Articles containing the keyword 'function'

An ecophysiological growth process model, called INCA, for simulating the growth and development of a young walnut tree (Juglans regia L.) during three or four years, is presented. This tool, currently under development, aims at integrating architectural and physiological knowledge of the processes involved, in order to give a more rational understanding of the pruning operation. The model describes a simple three-dimensional representation of tree crown, solar radiation interception, photosynthesis, respiration, growth and partitioning of assimilates to leaves, stems, branches and roots. It supports the hypothesis that the tree grows as a collection of semiautonomous, interacting organs that compete for resources, based on daily sink strengths and proximity to sources. The actual growth rate of organs is not predetermined by empirical data, but reflects the pattern of available resources. The major driving variables are solar radiation, temperature, topological, geometrical and physiological factors. Outputs are hourly and daily photosynthate production and respiration, daily dimensional growth, starch storage, biomass production and total number of different types of organ. The user can interact or override any or all of the input variables to examine the effects of such changes on photosynthate production and growth. Within INCA, the tree entities and the surrounding environment are structured in a frame-based representation whereas the processes are coded in a rule-based language. The simulation mechanism is primarily based on the rule chaining capabilities of an inference engine.

• Le Dizès, E-mail: sl@mm.unknown
• Balandier, E-mail: pb@mm.unknown
• Cruiziat, E-mail: pc@mm.unknown
• Jacquet, E-mail: pj@mm.unknown
• Lacointe, E-mail: al@mm.unknown
• Le Roux, E-mail: xl@mm.unknown
• Sinoquet, E-mail: hs@mm.unknown

Process-based tree growth models are recognized to be flexible tools which are valuable for investigating tree growth in relation to changing environment or silvicultural treatments. In the context of forestry, we address two key modelling problems: allocation of growth which determines total wood production, and distribution of wood along the stem which determines stem form and wood quality. Growth allocation and distribution are the outcome of carbon translocation, which may be described by the Munch theory. We propose a simpler gradient process to describe the carbon distribution in the phloem of conifers. This model is a reformulation of a carbon diffusion-like process proposed by Thornley in 1972. By taking into account the continuity of the cambium along the stem, we obtain a one-dimensional reaction-diffusion model which describes both growth allocation between foliage, stem and roots, and growth distribution along the stem. Distribution of wood along the stem is then regarded as an allocation process at a smaller scale. A preliminary sensitivity analysis is presented. The model predicts a strong relationship between morphology and foliage-root allocation. It also suggests how empirical data, such as stem analysis, could be used to calibrate and validate allocation rules in process-based growth models.

• Deleuze, E-mail: cd@mm.unknown
• Houllier, E-mail: fh@mm.unknown

The horizontal and vertical stand structure of living trees was examined in a managed and in a primeval Norway spruce-dominated forest in Southern Finland. Tree size distributions (DBHs, tree height) were compared using frequency histograms. The vertical distribution of tree heights was illustrated as tree height plots and quantified as the tree height diversity (THD) using the Shannon-Weaver formula. The horizontal spatial pattern of trees was described with stem maps and quantified with Ripley's K-function. The spatial autocorrelation of tree sizes was examined with semivariogram analysis. In the managed forest the DBH and height distributions of trees were bimodal, indicating a two-layered vertical structure with a single dominant tree layer and abundant regeneration in the understory. The primeval forest had a much higher total number of trees which were rather evenly distributed in different diameter and tree height classes. The K-function summaries for trees taller than 15 m indicated that the primeval stand was close to complete random pattern. The managed stand was regular at small distances (up to 4 m). The semivariograms of tree sizes (DBH tree height) showed that the managed forest had a clear spatial dependence in tree sizes up to inter-tree distances of about 12 meters. In contrast, the primeval spruce forest had a variance peak at very short inter-tree distances (< 1 m) and only weak spatial autocorrelation at short inter-tree distances (1–5 m). Excluding the understory trees (h < 15 m) from the analysis drastically changed the spatial structure of the forest as revealed by semivariograms. ln general, the structure of the primeval forest was both horizontally and vertically more variable and heterogeneous compared to the managed forest. The applicability of the used methods in describing fine-scale forest structure i discussed.

• Kuuluvainen, E-mail: tk@mm.unknown
• Leinonen, E-mail: kl@mm.unknown
• Nygren, E-mail: mn@mm.unknown
• Penttinen, E-mail: ap@mm.unknown

In the method presented in this study, a group of experts evaluate, in a pairwise manner, a set of forest areas with respect to the game species considered. On the basis of these comparisons, relative priorities of forest areas are estimated using the eigenvalue technique. Using regression analysis, a habitat suitability function is estimated in which the priority is predicted by measures already familiar in forest planning. As a case study, a habitat suitability function was estimated for black grouse (Tetrao tetrix, Lururus tetrix L.). The function is applicable in forestry planning carried out using modern planning techniques.

The PDF includes an abstract in Finnish.

• Kangas, E-mail: jk@mm.unknown
• Karsikko, E-mail: jk@mm.unknown
• Laasonen, E-mail: ll@mm.unknown
• Pukkala, E-mail: tp@mm.unknown

The paper continues an earlier study by Kilkki and Päivinen concerning the use of the Weibull function in modelling the diameter distribution. The data consists of spruces (Picea abies (L.) H. Karst.) measured on angle count sample points of the National Forest Inventory of Finland. First, maximum likelihood estimation method was used to derive the Weibull parameters. Then, regression models to predict the values of these parameters with stand characteristics were calculated. Several methods to describe the Weibull function by a tree sample were tested. It is more efficient to sample the trees at equal frequency intervals than at equal diameter intervals. It also pays to take separate samples for pulpwood and saw timber.

