Current issue: 56(1)

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Scopus CiteScore 2019: 3.1
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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles containing the keyword 'growth model'.

Category: Research article

article id 10055, category Research article
Jaakko Repola, Hannu Hökkä, Hannu Salminen. (2018). Models for diameter and height growth of Scots pine, Norway spruce and pubescent birch in drained peatland sites in Finland. Silva Fennica vol. 52 no. 5 article id 10055.
Highlights: Tree growth strongly correlated with site drainage status; Between-tree competition had a higher impact on tree diameter growth than on height growth; Growth predicted by the constructed models were calibrated using NFI11 data to ensure generally applicable growth predictions level in whole country.

The aim of this study was to develop individual-tree diameter and height growth models for Scots pine, Norway spruce, and pubescent birch growing in drained peatlands in Finland. Trees growing in peatland sites have growth patterns that deviate from that of trees growing in mineral soil sites. Five-year growth was explained by tree diameter, different tree and stand level competition measures, management operations and site characteristics. The drainage status of the site was influencing growth directly or in interaction with other variables. Site quality had a direct impact but was also commonly related to current site drainage status (need for ditch maintenance). Recent thinning increased growth of all species and former PK fertilization increased growth of pine and birch. Temperature sum was a significant predictor in all models and altitude for spruce and birch. The data were a subsample of the 7th National Forest Inventory (NFI) sample plots representing northern and southern Finland and followed by repeated measurements for 15–20 yrs. Growth levels predicted by the models were calibrated using NFI11 data to remove bias originating from the sample of the modelling data. The mixed linear models technique was used in model estimation. The models will be incorporated into the MOTTI stand simulator to replace the current peatlands growth models.

  • Repola, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: (email)
  • Hökkä, Natural Resources Institute Finland (Luke), Natural resources, Paavo Havaksen tie 3, FI-90014 University OF Oulu, Finland ORCID ID:E-mail:
  • Salminen, Natural Resources Institute Finland (Luke), Natural resources, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail:
article id 5662, category Research article
Samuel Egbäck, Urban Nilsson, Kenneth Nyström, Karl-Anders Högberg, Nils Fahlvik. (2017). Modeling early height growth in trials of genetically improved Norway spruce and Scots pine in southern Sweden. Silva Fennica vol. 51 no. 3 article id 5662.
Highlights: The developed height growth model based on unimproved material predicted the development relatively well for genetically improved Norway spruce; For genetically improved Scots pine, however, the model needed to be modified; By incorporating a genetic component into the Scots pine model, the prediction errors were reduced.

Genetically improved Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.) are used extensively in operational Swedish forestry plantations to increase production. Depending on the genetic status of the plant material, the current estimated genetic gain in growth is in the range 10–20% for these species and this is expected to increase further in the near future. However, growth models derived solely from data relating to genetically improved material in Sweden are still lacking. In this study we investigated whether an individual tree growth model based on data from unimproved material could be used to predict the height increment in young trials of genetically improved Norway spruce and Scots pine. Data from 11 genetic experiments with large genetic variation, ranging from offspring of plus-trees selected in the late 1940s to highly improved clonal materials selected from well performing provenances were used. The data set included initial heights at the age of 7–15 years and 5-year increments for almost 2000 genetic entries and more than 20 000 trees. The evaluation indicated that the model based on unimproved trees predicted height development relatively well for genetically improved Norway spruce and there was no need to incorporate a genetic component. However, for Scots pine, the model needed to be modified. A genetic component was developed based on the genetic difference recorded within each trial, using mixed linear models and methods from quantitative genetics. By incorporating the genetic component, the prediction errors were significantly reduced for Scots pine. This study provides the first step to incorporate genetic gains into Swedish growth models and forest management planning systems.

