The size of knots is negatively correlated with bending strength in sawn timber and it is therefore used as a quality grading criterion in national roundwood grading standards. Some standards even use the size of the largest knot as the sole estimate for individual log knottiness. The size of knots is determined by crown horizontal extension, which in turn is dependent on the impact of competing trees. Thus, with knot size models that are competition-dependent, roundwood quality due to knottiness can be simulated for different management al-ternatives. However, these types of models, calibrated on uneven-sized Norway spruce in Fennoscandia, are currently not available. Therefore, the objective of this study is to develop a competition-dependent model framework for prediction of the largest knot size per stem height section, for application within uneven-sized Norway spruce stands. Data from terrestrial laser scanning of an uneven-sized stand in southern Sweden are used to calibrate a modular prediction framework, consisting of interlinked allometric statistical models. Alternative framework sub-models are presented and the preferred model combination can be selected according to context and available input data. The flexible modular format enables further development of separate sub-components for adaptation to growing conditions not covered by the current calibration range.

To develop recommendations for tree selection in Continuous Cover Forestry (CCF), access to valid tools for simulating growth at individual tree-level is necessary. To assist efforts to develop such tools, in this study, long-term observation data from two uneven-sized Norway spruce plots in southern Sweden are used to evaluate old and new individual-tree growth models (two established Swedish models, two new preliminary models and included as a reference, a Finnish model). The plots' historical management records and site conditions are the same, but their last thinning treatment differs. Observed diameter increment at tree-level is investigated in relation to treatment. Individual tree growth residuals of tested models are evaluated in relation to tree diameter, treatment, projection length and sensitivity to the predictor mean stand age. Furthermore, the relations between displayed residuals and basal area local competition are analysed. The analyses indicate that active thinning made annual diameter increment independent of tree diameter above a threshold level, while the absence of thinning supported a concave relationship. All tested models displayed a significant linear bias leading to overestimation of small trees' growth and increasing underestimations of larger trees' growth with tree diameter. All distance-independent models displayed residual trends related to local competition.

Individual tree selection (ITS) is one option to manage uneven-sized forest ecosystems. However, scientifically based field guidelines adapted to ITS and economic profitability are rare, often because there is a lack of suitable tree models to use in growth and treatment simulations. The objective of this study is to develop individual-tree distance-dependent growth models focusing on Norway spruce dominated uneven-sized stands. Three models of different complexity, but with the same structural basis, are presented, followed by some examples of growth patterns for the subject trees. The data include 1456 trees (307 sample trees) collected from five sites in southern Sweden. The basic model (S) depends on subject tree size as the predictor, the second model (SD) adds distance to competitors as a predictor, and the third model (SDC) adds crown ratio as a predictor to the structure. R-Adj(2) increases with number of predictors from 0.48 to 0.58 to 0.62. The levels of RMSE improve accordingly from 5.02 cm(2) year(-1) (S) to 4.43 cm(2) year(-1) (SD) and 4.26 cm(2) year(-1) (SDC). The present calibration range and model structures primarily make the models suitable for management simulation of individual-tree selection of Norway spruce in southern Sweden. The format of the models allows for further extension with additional predictors and calibration data with greater coverage.

Continuous cover forests contain large numbers of spatially distributed trees of different sizes. The growth of a particular tree is a function of the properties of that tree and the neighbor trees, since they compete for light, water and nutrients. Such a dynamical system is highly nonlinear and multidimensional. In this paper, a particular tree is instantly harvested if a control function based on two local state variables, S and Q, is satisfied, where S represents the size of the particular tree and Q represents the level of local competition. The control function has two parameters. An explicit nonlinear present value function, representing the total value of all forestry activities over time, is defined. This is based on the parameters in the control function, now treated as variables, and six new parameters. Explicit functions for the optimal values of the two parameters in the control function are determined via optimization of the present value function. Two equilibria are obtained, where one is a unique local maximum and the other is a saddle point. An equation is determined that defines the region where the solution is a unique local maximum. Then, a case study with a continuous cover Picea abies forest, in southern Sweden, is presented. A new growth function is estimated and used in the simulations. The following procedure is repeated for five alternative levels of the interest rate: The total present value of all forest management activities in the forest, during 300 years, is determined for 1000 complete system simulations. In each system simulation, different random combinations of control function parameters are used and the total present value of all harvest activities is determined. Then, the parameters of the present value function are estimated via multivariate regression analysis. All parameters are determined with high precision and high absolute t-values. The present value function fits the data very well. Then, the optimal control function parameters and the optimal present values are analytically determined for alternative interest rates. The optimal solutions found within the relevant regions are shown to be unique maxima and the solutions that are saddle points are located far outside the relevant regions. 