The PDF includes an abstract in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Maltamo, E-mail: mm@mm.unknown
• Mykkänen, E-mail: rm@mm.unknown
• Päivinen, E-mail: rp@mm.unknown

The paper presents aspects of town and forest architecture. A feature of the Finnish building tradition is that the forest is allowed to grow next to buildings. After the Second World War a new type of town was created in Finland, ”the forest town”. The most prominent feature of the history of Finnish architecture, from national romanticism to functionalism and up to the present day, is the modification of international ideals to a certain ”forest culture” style.

The paper is based on a lecture given in the seminar ‘The forest as a Finnish cultural entity’, held in Helsinki in 1986. The PDF includes a summary in English.

• Pallasmaa, E-mail: jp@mm.unknown

The paper demonstrates the possibility of using data from small relascope sample plots in the derivation of the regression models which predict the Weibull function parameters for the dbh-distribution. The Weibull parameters describing the basal area dbh-distribution were estimated for relascope sample plots from the Finnish National Forest Inventory. In the first stage of the estimation nonlinear regression analysis was employed to derive initial parameter estimates for the second stage, in which the maximum likelihood method was used. The parameter estimates were employed as dependent variables for the derivation of the regression models; the independent variables comprised of the compartment-wise stand variables generally estimated in ocular inventories.

The PDF includes an abstract in Finnish.

• Kilkki, E-mail: pk@mm.unknown
• Päivinen, E-mail: rp@mm.unknown

The objective of this study has been to discover some of the basic principles on which an increment for a large forest area might be forecast. Because the stands in a large forest area vary considerably in density and are subject to different kinds of treatment, the main interest falls on the stand characteristics which determine the increment percentage in such forest conditions as these. The material used in the study has been published earlier, it consisted of sample plots of Scots pine (Pinus sylvestris L.) stands (Nyyssönen 1954).

Increment functions are of great importance in the increment forecast for cutting budget. Because 60-80% of the variation in the increment percentage can be explained by stand characteristics in circumstances where the age of the stand is 40-130 years and the volume vary with a coefficient of variation 0.6-0.7, regression equations for increment percentage may be based on a number of sample plots smaller than in a growing stock inventory in the same conditions. It is possible to get accurate results with relatively small number of sample plots. Furthermore, the smaller amount of increment sample plots makes it possible to develop measurement techniques.

The increment functions enable study of increment as a biological process. However, conclusions about biological process on the basis of regression equations should be made with caution. Still, regression analysis is a powerful tool in yield studies.

The PDF includes a summary in Finnish.

• Kuusela, E-mail: kk@mm.unknown
• Kilkki, E-mail: pk@mm.unknown

The dependence of elastic and tensile properties of coniferous trees on the share of summer wood can be presented as linear functions, if the soft wood is considered as a statically indefinite structure. By eliminating the share of summer wood by a certain function presented in the article, the elastic and tensile properties are the linear functions of density.

The functions are proved right by conducting strength tests on pine. Practical implications of the derived functions in rating the quality of wood are also presented.

The PDF contains a summary in Finnish. 

• Ylinen, E-mail: ay@mm.unknown

Knowledge on the roots systems and their properties is needed when for example assessing the wintering properties of a plant. The article presents the studies on the roots and their functions made with rye, wheat, oat and barley.

The data has been collected during the whole growing season. The experiments took place in the green houses of the University of Helsinki and on the experiment field in Tikkurila, some kilometres north from Helsinki.

The roots of cultivable crop can be divided according their function, state of development, structure and position in the root system into four classes. The classes are sprouting roots, nutriment roots, nutriment-support roots and support roots.

The PDF contains a summary in Finnish. 

• Kokkonen, E-mail: pk@mm.unknown

In the study, the potential allowable cut in the district of North-Savo, Eastern Finland was clarified  based on the non-industrial private forest landowners’ (NIPF) choices of timber management strategies. Alternative timber management strategies were generated, and the choices and factors affecting the choices of timber management strategies by NIPF landowners were studied. The choices of timber management strategies were solved by maximizing the utility functions of the NIPF landowners. The parameters of the utility functions were estimated using the Analytic Hierarchy Process (AHP).

The level of the potential allowable cut was compared to the cutting budgets based on the 7th and 8th National Forest Inventories (NFI7, NFI8) in Finland, to the combining of private forestry plans, and to the realized drain from non-industrial private forests. The potential allowable cut was calculated using the MELA system that has been used in calculating the national cutting budget.

The data consisted of the NIPF holdings that had been inventoried compartmentwise and had forestry plans made in 1984–92. The NIPF landowners’ choices of timber management strategies were clarified by a mail inquiry.

The most preferred strategy obtained was ”sustainability” (chosen by 62% of landowners). The second was ”finance” (17%) and the third ”savings” (11%). ”No cuttings”, and ”maximum cuttings” were the least preferred (9% and 1%, resp.). The factors promoting the choices of strategies with intensive cuttings were: a) ”farmer as forest owner” and ”owing fields”, b) ”increase in the size of the forest holding”, c) agriculture and forestry orientation in production, d) ”decreasing short-term stumpage earnings expectations”, e) ”increasing intensity of future cuttings”, and f) ”choice of forest taxation system based on site productivity”.