  • Egbäck, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden ORCID ID:E-mail: (email)
  • Nilsson, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden ORCID ID:E-mail:
  • Nyström, Swedish University of Agricultural Sciences, Department of Forest Resource Management, Skogsmarksgränd, 901 83 Umeå, Sweden ORCID ID:E-mail:
  • Högberg, Skogforsk, Ekebo, 268 90 Svalöv, Sweden ORCID ID:E-mail:
  • Fahlvik, Swedish University of Agricultural Sciences, Southern Swedish Forest Research Centre, P.O. Box 49, 230 53 Alnarp, Sweden ORCID ID:E-mail:
article id 1192, category Research article
Hannu Hökkä, Hanna Mäkelä. (2014). Post-harvest height growth of Norway spruce seedlings in northern Finland peatland forest canopy gaps and comparison to partial and complete canopy removals and plantations. Silva Fennica vol. 48 no. 5 article id 1192.
Highlights: Norway spruce seedlings’ height growth recovered within four years after the cutting of canopy gaps; Growth was linearly related to tree height, being highest for tallest seedlings; Seedlings in the 20 m diameter gap and in the central and northern parts in the 15 m diameter gap showed the best growth; In gaps early height growth was 60% of that in peatland spruce plantations but 2–3 times higher than in uneven-aged cut forests.
Recent studies have shown the establishment of Norway spruce (Picea abies (L.) Karst.) to be successful in small canopy gaps cut in drained spruce mire stands in northern Finland. The aim of this study was to quantify seedling height growth in gaps and compare it to that observed in other canopy cuttings and plantations. We sampled spruce crop seedlings (maximum density ca. 3000 ha–1) in the spring of 2013 in a field experiment in which canopy gaps of 10, 15 and 20 m in diameter had been cut in winter 2004. The total seedling height in 2013 and the length of annual shoots over the past five years (2012–2008) were recorded in the survey. Seedling height varied from 20 cm to 2.7 m, with an average of 65 cm. The average annual height growth was 7.1 cm. A mixed linear model analysis was carried out to investigate seedling height growth variation. Seedling height was linearly and positively related to growth. Height growth started to increase in the fifth growing season after cutting. Seedling height growth in the 20 m gap was slightly better than in the smaller ones. In the 15 m gap, both the centrally located seedlings and those located at the northern edge grew best. In the 20 m gap, southerly located seedlings grew more slowly than seedlings in all other locations. The average seedling height growth in this study was about 60% of that in peatland plantations, but comparable to that in mineral soil gaps, and 2–3 times higher than in uneven-age cut stands.
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Unit, Eteläranta 55, FI-96300 Rovaniemi, Finland ORCID ID:E-mail: (email)
  • Mäkelä, Lapland University of Applied Sciences, Jokiväylä 11 C, FI-96300 Rovaniemi, Finland ORCID ID:E-mail:
article id 1019, category Research article
Michael Henke, Stephan Huckemann, Winfried Kurth, Branislav Sloboda. (2014). Reconstructing leaf growth based on non-destructive digitizing and low-parametric shape evolution for plant modelling over a growth cycle. Silva Fennica vol. 48 no. 2 article id 1019.
Highlights: A complete pipeline for plant organ modelling (at the example of poplar leaves) is presented, from non-destructive data acquisition, over automated data extraction, to growth and shape modelling; Leaf contour models are compared; Resulting “organ” modules are ready for use in FSPMs.
A simple and efficient photometric methodology is presented, covering all steps from field data acquisition to binarization and allowing for leaf contour modelling. This method comprises the modelling of area and size (correlated and modelled with a Chapman-Richards growth function, using final length as one parameter), and four shape descriptors, from which the entire contour can be reconstructed rather well using a specific spline methodology. As an improvement of this contour modelling method, a set of parameterized polynomials was used. To model the temporal kinetics of the shape, geodesics in shape spaces were employed. Finally it is shown how this methodology is integrated into the 3D modelling platform GroIMP.
  • Henke, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany ORCID ID:E-mail: (email)
  • Huckemann, Institute of Mathematical Stochastics, University of Göttingen, 37077 Göttingen, Germany ORCID ID:E-mail:
  • Kurth, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany ORCID ID:E-mail:
  • Sloboda, Department Ecoinformatics, Biometrics & Forest Growth, University of Göttingen, 37077 Göttingen, Germany ORCID ID:E-mail:
article id 262, category Research article
Julian C. Fox, Huiquan Bi, Peter K. Ades. (2008). Modelling spatial dependence in an irregular natural forest. Silva Fennica vol. 42 no. 1 article id 262.
The spatial dependence present in a natural stand of Eucalyptus pilularis (Smith) dominated mixed species forest was characterised and modelled. Two wildfires imposed a significant spatial dependence on the post disturbance stand. It was hypothesised that spatial variation in the intensity of the wildfires generated the observed structures. The influence of patch formation, micro-site variability and competitive influences were also noted in the residuals of a distance-dependent individual-tree growth model. A methodology capable of modelling these complicated patterns of observed dependence was sought, and candidates included the spatial interaction, direct specification and Papadakis methods. The spatial interaction method with a moving average autoregression was identified as the most appropriate method for explicitly modelling spatial dependence. Both the direct specification and Papadakis methods failed to capture the influence of competition. This study highlights the possibility that stand disturbances such as natural and artificial fires, insect and fungal attacks, and wind and snow damage are capable of imposing powerful spatial dependencies on the post disturbance stand. These dependencies need to be considered if individual tree growth models are to provide valid predictions in disturbed stands.
  • Fox, School of Forest and Ecosystem Science, University of Melbourne, Burnley Campus, 500 Yarra Blvd, Richmond, Victoria 3121 Australia ORCID ID:E-mail: (email)
  • Bi, Forest Resources Research, New South Wales Department of Primary Industries, PO Box 100, Beecroft, NSW 2119 Australia ORCID ID:E-mail:
