizontal and vertical competition; (2) An alternative distance-dependent competition index was introduced to estimate individual basal area increment according to tree-specific growing conditions; (3) A modified logistic mortality model was parameterized for the most important Saxon species based on tree dimensions and basal area increment. Data came from permanent sample plots distributed throughout the region and from three chronosequence plot series established specifically for obtaining model input data. The new components were included into the existing structure of BWINPro. As a result of the adaption, the regional version BWINPro-S provides enhanced opportunities of planning and management for forest conversion and for multi-storied stands.     

Influence of umbrella pine (<Emphasis Type="Italic">Pinus</Emphasis><Emphasis Type="Italic">pinea</Emphasis> L.) stand type and tree characteristics on cone production

Most umbrella pine (Pinus pinea L.) stands are managed as agroforestry systems, whose main production is fruit, due to the edible and highly nutritious kernels, and are frequently associated to natural or seeded pastures and grazing. The stands have low density, in order to enhance crown growth and fruit production. Nevertheless, cone production, both with regard to number and weight, varies greatly between stands, trees and years. In this study were selected three agroforestry systems, representative of umbrella pine stands whose main production is fruit, and one stand representative of the timber production system, where fruit is the secondary production. It was evaluated the variability in cone production as a function of the tree’s diameter at breast height and crown diameter and the individual tree’s competition status. The results indicate that stands managed in agroforestry systems with lower competition and individuals with larger diameter at breast height and crown diameter tend to produce more and heavier cones per tree. The first two principal components of the principal component analysis explain 84 % of the variance in cone production, trees’ dimensions and competition index. Tree competition status has a negative impact on production per tree.     

Development of a linear mixed-effects individual-tree basal area increment model for masson pine in Hunan Province,South-central China

ABSTRACT

An individual-tree basal area increment model was developed for masson pine based on 26276 observations of 13,138 trees in 987 sample plots from the 7th (2004), 8th (2009), and 9th (2014) Chinese National Forest Inventory in Hunan Province, South-central China. The model was built using a linear mixed-effects approach with sample plots included as random effects since the data have a hierarchical stochastic structure and biased estimates of the standard error of parameter estimates could be a consequence of applying ordinary least square (OLS) for regression. In addition, within-plot heteroscedasticity and autocorrelation were also considered. The final mixed-effects model was determined according to the Akaike information criterion (AIC), Bayesian information criterion (BIC), log-likelihood (Loglik), and the likelihoodratio test (LRT). The results revealed that initial diameter (DBH), the sum of the basal area (m²/ha) in trees with DBHs larger than the DBH of the subject tree (BAL), number of trees per hectare (NT), and elevation (EL) had a significant impact on individual-tree basal area increment. The mixed-effects model performed much better than the basic model produced using OLS. Additionally, the variance structure of the model errors was successfully modeled using the power function. However, the autocorrelation structures were not defined because there was no autocorrelation amongst the data. It is believed that the final model will contribute to the scientific management of the masson pine.     

Modelling the edge effect in even-aged Monterey pine (Pinus radiata D. Don) stands

Six edge effect models are presented. Modelling results for the edge effect on the DBH, total height, crown height, and basal area in even-aged stands of Monterey pine (Pinus radiata D. Don) are provided. Free edges and edges under external competition pressure were analysed. Model fitting was carried out in two phases. In the first phase, independent fittings for each border type by sampled cardinal point in each stand were carried out to detect differences in edge effect intensity and depth according to edge aspect. In the second fitting phase, the best models selected by edge aspect in the first phase were restricted to estimate the same value for each variable in the stand interior, independently of the border where it was analysed.

The edge effect intensity and depth varied depending on the analysed variable and edge type. Modelling of the edge effect on DBH and total height on free edges of old stands requires a model with independent parameters for each border aspect; the models can be restricted to estimate the average value of each variable in stand interior. A model with independent parameters for each border aspect should be also used for modelling the effect on total height, crown height and basal area for the edges of young stands under external competition pressure. The modelling of basal area and crown height on free edges of old stands, DBH on edges of young stands under external competition pressure, and all variables mentioned on free edges of young stands can be carried out through an average fitting. DBH and basal area are directly affected by stand density; thus, modelling of edge effect on these and others variables which are affected by stand density can improve with the inclusion of a competition index or a point density index.