The potential allowable cut defined in the study was 20% higher than the average of the realized drain in 1988–93, which was at the same level as the cutting budget based on the combining of forestry plans in Eastern Finland. The potential allowable cut defined in the study was 12% lower than the NFI8-based greatest sustained allowable cut for the 1990. Using the method, timber management strategies can be clarified for private forest owners.

• Pesonen, E-mail: mp@mm.unknown

The study presents a growth and yield prediction model for a Pinus kesiya (Royle ex Gordon) stand by diameter classes. The material consists of temporary sample plots taken from a plantation inventory, of permanent sample plots established in commercial compartments and of an espacement trial. The mean basal area of the stand, variance and skewness of the diameter distribution are predicted. From these variables the parameters of the Weibull function are derived. Site class is assumed to be known or is calculated from measured information. Mortality is also predicted by estimating the number and mean size of dead trees. Thinnings are defined by the number of trees removed and by their relative size. If measured tree level data at the initial situation is available it can be utilized in the predictions, however, simulations can also be performed with stand level information. The minimum information needed for the prediction is planting density, site class as well as the times and removals of thinnings.

The calculations show that by decreasing the planting density of P. Kesiya from the present 1,330 stems/ha or by conducting early precommercial thinning both the relative and absolute amount of large sawlogs in the total production increase. An increase in the present planting density only slightly increases total yield. It is obvious that the presently recommended rotation of 25 years is too short for producing large sawlogs, especially on poor sites. This rotation period is suitable for small sawlog production while for pulpwood regimes shorter rotation periods can be used. If thinnings are done before the maximum current annual growth is reached stands will react well, but later on the ability to respond to thinnings decreases rapidly. Thinnings from below accelerates the production of large sawlogs more than thinning from above or systematic thinning. If all sawlog sizes are considered no great differences between thinning type exist. The study recommends different thinning regimes according to site class. Separate programs are recommended for the production of sawlogs and pulpwood.

The used thinning reaction model needs refinement and further studies with annual measured thinning trial material.

The PDF includes a summary in Finnish.

• Saramäki, E-mail: js@mm.unknown

The study examines the factor demands of the Finnish pulp and paper industry. In the theoretical part of the study, factor demand equations are derived using neoclassical production theory. In the empirical part, econometric factor demand model is estimated using annual time-series data for the period 1960–86. The relationship of factor demands and their prices are examined in terms of own price, cross price and substitution elasticities.

It is assumed that the ”representative firm” in the pulp and paper industry is minimizing its costs of production at a given output level. In addition, a number of other assumptions are made which enable the production technology to be represented by a cost function, in which the inputs are capital, labour, energy and raw materials. From the cost function, the factor demand equations, i.e., the cost share equations are derived by applying Shephard’s lemma. The equations are transformed to estimable form using translog approximation for the underlying factor share functions.

The study differs from the previous factor demand studies by applying the error correction model based on the Granger Representation Theorem and the results of the cointegration literature to model the dynamics of the factor demand. This approach provides a statistically consistent method for estimating the long-run static factor demand equations and the corresponding short-run equations. In general, the econometrics of integrated processes (e.g. stationarity and cointegration tests) applied in the present study have not been applied before in factor demand systems models.

The empirical results of the study indicate that the error correction approach can be applied to estimations of the factor demands for the pulp and paper industry. In both industry sectors, the adjustment to short run disequlibrium (price shocks) appears to be fairly rapid. The most significant results of the calculated elasticities are that the factor demands of pulp and paper industries clearly react to changes in factor prices and that there are significant substitution possibilities between the different inputs. The absolute values of the elasticities are, on average, somewhat larger than have been obtained in previous studies.

The PDF includes a summary in Finnish.

• Hetemäki, E-mail: lh@mm.unknown

Mechanical site preparation (MSP) is used prior to planting to control competing vegetation and enhance soil conditions, particularly in areas prone to paludification. Tree planting density can be adapted to the management context and objectives, as it influences yield and wood quality. However, the combined effects of MSP and planting density on understory vegetation composition, functional traits, and diversity remain uncertain. We thus conducted a study in the Clay Belt region of northwestern Quebec, Canada. After careful logging, the study area was divided into nine sites, each receiving one of three treatments: plowing, disc trenching, or no preparation. Sites were further divided into two, with black spruce (Picea mariana [Mill.] Britton, Sterns & Poggenb.) seedlings planted at either a low planting density of 1100 seedlings ha^-1 or a high planting density of 2500 seedlings ha^-1. After nine years, we assessed understory composition, diversity, key functional traits, sapling density and growth of planted trees. Careful logging alone led to a higher density of naturally established conifers compared to plowing or disc trenching. The interaction between planting density and MSP significantly influenced understory diversity and composition in plowed plots. Understory composition was affected by the soil C/N ratio, coniferous species, and deciduous species density. The growth of black spruce was notably enhanced with higher planting density in the plow treatment only. Neither planting density nor MSP alone affected tree height and diameter. Our results suggest that combining plowing with high-density planting can enhance stand growth and improve forest productivity. These findings guide future research on paludified forests.