  • Ades, School of Forest and Ecosystem Science, University of Melbourne, Burnley Campus, 500 Yarra Blvd, Richmond, Victoria 3121 Australia ORCID ID:E-mail:
article id 320, category Research article
Saija Huuskonen, Jari Hynynen. (2006). Timing and intensity of precommercial thinning and their effects on the first commercial thinning in Scots pine stands. Silva Fennica vol. 40 no. 4 article id 320.
The effects of the timing and intensity of precommercial thinning on the stand diameter development and wood production in Scots pine stands was addressed. A model was developed in order to assess the thinning response of the stand diameter development. The effect of precommercial and first commercial thinning on the stand volume and the thinning removal at first commercial thinning were also modelled. The models were developed to be applicable for forest management planning purposes. The results are based on Scots pine (Pinus sylvestris L.) trials (13 experiments and 169 plots) located in Southern and Central Finland. Precommercial thinning considerably enhanced the diameter development. Precommercial thinning (at Hdom 3 m to 2000 trees per hectare) increased the mean diameter by 15% at the first commercial thinning stage (Hdom 14 m) compared to the unthinned stand (3000 trees ha–1). Early and intensive precommercial thinning resulted in the strongest response in diameter development. Wide spacing also enhanced the diameter increment. In naturally regenerated stands the diameter development was ca 13% slower than that in seeded stands. The total volume at the time of first commercial thinning was affected by the timing of thinning and the stand structure. The volume of merchantable thinning removal depended on the timing and intensity of precommercial and first commercial thinnings. Delaying the first commercial thinning from 12 meters (Hdom) to 16 meters increased the volume of thinning removal by ca.70%. The early and light precommercial thinning (Hdom 3 m, to density of 3000 trees per hectare) increased the thinning removal by 40% compared to the late and intensive precommercial thinning (at 7 meters to the density of 2000 trees per hectare).
  • Huuskonen, University of Helsinki, Dept. of Forest Ecology, P.O. Box 27, FI-00014 University of Helsinki, Finland ORCID ID:E-mail:
  • Hynynen, The Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland ORCID ID:E-mail:
article id 409, category Research article
Hubert Sterba. (2004). Equilibrium curves and growth models to deal with forests in transition to uneven-aged structure – application in two sample stands. Silva Fennica vol. 38 no. 4 article id 409.
Stem number distributions in uneven-aged forests are assumed to be stable, if they follow special functions, e.g. de Liocourt’s reverse J-shaped breast height diameter distribution. These distributions therefore are frequently regarded as a target in all-aged forests. Intending to convert an even-aged forest or any other forest, not yet exhibiting this sort of equilibrium, towards a steady state forest, the question rises, how to choose an appropriate equilibrium curve and how to achieve this stem number distribution by an appropriate thinning and harvesting schedule. Two stands are investigated: One dominated by Norway spruce (Picea abies), having developed from a 120 year old even-aged stand 25 years ago, after several “target diameter thinnings”. The other one is a mixed species stand of Norway spruce, white fir (Abies alba), larch (Larix europea), common beech (Fagus silvatica), and Scots pine (Pinus sylvestris), having lost its typical uneven-aged structure 20 years ago. These stands were used, together with the distance independent individual tree growth model PrognAus, to reveal that 1) there are more than only one equilibrium curve per stand, 2) not every hypothesised equilibrium can be reached with any stand, 3) an equilibrium in stem number does not necessarily mean a stable species distribution, and 4) growth models provide an excellent help to decide between several equilibrium curves and harvesting schedules to reach them.
  • Sterba, BOKU – University of Natural Resources an Applied Life Sciences, Vienna, Peter Jordanstrasse 82, A-1190 Vienna, Austria ORCID ID:E-mail: (email)
article id 524, category Research article
Timo Pukkala, Jari Miina, Marc Palahí. (2002). Thinning response and thinning bias in a young Scots pine stand. Silva Fennica vol. 36 no. 4 article id 524.
The study analyses the annual post-thinning response and thinning bias of a young Scots pine stand as a function of tree size, competition faced by the tree, and competition that is removed around the tree in the thinning treatment. The thinning response of a tree was defined as the change of tree growth due to a thinning treatment. The thinning bias was defined as the difference between the true growth and model prediction. A distance-dependent (spatial) and a distance-independent (non-spatial) growth model were used in the calculations. The empirical data were measured from a thinning experiment consisting of ten plots, each 40 x 30 m in size, which were thinned to different stand densities. The ten-year post-thinning growth of every remaining tree was measured. The results indicated that the highest thinning response is among medium-sized and co-dominant trees. The thinning response is quite small, and even negative for some trees, for two years after thinning but it becomes clearly positive from the third year onwards. The spatial model underestimated the growth of small trees (which usually face high competition) while the non-spatial model overestimated the growth of trees that are small or face much competition. The spatial model used in this study overemphasized the effect of competition while the non-spatial model underestimated this effect. Both growth models overestimated the growth of trees in heavily thinned places, but this bias disappeared in two years. The negative bias was more pronounced with a spatial growth model because the tendency of the non-spatial model to underestimate the growth of trees facing little competition partly compensated for the negative bias.
  • Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland ORCID ID:E-mail: (email)
  • Miina, Finnish Forest Research Institute, Joensuu Research Centre, P.O. Box 68, FIN-80101 Joensuu, Finland ORCID ID:E-mail:
  • Palahí, European Forest Institute, Torikatu 34, FIN-80100 Joensuu, Finland ORCID ID:E-mail:
article id 580, category Research article
Susanna Sironen, Annika Kangas, Matti Maltamo, Jyrki Kangas. (2001). Estimating individual tree growth with the k-nearest neighbour and k-Most Similar Neighbour methods. Silva Fennica vol. 35 no. 4 article id 580.