The aim of this study was to develop and test a new basal area growth model in mixed species continuous cover forests in northern Iran. We analyzed 421 core samples from 6 main species in the forest area to develop our growth model. In each plot, we measured variables such as total tree height (m), diameter at breast height (DBH) (cm) and basal area of larger trees as cumulative basal areas of trees (GCUM) of DBH > 5 cm. The empirical data were analyzed using regression analysis. There was a statistically significant nonlinear function between the annual basal area increment, as the dependent variable, and the basal area of the individual trees and competition as explanatory variables. Reference area from the largest trees, was circular plot with area of 0.1 ha. GCUM was estimated for trees of DBH > 5 cm. Furthermore, we investigated the dependencies of diameter growth of different species on stand density at different levels of competition, and diameter development of individual trees through time. The results indicate that competition caused by larger neighborhood trees has a negative effect on growth. In addition, the maximum diameter increment is affected by competition level. Therefore, the maximum diameter increment of species occurs when the trees are about 35-40 cm in dense-forest (40 to 0 m(2) per ha) and when the trees are about 60 to 70 cm in very dense forest (60 to 0 m(2) per ha) which is more likely to Caspian natural forests with high level density due to uneven-aged composition of stands.

Economically optimal management of a continuous cover forest is considered here. Initially, there is a large number of trees of different sizes and the forest may contain several species. We want to optimize the harvest decisions over time, using continuous cover forestry, which is denoted by CCF. We maximize our objective function, the expected present value, with consideration of stochastic prices, timber quality variations and dynamically changing spatial competition. The problem is solved using an adaptive control function. The parameters of the control function are optimized via the first order optimum conditions based on a multivariate polynomial approximation of the objective function. The second order maximum conditions are investigated and used to determine relevant parameter ranges. The procedure is described and optimal results are derived for a general function multi-species CCF forest. Concrete examples from Germany, with beech, and from Sweden, with Norwegian spruce, are used to illustrate the methodology and typical numerical results. It is important to make market adapted harvest decisions. If the stochastic price variations are not considered when the harvest decisions are taken, the expected present value is reduced by 23%.

The aim of this study was to estimate a basal area growth model for individual trees in uneven-aged Caspian forests. A survey was conducted in order to find a natural forest without any harvesting activities, a so called 'untouched forest' and an area was selected from the Iranian Caspian forest. Three sample plots in the same aspect and of the same forest type were selected. In each plot, total tree height, diameter at breast height, distance of neighbor trees and azimuth were measured. Thirty trees were selected and drilled with increment borer to determine the increment model. Regression analysis was used to estimate the growth model. Results show that, for individual trees, there is a significant nonlinear relationship between the annual basal area increment, as the dependent variable, and the basal area. The results also show that the basal area of competing trees has a positive influence on growth. That the increment is higher with more competing neighboring trees is possibly because plots with higher volume per hectare and more competition, most likely also have higher site index or better soil or better site productivity than the plot with lower volume per hectare.

The management of forests may be motivated from production economic and environmental perspectives. The dynamically changing properties of trees affect environmental objectives and values of trees as raw material in the construction sector and in the energy sector. In order to optimize the management of forests, it is necessary to have access to reliable functions that predict how trees develop over time. One central property of a tree is the basal area, the area of the stem segment 1.3 meters above ground. In this paper, a general dynamic function for the basal area of individual trees has been developed from a production theoretically motivated autonomous differential equation. A closed form solution is derived and analyzed. Several examples of recent application of this function in Iran and Sweden are reported.