• Fetouab, Institute for Forest Research and Centre for Forest Research, Université du Québec en Abitibi-Témiscamingue, 445 boul. de l’Université, Rouyn-Noranda, QC J9X 5E4, Canada E-mail: amira.fetouab@uqat.ca
• Fenton, Institute for Forest Research and Centre for Forest Research, Université du Québec en Abitibi-Témiscamingue, 445 boul. de l’Université, Rouyn-Noranda, QC J9X 5E4, Canada https://orcid.org/0000-0002-3782-2361 E-mail: nicole.fenton@uqat.ca
• Thiffault, Institute for Forest Research and Centre for Forest Research, Université du Québec en Abitibi-Témiscamingue, 445 boul. de l’Université, Rouyn-Noranda, QC J9X 5E4, Canada; Canadian Wood Fibre Centre, Natural Resources Canada, 1055 du P.E.P.S, P.O. Box 10380, Sainte-Foy Stn, Québec, QC G1V 4C7, Canada https://orcid.org/0000-0003-2017-6890 E-mail: nelson.thiffault@canada.ca
• Barrette, Institute for Forest Research and Centre for Forest Research, Université du Québec en Abitibi-Témiscamingue, 445 boul. de l’Université, Rouyn-Noranda, QC J9X 5E4, Canada; Direction de la recherche forestière, Ministère des Ressources naturelles et des Forêts, 2700 rue Einstein, Québec, QC G1P 3W8, Canada https://orcid.org/0000-0001-5937-382X E-mail: martin.barrette@mffp.gouv.qc.ca

Investing in planting genetically improved silver birch (Betula pendula Roth) in Swedish plantations requires understanding how birch stands will develop over their entire rotation. Previous studies have indicated relatively low production of birch compared to Norway spruce (Picea abies (L.) Karst.) and Scots pine (Pinus sylvestris L.). This could result from using unrepresentative basic data, collected from unimproved, naturally-regenerated birch (Betula spp.) growing on inventory plots often located in coniferous stands. The objective of this study was to develop a basal area development function of improved silver birch and evaluate production over a full rotation period. We used data from 52 experiments including planted silver birch of different genetic breeding levels in southern and central Sweden. The experimental plots were established on fertile forest sites and on former agricultural lands, and were managed with different numbers of thinnings and basal area removal regimes. The model best describing total stand basal area development was a dynamic equation derived from the Korf base model. The analysis of the realized gain trial for birch showed a good stability of the early calculated relative differences in basal area between tested genotypes over time. Thus, the relative difference in basal area might be with cautious used as representation of the realized genetic gain. On average forest sites in southern Sweden, improved and planted silver birch could produce between 6–10.5 m³ ha^–1 year^–1, while on fertile agriculture land the average productivity might be higher, especially with material coming from the improvement program. The performed analysis provided a first step toward predicting the effects of genetic improvement on total volume production and profitability of silver birch. However, more experiments are needed to set up the relative differences between different improved material.

• Liziniewicz, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: mateusz.liziniewicz@skogforsk.se
• Barbeito, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Alnarp, Sweden; Université de Lorraine, AgroParisTech, INRAE, UMR Silva, Nancy, France E-mail: ignacio.barbeito@slu.se
• Zvirgzdins, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Box 49, 23053 Alnarp, Sweden E-mail: andis.zvirgzdins@slu.se
• Stener, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: lg.stener@telia.com
• Niemistö, Natural Resources In-stitute Finland (Luke), Natural resources, Seinäjoki, Finland E-mail: pentti.niemisto@luke.fi
• Fahlvik, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: nils.fahlvik@skogforsk.se
• Johansson, Tönnersjöheden Experimental Forest, SLU, Simlångsdalen, Sweden E-mail: ulf.johansson@slu.se
• Karlsson, The Forestry Research Institute of Sweden, Ekebo, SE-268 90 Svalöv, Sweden E-mail: curly.birch@gmail.com
• Nilsson, Southern Swedish Forest Research Centre, Swedish University of Agricultural Sciences, Box 49, 23053 Alnarp, Sweden E-mail: urban.nilsson@slu.se

New mortality models were developed for the purpose of improving long-term growth and yield simulations in Finland, Norway, and Sweden and were based on permanent national forest inventory plots from Sweden and Norway. Mortality was modelled in two steps. The first model predicts the probability of survival, while the second model predicts the proportion of basal area in surviving trees for plots where mortality has occurred. In both models, the logistic function was used. The models incorporate the variation in prediction period length and in plot size. Validation of both models indicated unbiased mortality rates with respect to various stand characteristics such as stand density, average tree diameter, stand age, and the proportion of different tree species, Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) Karst.), and broadleaves. When testing against an independent dataset of unmanaged spruce-dominated stands in Finland, the models provided unbiased prediction with respect to stand age.