The purpose of this study was to examine the use of non-parametric methods in estimating tree level growth models. In non-parametric methods the growth of a tree is predicted as a weighted average of the values of neighbouring observations. The selection of the nearest neighbours is based on the differences between tree and stand level characteristics of the target tree and the neighbours. The data for the models were collected from the areas owned by Kuusamo Common Forest in Northeast Finland. The whole data consisted of 4051 tally trees and 1308 Scots pines (Pinus sylvestris L.) and 367 Norway spruces (Picea abies Karst.). Models for 5-year diameter growth and bark thickness at the end of the growing period were constructed with two different non-parametric methods: the k-nearest neighbour regression and k-Most Similar Neighbour method. Diameter at breast height, tree height, mean age of the stand and basal area of the trees larger than the subject tree were found to predict the diameter growth most accurately. The non-parametric methods were compared to traditional regression growth models and were found to be quite competitive and reliable growth estimators.
  • Sironen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland ORCID ID:E-mail: (email)
  • Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland ORCID ID:E-mail:
  • Maltamo, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland ORCID ID:E-mail:
  • Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland ORCID ID:E-mail:
article id 595, category Research article
Kenneth Nyström, Göran Ståhl. (2001). Forecasting probability distributions of forest yield allowing for a Bayesian approach to management planning. Silva Fennica vol. 35 no. 2 article id 595.
Probability distributions of stand basal area were predicted and evaluated in young mixed stands of Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) Karst.) and birch (Betula pendula Roth and Betula pubescens Ehrh.) in Sweden. Based on an extensive survey of young stands, individual tree basal area growth models were estimated using a mixed model approach to account for dependencies in data and derive the variance/covariance components needed. While most of the stands were reinventoried only once, a subset of the stands was revisited a second time. This subset was used to evaluate the accuracy of the predicted stand basal area distributions. Predicting distributions of forest yield, rather than point estimates, allows for a Bayesian approach to planning and decisions can be made with due regard to the quality of the information.
  • Nyström, SLU, Department of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden ORCID ID:E-mail: (email)
  • Ståhl, SLU, Department of Forest Resource Management and Geomatics, SE-901 83 Umeå, Sweden ORCID ID:E-mail:
article id 603, category Research article
Kari Minkkinen, Jukka Laine, Hannu Hökkä. (2001). Tree stand development and carbon sequestration in drained peatland stands in Finland – a simulation study. Silva Fennica vol. 35 no. 1 article id 603.
Drained peatland forests form an important timber resource in Finland. They also form a sink for atmospheric carbon (C) because of the increased growth and C sequestration rates following drainage. These rates have, however, been poorly quantified. We simulated the tree stand dynamics for drained peatland stands with and without cuttings over two stand rotations. Simulations were done on four peatland site types and two regions in Finland with different climatic conditions, using recently published peatland tree growth models applied in a stand simulator. We then calculated the amount of C stored in the stands on the basis of previously published tree-level biomass and C content models. Finally, we developed regression models to estimate C stores in the tree stands using stand stem volume as the predictor variable. In the managed stands, the mean growth (annual volume increment) ranged from 2 to 9 m3 ha–1 a–1, depending on the rotation (first/second), site type and region. Total yield during one rotation varied from 250 to 920 m3 ha–1. The maximum stand volumes varied from 220 to 520 m3 ha–1 in the managed stands and from 360 to 770 m3 ha–1 in the unmanaged. By the end of the first post-drainage rotation the total C store in the managed stands had increased by 6–12 kg C m–2 (i.e. 45–140 g C m–2 a–1) compared to that in the undrained situation. Averaged over two rotations, the increase in the total C store was 3–6 kg C m–2. In the corresponding unmanaged stands the C stores increased by 8–15 kg m–2 over the same periods. At stand level, the C stores were almost linearly related to the stem volume and the developed regression equations could explain the variation in the simulated C stores almost entirely.
  • Minkkinen, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland ORCID ID:E-mail: (email)
  • Laine, University of Helsinki, Department of Forest Ecology, P.O. Box 27, FIN-00014 University of Helsinki, Finland ORCID ID:E-mail:
  • Hökkä, Finnish Forest Research Institute, Rovaniemi Research Station, P.O. Box 16, FIN-96301 Rovaniemi, Finland ORCID ID:E-mail:
article id 670, category Research article
Jouni Vettenranta. (1999). Distance-dependent models for predicting the development of mixed coniferous forests in Finland. Silva Fennica vol. 33 no. 1 article id 670.
Distance-dependent growth models and crown models, based on extensive material, were built for Scots pine and Norway spruce growing in a mixed forest. The crown ratio was also used as a predictor in a diameter growth model to better describe the thinning reaction. The effect of crown ratio on the growth dynamics was studied in simulation examples. Monte Carlo simulation was used to correct the bias caused by nonlinear transformations of predictors and response. After thinnings the crown ratio as a predictor was found to be a clear growth-retarding factor. The growth retarding effect was stronger among pines with thinnings from below, whereas the estimated yield of spruces over rotation was slightly greater when the crown ratio was included than without it. With each type of thinning the effect of crown ratio on pine growth was almost the same, but the growth of spruces was clearly delayed when the stand was thinned from above. Simulation examples also showed that it is profitable to raise the proportion of spruces during rotation, since spruces maintain the growth more vigorous at older ages. The total yield during 90 years rotation was about 20% higher if the stand was transformed into a pure spruce stand instead of pine.
  • Vettenranta, Kivirinnanpolku 4, FIN-40950 Muurame, Finland ORCID ID:E-mail: (email)