• Siipilehto, Natural Resources Institute Finland (Luke), Natural resources, P.O. Box 2, FI-00790 Helsinki, Finland E-mail: jouni.siipilehto@luke.fi
• Allen, Norwegian Institute of Bioeconomy Research (NIBIO), Division of Forest and Forest Products, NO-1431 Ås, Norway; Larson and McGowin Inc., Mobile, AL 36607, USA https://orcid.org/0000-0002-7824-2849 E-mail: micky.allen@nibio.no
• Nilsson, Swedish University of Agricultural Sciences (SLU), Southern Swedish Forest Research Centre, SE-23053 Alnarp, Sweden https://orcid.org/0000-0002-7624-4031 E-mail: urban.nilsson@slu.se
• Brunner, Norwegian University of Life Sciences (NMBU), Faculty of Environmental Sciences and Natural Resource Management, NO-1432 Ås, Norway https://orcid.org/0000-0003-1668-9714 E-mail: andreas.brunner@nmbu.no
• Huuskonen, Natural Resources Institute Finland (Luke), Natural resources, P.O. Box 2, FI-00790 Helsinki, Finland https://orcid.org/0000-0001-8630-3982 E-mail: saija.huuskonen@luke.fi
• Haikarainen, Natural Resources Institute Finland (Luke), Natural resources, P.O. Box 2, FI-00790 Helsinki, Finland https://orcid.org/0000-0001-8703-3689 E-mail: soili.haikarainen@luke.fi
• Subramanian, Swedish University of Agricultural Sciences (SLU), Southern Swedish Forest Research Centre, SE-23053 Alnarp, Sweden https://orcid.org/0000-0003-2777-3241 E-mail: narayanan.subramanian@slu.se
• Antón-Fernández, Norwegian Institute of Bioeconomy Research (NIBIO), Division of Forest and Forest Products, NO-1431 Ås, Norway https://orcid.org/0000-0001-5545-3320 E-mail: clara.anton.fernandez@nibio.no
• Holmström, Swedish University of Agricultural Sciences (SLU), Southern Swedish Forest Research Centre, SE-23053 Alnarp, Sweden https://orcid.org/0000-0003-2025-1942 E-mail: emma.holmstrom@slu.se
• Andreassen, Norwegian Institute of Bioeconomy Research (NIBIO), Division of Forest and Forest Products, NO-1431 Ås, Norway https://orcid.org/0000-0003-4272-3744 E-mail: kjellandreassen@gmail.com
• Hynynen, Natural Resources Institute Finland (Luke), Natural resources, P.O. Box 2, FI-00790 Helsinki, Finland E-mail: jari.hynynen@luke.fi

Based on data from long-term experimental fields with Norway spruce (Picea abies (L.) H. Karst.), we developed new stem taper and bark functions for Norway. Data was collected from 477 trees in stands across Norway. Three candidate functions which have shown good performance in previous studies (Kozak 02, Kozak 97 and Bi) were fitted to the data as fixed-effects models. The function with the smallest Akaike Information Criterion (AIC) was then chosen for additional analyses, fitting 1) site index-dependent and 2) age-dependent versions of the model, and 3) fitting a mixed-effects model with tree-specific random parameters. Kozak 97 was found to be the function with the smallest AIC, but all three tested taper functions resulted in fairly similar predictions of stem taper. The site index-dependent function reduced AIC and residual standard error and showed that the effect of site index on stem taper is different in small and large trees. The predictions of the age-independent and age-dependent models were very close to each other. Adding tree-specific random parameters to the model clearly reduced AIC and residual variation. However, the results suggest that the mixed-effects model should be used only when it is possible to calibrate it for each tree, otherwise the fixed-effects Kozak 97 model should be used. A model for double bark thickness was also fitted as fixed-effects Kozak 97 model. The model behaved logically, predicting larger relative but smaller absolute bark thickness for small trees.

• Pukkala, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland https://orcid.org/0000-0003-2853-9510 E-mail: timo.pukkala@uef.fi
• Holt Hanssen, Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway https://orcid.org/0000-0002-1715-3092 E-mail: kjersti.hanssen@nibio.no
• Andreassen, Norwegian Institute of Bioeconomy Research, P.O. Box 115, NO-1431 Ås, Norway https://orcid.org/0000-0003-4272-3744 E-mail: kjell.andreassen@nibio.no

This study examined a theoretical model for stand structures from the volumes of pulpwood and saw logs of clear-cut stands. The average stem size was used to estimate the number of cut trees. The distribution was solved using nonlinear derivative-free optimization. The truncated 2-parameter Weibull distribution was used to describe the stand structure of the commercial stems. This method was first tested with harvester data collected from seven clear-cut stands in southern Finland. Validation included reliability in the stand characteristics and goodness-of-fit of the species-specific distributions. The distributions provided unbiased estimates for the saw log volume, while the bias in the estimated pulpwood volume was 2%. The standard stand characteristics from the Weibull distributions corresponded notably well with the harvester data. A Kolmogorov-Smirnov (KS) test rejected two distributions out of 21 cases, when the accurate input variables were available for the theoretical model. The results of the study suggest that the presented method is a relevant option for predicting the stand structure. In practice, the reliability of the presented method was dependent on the quality of the information available from the stand prior to cutting. With a timber trade data set, the solution for the distribution for a clear-cut section was found. The goodness-of-fit was dependent on the accuracy of the visually assessed timber trade variables. Especially the average stem size proved difficult to assess due to high number of understorey pulpwood stems. Due to overestimated average stem sizes, the solved number of harvested trees was underestimated. Less than 50% of the distributions predicted for clear-cut sections passed the KS test.

• Siipilehto, Natural Resources Institute Finland (Luke), Latokartanonkaari 9, P.O. Box 2, FI-00790 Helsinki, Finland E-mail: jouni.siipilehto@luke.fi
• Rajala, Metsä Group, Revontulenpuisto 2, P.O. Box 10, 02020 METSÄ, FI-02100 Espoo, Finland E-mail: miika.rajala@metsagroup.com

Accurate assessment of canopy structure is crucial in studying plant-environment interactions. The advancement of functional-structural plant models (FSPM), which incorporate the 3D structure of individual plants, increases the need for a method for accurate mathematical descriptions of leaf shape. A model was developed as an improvement of an existing leaf shape algorithm to describe a large variety of leaf shapes. Modelling accuracy was evaluated using a spatial segmentation method and shape differences were assessed using principal component analysis (PCA) on the optimised parameters. Furthermore, a method is presented to calculate the mean shape of a dataset, intended for obtaining a representative shape for modelling purposes. The presented model is able to accurately capture a large range of single, entire leaf shapes. PCA illustrated the interpretability of the parameter values and allowed evaluation of shape differences. The model parameters allow straightforward digital reconstruction of leaf shapes for modelling purposes such as FSPMs.

• Coussement, Plant Sciences Unit, Institute for Agricultural and Fisheries Research (ILVO), Caritasstraat 39, B-9090 Melle, Belgium; Laboratory of Plant Ecology, Department of Plants and Crops, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, B-9000 Ghent, Belgium E-mail: jonas.coussement@ilvo.vlaanderen.be
• Steppe, Laboratory of Plant Ecology, Department of Plants and Crops, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, B-9000 Ghent, Belgium E-mail: kathy.steppe@ugent.be
• Lootens, Plant Sciences Unit, Institute for Agricultural and Fisheries Research (ILVO), Caritasstraat 39, B-9090 Melle, Belgium E-mail: peter.lootens@ilvo.vlaanderen.be
• Roldán-Ruiz, Plant Sciences Unit, Institute for Agricultural and Fisheries Research (ILVO), Caritasstraat 39, B-9090 Melle, Belgium; Department of Plant Biotechnology and Bioinformatics, Faculty of Sciences, Ghent University, Technologiepark Zwijnaarde 927, B-9052 Zwijnaarde, Belgium E-mail: isabel.roldan-ruiz@ilvo.vlaanderen.be
• De Swaef, Plant Sciences Unit, Institute for Agricultural and Fisheries Research (ILVO), Caritasstraat 39, B-9090 Melle, Belgium E-mail: tom.deswaef@ilvo.vlaanderen.be

Crown dimensions are correlated to growth of other parts of a tree and often used as predictors in growth models. The crown-to-bole diameter ratio (CDBDR), which is a ratio of maximum crown width to diameter at breast height (DBH), was modelled using data from permanent sample plots located on Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) stands in different parts of the Czech Republic. Among various tree and stand-level measures evaluated, DBH, height to crown base (HCB), dominant height (HDOM), basal area of trees larger in diameter than a subject tree (BAL), basal area proportion of the species of interest (BAPOR), and Hegyi’s competition index (CI) were found to be significant predictors in the CDBDR model. Random effects were included using the mixed-effects modelling to describe sample plot-level variation. For each species, the mixed-effects model described a larger part of the variation of the CDBDR than nonlinear ordinary least squares model with no trend in the residuals. The spatially explicit mixed-effects model showed more attractive fit statistics [conditional R² ≈ 0.73 (spruce), 0.78 (beech)] than its spatially inexplicit counterpart [conditional R² ≈ 0.71 (spruce), 0.76 (beech)]. The model showed that CDBDR increased with increasing HDOM – a measure that combines the stand development stage and site quality – but decreased with increasing HCB and competition (increasing BAL and CI), and decreasing proportions of the species of interest (increasing BAPOR). For both species, the spatially explicit mixed-effects model should be a preferred choice for a precise prediction of the CDBDR. The CDBDR model will have various management implications such as determination of spacing, stand basal area, stocking, and planning of appropriate species mixture.

• Sharma, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 16521, Praha 6 – Suchdol, Czech Republic E-mail: sharmar@fld.czu.cz
• Vacek, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 16521, Praha 6 – Suchdol, Czech Republic E-mail: vacekz@fld.czu.cz
• Vacek, Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Prague, Kamýcká 129, 16521, Praha 6 – Suchdol, Czech Republic E-mail: vacekstanislav@fld.czu.cz

Timber production is an economically important provisioning ecosystem service in forests, but is often in conflict with the provision of other ecosystem services. In multifunctional forestry, the production of timber and non-timber ecosystem services should coexist in the same landscape. To this end, we explored the capacity of a boreal landscape to simultaneously produce collectable goods − bilberry (Vaccimium myrtillus L.), cowberry (Vaccinium vitis-idaea L.) and cep (Boletus edulis Bull.) − alongside timber revenues. We also identified optimal forest management plans to achieve this. Furthermore, we analyzed trade-offs between collectable good yields and timber production, as well as between their economic values. We ran forest growth simulations under seven alternative management regimes at a landscape level across 50-year planning horizons. Then, we used multi-objective optimization to explore trade-offs and identify optimal forest management plans. The results showed that the strongest trade-off was between bilberry and timber production, resulting in a large loss in timber revenues for a gain in bilberry production. However, the conflicts between other collectables and timber production were relatively small: it was possible to increase the provision of collectable goods 4–15% with small reductions (3−5%) from timber revenues. With careful forest planning, there is the potential to simultaneously produce high levels of collectable goods and timber revenues in the landscape.

• Peura, University of Jyvaskyla, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014, University of Jyväskylä, Finland E-mail: maiju.h.peura@jyu.fi
• Triviño, University of Jyvaskyla, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014, University of Jyväskylä, Finland E-mail: maria.trivino@jyu.fi
• Mazziotta, University of Jyvaskyla, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014, University of Jyväskylä, Finland; Center for Macroecology, Evolution and Climate, Natural History Museum of Denmark, University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen, Denmark E-mail: adriano.mazziotta@snm.ku.dk
• Podkopaev, University of Jyvaskyla, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014, University of Jyväskylä, Finland; Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447 Warsaw, Poland E-mail: dmitry.podkopaev@gmail.com
• Juutinen, Natural Resources Institute Finland (Luke), Economics and Society, P.O. Box 413, FI-90014 University of Oulu, Finland; University of Oulu, Department of Economics, P.O. Box 4600, FI-90014 University of Oulu, Finland E-mail: artti.juutinen@luke.fi
• Mönkkönen, University of Jyvaskyla, Department of Biological and Environmental Sciences, P.O. Box 35, FI-40014, University of Jyväskylä, Finland E-mail: mikko.monkkonen@jyu.fi