Category: Article

article id 5632, category Article
Annikki Mäkelä, Veli-Pekka Ikonen, Petteri Vanninen. (1997). An application of process-based modelling to the development of branchiness in Scots pine. Silva Fennica vol. 31 no. 3 article id 5632.

A process-oriented tree and stand growth model is extended to be applicable to the analysis of timber quality, and how it is influenced by silvicultural treatments. The tree-level model is based on the carbon balance and it incorporates the dynamics of five biomass variables as well as tree height, crown base, and breast height diameter. Allocation of carbon is based on the conservation of structural relationships, in particular, the pipe model. The pipe-model relationships are extended to the whorl level, but in order to avoid a 3-dimensional model of entire crown structure, the branch module is largely stochastic and aggregated. In model construction, a top-down hierarchy is used where at each step down, the upper level sets constraints for the lower level. Some advantages of this approach are model consistency and efficiency of calculations, but probably at the cost of reduced flexibility. The detailed structure related with the branching module is preliminary and will be improved when more data becomes available. Model parameters are identified for Scots pine (Pinus sylvestris L.) in Southern Finland, and example simulations are carried out to compare the development of quality characteristics in different stocking densities.

  • Mäkelä, ORCID ID:E-mail:
  • Ikonen, ORCID ID:E-mail:
  • Vanninen, ORCID ID:E-mail:
article id 5629, category Article
Risto Sievänen, Eero Nikinmaa, Jari Perttunen. (1997). Evaluation of importance of sapwood senescence on tree growth using the model Lignum. Silva Fennica vol. 31 no. 3 article id 5629.

The effects of two alternative formulations of sapwood senescence on the behaviour of model LIGNUM (with parameter values adjusted for Scots pine (Pinus sylvestris L.) growing southern Finland) were studied. The two alternatives were autonomous sapwood senescence assuming a maximum age for the tree ring, and sapwood senescence that is controlled by the mortality of foliage. For the latter alternative two hypothetical further mechanisms were stipulated. All the formulations were implemented in LIGNUM. Simulations were made with all model variants for fertile and poor soil conditions using high, normal and low rates of foliage mortality. The simulation results were compared against of a data set consisting of 11 open grown Scots pine trees from southern Finland. Observations of heartwood proportion were used in this study. They show that heartwood starts to increase in trees from age of approximately 20 years onwards. The simulation results showed no differences between fertile and poor soil conditions as regards heartwood formation. Of the variants of foliage-controlled sapwood senescence the one where death of sapwood in a tree segment induces sapwood senescence in the tree parts below only slightly was the best. This and the autonomous sapwood senescence corresponded equally well to the observations. In order to make more refined conclusions additional data and simulations are necessary.

  • Sievänen, ORCID ID:E-mail:
  • Nikinmaa, ORCID ID:E-mail:
  • Perttunen, ORCID ID:E-mail:
article id 5616, category Article
Hannu Hökkä, Virpi Alenius, Timo Penttilä. (1997). Individual-tree basal area growth models for Scots pine, pubescent birch and Norway spruce on drained peatlands in Finland. Silva Fennica vol. 31 no. 2 article id 5616.

Models for individual-tree basal area growth were constructed for Scots pine (Pinus sylvestris L.), pubescent birch (Betula pubescens Ehrh.) and Norway spruce (Picea abies (L.) Karst.) growing in drained peatland stands. The data consisted of two separate sets of permanent sample plots forming a large sample of drained peatland stands in Finland. The dependent variable in all models was the 5-year basal area growth of a tree. The independent tree-level variables were tree dbh, tree basal area, and the sum of the basal area of trees larger than the target tree. Independent stand-level variables were stand basal area, the diameter of the tree of median basal area, and temperature sum. Categorical variables describing the site quality, as well as the condition and age of drainage, were used. Differences in tree growth were used as criteria in reclassifying the a priori site types into new yield classes by tree species. All models were constructed as mixed linear models with a random stand effect. The models were tested against the modelling data and against independent data sets.

  • Hökkä, ORCID ID:E-mail:
  • Alenius, ORCID ID:E-mail:
  • Penttilä, ORCID ID:E-mail:
article id 5607, category Article
Paola Virgilietti, Joseph Buongiorno. (1997). Modeling forest growth with management data: A matrix approach for the Italian Alps. Silva Fennica vol. 31 no. 1 article id 5607.

This paper reports on the possibility and difficulties in building growth models from past Forest Administration records on cut and growth in the Italian Alps. As a case study, a matrix model was calibrated for uneven-aged forests in the Valsugana valley of the Trentino province. The model gave reliable predictions over 30 years, and plausible long-term forest dynamics, including steady-states that are similar to virgin forests. The results support the view that the current forests are deeply altered as to composition, relative to what would obtain from natural growth. They also support the concept of long cyclic changes in natural stands, gradually approaching a climax state. Shortcomings of the data are that they do not come from an experimental design, they are not always accurate, and they must be supplemented with other information, especially concerning mortality. Still, these cheap and available data can lead to workable models adapted to local conditions, with many management applications.

  • Virgilietti, ORCID ID:E-mail:
  • Buongiorno, ORCID ID:E-mail:
article id 5574, category Article
Jouni Vettenranta. (1996). Effect of species composition on economic return in a mixed stand of Norway spruce and Scots pine. Silva Fennica vol. 30 no. 1 article id 5574.

The effect of species mixture was studied in a mixed stand of Norway spruce (Picea abies (L.) H. Karst.) and Scots pine (Pinus sylvestris L.) by simulating around 100 different treatment schedules during the rotation in a naturally regenerated even-aged stand located on a site of medium fertility in North Karelia, Finland. Both thinning from below and thinning from above were applied. Optimum rotations were determined by maximising the net present value calculated to infinity and different treatment schedules were compared with the net present value over one rotation as per rotation applied. In the optimum treatment programme, the proportion of pines was decreased by half of the basal area in the first thinning stage and by the end of the rotation to about one third. In thinning from above, the proportion of pines can be maintained at a slightly higher level. It is economically profitable to maintain the growing stock capital at approximately the level recommended by Forest Centre Tapio, a semi-governmental forestry authority. With non-optimum species composition, the loss in net present value over one rotation can be about 10 % in thinning from below and about 20 % in thinning from above.

  • Vettenranta, ORCID ID:E-mail:
article id 5559, category Article
Jari Hynynen. (1995). Predicting the growth response to thinning for Scots pine stands using individual-tree growth models. Silva Fennica vol. 29 no. 3 article id 5559.

Individual tree-growth models for diameter and height, and a model for the cylindrical stem form factor are presented. The aims of the study were to examine modelling methods in predicting growth response to thinning, and to develop individual-tree, distance-independent growth models for predicting the development of thinned and unthinned stands of Scots pine (Pinus sylvestris L.). The models were constructed to be applicable in simulation systems used in practical forest management planning. The models were based on data obtained from eleven permanent thinning experiments located in even-aged Scots pine stands in Southern and Central Finland.