We introduce a general procedure to match a stochastic functional-structural tree model (here LIGNUM augmented with stochastic rules) with real tree structures depicted by quantitative structure models (QSMs) based on terrestrial laser scanning. The matching is done by iteratively finding the maximum correspondence between the measured tree structure and the stochastic choices of the algorithm. First, we analyze the match to synthetic data (generated by the model itself), where the target values of the parameters to be estimated are known in advance, and show that the algorithm converges properly. We then carry out the procedure on real data obtaining a realistic model. We thus conclude that the proposed stochastic structure model (SSM) approach is a viable solution for formulating realistic plant models based on data and accounting for the stochastic influences.

• Potapov, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland E-mail: ilya.potapov@tut.fi
• Järvenpää, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland E-mail: marko.jarvenpaa@tut.fi
• Åkerblom, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland E-mail: markku.akerblom@tut.fi
• Raumonen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland E-mail: pasi.raumonen@tut.fi
• Kaasalainen, Tampere University of Technology, Department of Mathematics, P.O. Box 553, FI-33101 Tampere, Finland E-mail: mikko.kaasalainen@tut.fi

Growth and yield tables are constrained by a standard production regime and the stand-level dynamic models are an attractive alternative for the even-aged monospecific stands. The objective of this study is to derive a parsimonious and biologically sound whole-stand dynamic growth model and to validate its consistency and relevance for prediction of stand growth and yield. The state-space modelling approach was employed, introducing several novelties in comparison with its current usage. The model consists of a three-dimensional state vector, defined by dominant stand height, number of trees per hectare and mean stem volume, and three transition functions. A site index model was incorporated for height growth projection and transition functions for stand density and mean stem volume with respect to dominant height increase were derived from simple allometries and biological rationale. The model was examined with data from 79 permanent sample plots in Scots pine plantations. Nonlinear Seemingly Unrelated Regression was used to account for cross-equation correlations, and the Base-Height-Invariant dummy variable method was employed to estimate dynamic-form equations. Model consistency was validated in terms of accuracy of predictions and applicability to both thinned and unthinned stands. The new dynamic growth model is a parsimonious biometric whole-stand model that simulates the expected stand development for a broad spectrum of potential management alternatives and can be incorporated in a computer program for further use. It may be especially useful for application when a scarcity of longitudinal data prevents the use of more complicated modelling approaches.

• Stankova, Forest Research Institute of Bulgarian Academy of Sciences, Department of Forest Genetics, Physiology and Plantations, 132 “St. Kliment Ohridski” Blvd., 1756 Sofia, Bulgaria http://orcid.org/0000-0002-9932-7286 E-mail: tatianastankova@yahoo.com

• Wolfsmayr, University of Natural Resources and Life Sciences, Vienna, Gregor Mendel Straße 33, A-1180 Wien, Austria E-mail: ulrich.wolfsmayr@boku.ac.at
• Rauch, University of Natural Resources and Life Sciences, Vienna, Gregor Mendel Straße 33, A-1180 Wien, Austria E-mail: peter.rauch@boku.ac.at

• Rantala, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: mr@nn.fi
• Hujala, Finnish Forest Research Institute, Vantaa Unit, Vantaa, Finland E-mail: th@nn.fi
• Kurttila, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: mikko.kurttila@metla.fi

• Hautamäki, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: sh@nn.fi
• Mutanen, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: antti.mutanen@metla.fi
• Viitanen, Finnish Forest Research Institute, Joensuu Unit, P.O. Box 68, FI-80101 Joensuu, Finland E-mail: jv@nn.fi

• Belbo, Norwegian Forest and Landscape Institute, Box 115, 1431 Ås, Norway E-mail: helmer.belbo@skogoglandskap.no

• Rørstad, Norwegian University of Life Sciences, Dept of Ecology and Natural Resource Management, Ås, Norway E-mail: per.kristian.rorstad@umb.no
• Trømborg, Norwegian University of Life Sciences, Dept of Ecology and Natural Resource Management, Ås, Norway E-mail: et@nn.no
• Bergseng, Norwegian University of Life Sciences, Dept of Ecology and Natural Resource Management, Ås, Norway E-mail: eb@nn.no
• Solberg, Norwegian University of Life Sciences, Dept of Ecology and Natural Resource Management, Ås, Norway E-mail: bs@nn.no

• Repola, Finnish Forest Research Institute, Rovaniemi Research Unit, P.O. Box 16, FI-96301 Rovaniemi, Finland E-mail: jaakko.repola@metla.fi

• Laturi, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jani.laturi@metla.fi
• Mikkola, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jm@nn.fi
• Uusivuori, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: ju@nn.fi

• Siipilehto, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jouni.siipilehto@metla.fi
• Sarkkola, Finnish Forest Research Institute, Vantaa Research Unit, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: ss@nn.fi
• Mehtätalo, University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuu, Finland E-mail: lm@nn.fi

• Palahí, Centre Tecnológic Forestal de Catalunya. Passeig Lluis Companys, 23, 08010, Barcelona, Spain E-mail: marc.palahi@ctfc.es
• Pukkala, University of Joensuu, Faculty of Forestry, P.O. Box 111, 80101 Joensuu, Finland E-mail: tp@nn.fi
• Trasobares, Foreco Technologies, Av. Diagonal 416, Estudio 2, Barcelona 08037, Spain E-mail: at@nn.es

• Siipilehto, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: jouni.siipilehto@metla.fi

• Kangas, Finnish Forest Research Institute, Kannus Research Station, P.O. Box 44, FIN-69101 Kannus, Finland E-mail: annika.kangas@metla.fi
• Maltamo, Finnish Forest Research Institute, Joensuu Research Station, P.O. Box 68, FIN-80101 Joensuu, Finland E-mail: mm@nn.fi

• Pykäläinen, University of Joensuu, Faculty of Forestry, P.O. Box 111, FIN-80101 Joensuu, Finland E-mail: jouni.pykalainen@joensuu.fi

• McKay, Forest Commission Research Agency, Northern Research Station, Roslin, Midlothian, EH25 9SY, Scotland E-mail: h.mckay@forestry.gov.uk

• Szmyt, Department of Silviculture, Faculty of Forestry, Poznań University of Life Sciences, ul. Wojska Polskiego 69, 60-625 Poznań, Poland E-mail: jszmyt@up.poznan.pl

Use of fast-growing tree plantations on dedicated areas is proposed as a means of reconciling fibre production with conservation objectives. Success of this approach however requires fine-tuning silvicultural scenarios so that survival and growth are optimized while management and environmental costs are minimized. This is particularly challenging for hybrid larch (Larix × marschlinsii Coaz), a shade-intolerant species planted on fertile sites in Quebec (Canada) where legislation prevents the use of chemical herbicides. In this context, multiple motor-manual release treatments are often required, with high impacts on costs and social issues related to the scarcity of a qualified workforce. We established a split-split-plot design on a recently harvested site to assess the main and interaction effects of mechanical site preparation (MSP) intensity (five modalities of trenching or mounding), motor-manual release scenario (one or two treatments) and planting depth (0–3 cm or 3–10 cm) on hybrid larch seedling growth and survival six years after planting. Mechanical site preparation intensity and planting depth did not influence seedling growth after 6 years. The lack of significant interaction between MSP and release scenarios indicates that these operations should be planned independently. A more intensive MSP treatment cannot replace a second motor-manual release on fertile sites, as proposed to reduce costs. Our results also show the significant advantage of performing two motor-manual release treatments two years apart (the first one early in the scenario), over performing a single treatment. Our study provides silvicultural guidelines for the establishment of high-yield exotic larch plantations.

• Thiffault, Direction de la recherche forestière, Ministère des Forêts, de la Faune et des Parcs du Québec, 2700 rue Einstein, Québec, QC, Canada G1P 3W8; Centre d’étude de la forêt, CP 8888, Succursale Centre-ville, Montréal, QC, Canada H3C 3P8 http://orcid.org/0000-0003-2017-6890 E-mail: nelson.thiffault@mffp.gouv.qc.ca
• Paquette, Centre d’étude de la forêt, CP 8888, Succursale Centre-ville, Montréal, QC, Canada H3C 3P8; Université du Québec à Montréal, Département des sciences biologiques, CP 8888, Succursale Centre-ville, Montréal, QC, Canada H3C 3P8 http://orcid.org/0000-0003-1048-9674 E-mail: alain.paquette@gmail.com
• Messier, Centre d’étude de la forêt, CP 8888, Succursale Centre-ville, Montréal, QC, Canada H3C 3P8; Université du Québec à Montréal, Département des sciences biologiques, CP 8888, Succursale Centre-ville, Montréal, QC, Canada H3C 3P8; Institut des Sciences de la Forêt tempérée (ISFORT), 58 rue Principale, Ripon, QC, Canada JOV 1V0 E-mail nelson.thiff E-mail: christian.messier@uqo.ca

This study compares the responses of two Swedish 5-year predictive stand-level functions with the observed responses in 721 fertilization experiment plots in Norway fertilized with nitrogen (N). All plots are single-species consisting of Norway spruce (Picea abies (L.) H. Karst.) or Scots pine (Pinus sylvestris L.) fertilized with ammonium nitrate (AN) or urea. The correlations between the observed and the two predicted responses were 0.34–0.40 for all plots taken together. One response function performed well on average, but underestimated the response in pine plots and overestimated the response in spruce plots. The second function overpredicted the response on the full dataset, in spruce plots and old forest, but performed well in pine plots. Both functions overestimated the growth response in high-productive plots. Higher N deposition in Norway than in Sweden may count for parts of the deviations. Testing of fertilization functions on new datasets is rare, but important part of the evaluation of functions. As the functions are not well fit for predicting the growth response in spruce and high-productive plots in our sample, new functions that include N deposition are welcome.

• Sjølie, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, NO-1432 Ås, Norway E-mail: hanne.sjolie@nmbu.no
• Sørlie, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, NO-1432 Ås, Norway E-mail: hans.asbjorn.sorlie@slf.dep.no
• Tveite, Norwegian Forest and Landscape Institute, P.O. Box 115, NO-1431 Ås, Norway E-mail: bjorn.tveite@skogoglandskap.no
• Solberg, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, NO-1432 Ås, Norway E-mail: birger.solberg@nmbu.no

• Muukkonen, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: petteri.muukkonen@metla.fi
• Mäkipää, Finnish Forest Research Institute, P.O. Box 18, FI-01301 Vantaa, Finland E-mail: raisa.makipaa@metla.fi