Two alternative models were developed to predict tree diameter growth in thinned and unthinned stands. In the first model, the effect of stand density was described using stand basal area. In the alternative model, an explicit variable was incorporated referring to the relative growth response due to thinning. The magnitude of the growth response was expressed as a function of thinning intensity. The Weibull function was employed to describe the temporal distribution of the thinning response. Both models resulted in unbiased predictions in unthinned and in moderately thinned stands. An explicit thinning variable was needed for unbiased growth prediction in heavily thinned stands, and in order to correctly predict the dynamics of the growth response.

In the height growth model, no explicit thinnning variable referring thinning was necessary for growth prediction in thinned stands. The stem form factor was predicted using the model that included tree diameter and tree height as regressor variables. According to the results obtained, the information on the changes in the diameter/height ratio following the thinning is sufficient to predict the change in stem form.

  • Hynynen, ORCID ID:E-mail:
article id 5525, category Article
Jari Miina. (1994). Spatial growth model for Scots pine on drained peatland. Silva Fennica vol. 28 no. 1 article id 5525.

A spatial growth model is presented for Scots pine (Pinus sylvestris L.) on a dwarf-shrub pine mire drained 14 years earlier. The growth model accounts for the variation in tree diameter growth owing to the competition between trees, the distance between tree and ditch, and the time passed since drainage. The model was used to study the effect of tree arrangement on the post-drainage growth of a pine stand. Clustering of trees decreased the volume growth by 9–20% as compared to a regular spatial distribution. Stand volume growth, for a given number of stems, was at its maximum and variation in diameter growth at its minimum when the stand density on the ditch border was 1.5–5 higher than midway between two adjacent ditches.

  • Miina, ORCID ID:E-mail:
article id 5510, category Article
Esa Koistinen, Sauli Valkonen. (1993). Models for height development of Norway spruce and Scots pine advance growth after release in southern Finland. Silva Fennica vol. 27 no. 3 article id 5510.

Mixed linear models were constructed to describe the height development of Norway spruce (Picea abies (L.) H. Karst.) and Scots pine (Pinus sylvestris L.) advance growth after release cutting. The models related density of the overstory, time elapsed since release cutting and tree size with annual height increment. Parameters of preliminary models were estimated from a limited data set to judge the feasibility of the approach for further studies.

The PDF includes an abstract in Finnish.

  • Koistinen, ORCID ID:E-mail:
  • Valkonen, ORCID ID:E-mail:
article id 5388, category Article
Martti Varmola. (1989). Männyn istutustaimikoiden lustonleveysmalli. Silva Fennica vol. 23 no. 4 article id 5388.
English title: A model for ring width of planted Scots pine.

Ring width at breast height is presented as a function of stem radius at breast height, the ratio between the diameter of a tree and the basal area median diameter, site index, and density of stand. By means of a conversion model ring width at stump height can be estimated as a function of ring width at breast height.

According to previous studies substantially better wood quality can be expected if mean width near the pith at stump height decreases from 3 to 2 mm. According to the present study only on the poorest sites suitable for Scots pine (Pinus sylvestris L.) planting (poor Vaccinium type) the ring width is less than 3 mm at stump height even in the thickest trees. On more fertile sites a substantial increase in the recommended planting density is required, if the mean ring width is aimed to be less than 3 mm. On the best sites it is impossible to reach mean ring width of less than 2 mm, when the density is less than 4,000 stems/ha. Only the thinnest trees on the poorest sites can have a mean ring width less than 2mm.

The PDF includes an abstract in English.

  • Varmola, ORCID ID:E-mail:
article id 5376, category Article
Timo Pukkala. (1989). Predicting diameter growth in even-aged Scots pine stands with a spatial and non-spatial model. Silva Fennica vol. 23 no. 2 article id 5376.

The single tree growth models presented in this study were based on about 4,000 trees measured in 50 even-aged Scots pine (Pinus sylvestris L.) sample plots with varying density, spatial pattern of trees and stand age. Predictors that used information about tree locations decreased the relative standard error of estimate by 10 percentage points (15%), if past growth was not used as a predictor, and about 15 percentage points (30%) when past growth was one of the predictors. When ranked according to the degree of determination, the best growth models were obtained for the basal area increment, the next best for relative growth, and the poorest for diameter increment. The past growth decreased the relative standard error of estimate by 15–20 percentage points, but did not make the spatial predictors unnecessary. The degree of determination of the spatial basal area growth model was almost 80% if the past growth was unknown and almost 90% if the past growth was known. Variables that described the amount of removed competition did not improve the growth models.

The PDF includes an abstract in Finnish.

  • Pukkala, ORCID ID:E-mail:
article id 5338, category Article
Timo Pukkala. (1988). Effect of spatial distribution of trees on the volume increment of a young Scots pine stand. Silva Fennica vol. 22 no. 1 article id 5338.

The effect of grouping on 5-year old volume increment was studied by a simulation technique using spatial growth models estimated in Scots pine (Pinus sylvestris L.) stands in the phase of the first commercial thinning. A total of 24 model stands were regenerated by applying 12 spatial processes for two different diameter distributions. In addition to model stands, 6 different thinnings were simulated in two real stands. The clustering of trees was described with Fisher’s grouping index and by estimating the relative interception of diffuse radiation. In model stands with constant diameter distribution the correlation between the grouping index and volume increment ranged from -0.81 to -0.91. The correlation between volume increment and interception was 0.81–0.83 with one diameter distribution and 0.70 if both distributions were combined. In one thinned stand the correlation between the growth estimate and grouping index varied between -0.33 and 0.76. The correlation between interception and growth was about 0.30 in one stand and 0.72 if both stands were combined. Small irregularities do not decrease the volume production of a young Scots pine stand, but if the clustering is considerable or there are reasonably wide harvest strips, growth will be reduced by 10–20%.

The PDF includes a summary in Finnish.

  • Pukkala, ORCID ID:E-mail:
article id 7516, category Article
Euan G. Mason, A. Graham D. Whyte. (1997). Modelling initial survival and growth of radiata pine in New Zealand. Acta Forestalia Fennica no. 255 article id 7516.

A sensitive framework has been developed for modelling young radiata pine (Pinus radiata D. Don) survival, its growth and size class distribution, from time of planting to age 5 or 6 years. The data and analysis refer to the Central North Island region of New Zealand. The survival function is derived from a Weibull probability density function, to reflect diminishing mortality with the passage of time in young stands. An anamorphic family of trends was used, as very little between-tree competition can be expected in young stands. An exponential height function was found to fit best the lower portion of its sigmoid form. The most appropriate basal area/ha exponential function included an allometric adjustment which resulted in compatible mean height and basal area/ha models. Each of these equations successfully represented the effects of several establishment practices by making coefficients linear functions of site factors, management activities and their interactions. Height and diameter distribution modelling techniques that ensured compatibility with stand values were employed to represent the effects of management practices on crop variation. Model parameters for this research were estimated using data from site preparation experiments in the region and were tested with some independent data sets.

  • Mason, ORCID ID:E-mail:
  • Whyte, ORCID ID:E-mail:
article id 7681, category Article
Eero Nikinmaa. (1992). Analyses of the growth of Scots pine: matching structure with function. Acta Forestalia Fennica no. 235 article id 7681.

A theoretical framework to analyse the growth of Scots pine (Pinus sylvestris L.) is presented. Material exchange processes and internal processes that transport, transform and consume materials are identified as the components of growth. Hierarchical system is lined out. Momentary uptake of material at a single exchange site depends on the environmental condition next to the exchange site, the internal state of the biochemical system of the plant and the structure of the plant. The internal state depends on the exchange flows over period of time and the structural growth depends on the internal state. The response of these processes to the fluxes is controlled by the genetic composition of the plant.

The theoretical framework is formulated into a mathematical model. A concept of balanced internal state was applied to describe the poorly known internal processes. Internal substrate concentrations were assumed to remain constant but tissue-specific. A linear relationship between the quantity of foliage and wood cross-sectional area was assumed to describe balanced formation of structure. The exchange processes were thus described as a function of external conditions. The stand level interactions were derived from shading and effects of root density on nutrient uptake.

The approach was tested at different levels of hierarchy. Field measurements indicated that the hypothesis of the linear relationship described well the regularities between foliage and sapwood of a tree within a stand when measured at functionally corresponding height. There was considerable variation in the observed regularities in the range of geographic occurrence of Scots pine. Model simulations gave a realistic description of stand development in Southern Finland. The same model was also able to describe growth differences in Lapland after considering the effect of growing season length in the parameter values. Simulations to South Russia indicate stronger deviation from the observed patterns.

The simulations suggest interesting features of stand development. They indicate strong variability in the distribution of carbohydrates between tree parts during stand development. Internal circulation of nutrients and the reuse of the same transport structure by various needle generations had a strong influence on the simulation results.

The PDF includes a summary in Finnish.

  • Nikinmaa, ORCID ID:E-mail:

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