Laser scanning and individual-tree detection are used increasingly in forest inventories. As a consequence, methods that optimize forest management at the level of individual trees will be gradually developed and adopted.

The current study proposed a hierarchical two-level optimization method for tree-level planning where the cutting years are optimized at the higher level. The lower-level optimization allocates the trees to the cutting events in an optimal way. The higher-level optimization employed differential evolution whereas the lower-level problem was solved with the simulated annealing metaheuristic. The method was demonstrated with a 30 ​m ​× ​30 ​m sample plot of planted Larix olgensis. The baseline case maximized the net present value as the only management objective. The solution suggested heavy thinning from above and a rotation length of 62 years. The baseline problem was enhanced to mixed stands where species diversity was used as another management objective. The method was also demonstrated in a problem that considered the complexity of stand structure, in addition to net present value. The objective variables that were used to measure complexity were the Shannon index (species diversity), Gini index (tree size diversity), and the index of Clark and Evans, which was used to describe the spatial distribution of trees. The article also presents a method to include natural advance regeneration in the optimization problem and optimize the parameters of simulated annealing simultaneously with the cutting years.

The study showed that optimization approaches developed for forest-level planning can be adapted to problems where treatment prescriptions are required for individual trees.

Forest inventories are increasingly based on airborne laser scanning (ALS). In Finland, the results of these inventories are calculated for small grid cells, 16 m by 16 m in size. Use of grid data in forest planning results in the additional requirement of aggregating management prescriptions into large enough continuous treatment units. This can be done before the planning calculations, using various segmentation techniques, or during the planning calculations, using spatial optimization. Forestry practice usually prefers reasonably permanent segments created before planning. These segments are expected to be homogeneous in terms of site properties, growing stock characteristics and treatments. Recent research has developed methods for partitioning grids of ALS inventory results into segments that are homogeneous in terms of site and growing stock characteristics. The current study extended previous methods so that also the similarity of treatments was considered in the segmentation process. The study also proposed methods to deal with biases that are likely to appear in the results when grid data are aggregated into large segments.

The analyses were conducted for two datasets, one from southern and the other from northern Finland. Cellular automaton (CA) was used to aggregate the grid cells into segments using site characteristics with (1) growing stock attributes interpreted from ALS data, (2) predicted cutting prescriptions and (3) both stand attributes cutting prescriptions. The CA was optimized for each segmentation task. A method based on virtual stands was used to correct systematic errors in variable estimates calculated for segments.

The segmentation was rather similar in all cases. The result is not surprising since treatment prescriptions depend on stand attributes. The use of virtual stands decreased biases in growth prediction and in the areas of different fertility classes.

Automated stand delineation was not sensitive to the type of variables that were used in the process. Virtual stands are an easy method to decrease systematic errors in calculations.

Forestry offers possibilities to sequestrate carbon in living biomass, deadwood and forest soil, as well as in products prepared of wood. In addition, the use of wood may reduce carbon emissions from fossil fuels. However, harvesting decreases the carbon stocks of forests and increases emissions from decomposing harvest residues.

This study used simulation and optimization to maximize carbon sequestration in a boreal forest estate consisting of nearly 600 stands. A reference management plan maximized net present value and the other plans maximized the total carbon balance of a 100-, 200- or 300-year planning horizon, taking into account the carbon balances of living forest biomass, dead organic matter, and wood-based products

Maximizing carbon balance led to low cutting level with all three planning horizons. Depending on the time span, the carbon balance of these schedules was 2 to 3.5 times higher than in the plan that maximized net present value. It was not optimal to commence cuttings when the carbon pool of living biomass and dead organic matter stopped increasing after 150-200 years.

Letting many mature trees to die was a better strategy than harvesting them when the aim was to maximize the long-term carbon balance of boreal Fennoscandian forest. The reason for this conclusion was that large dead trees are better carbon stores than harvested trees. To alter this outcome, a higher proportion of harvested trees should be used for products in which carbon is stored for long time.

Forest fertilization offers a means to increase the production of renewable resources. Nitrogen is the most common fertilizer in boreal upland forests. There is plenty of research on the effect of nitrogen fertilization on volume growth, but less research on the optimal timing of fertilization and optimal management of fertilized stands.

This study used simulation and optimization to analyze the profitability of fertilization, optimal management of fertilized stands and the effects of fertilization on cash flows and timber yields. The management of 100 stands representing the most common growing sites of Scots pine and Norway spruce was optimized.

Fertilization improved profitability in most of the analyzed stands. Profitability improved most in spruce stands growing on mesic site. Improving stem quality increased the economic benefit of fertilization. The timber yields of medium-aged conifer stands can be increased by almost 1 m³ha^-1a^-1 (15%) in sub-xeric pine and mesic spruce sites and about 0.5 m³ha^-1a^-1 (5%) in mesic pine and herb-rich spruce sites when the recommended nitrogen dose (150 kg ha^-1) is applied once in 30 years.

Nitrogen fertilization of boreal conifer forest should be used mainly in spruce-dominated stands growing on medium sites. The gains are the highest in stands where the mean tree diameter is 16-20 cm and stand basal area is 14-20 m²ha^-1.

Forest ecosystems are increasingly seen as multi-functional production systems, which should provide, besides timber and economic benefits, also other ecosystem services related to biological diversity, recreational uses and environmental functions of forests. This study analyzed the performance of even-aged rotation forest management (RFM), continuous cover forestry (CCF) and any-aged forestry (AAF) in the production of ecosystem services. AAF allows both even-aged and uneven-aged management schedules. The ecosystem services included in the analyses were net present value, volume of harvested timber, cowberry and bilberry yields, scenic value of the forest, carbon balance and suitability of the forest to Siberian jay.

Data envelopment analysis was used to derive numerical efficiency ratios for the three management systems. Efficiency ratio is the sum of weighted outputs (ecosystem services) divided by the sum of weighted inputs. The linear programing model proposed by Charnes, Cooper and Rhodes was used to derive the weights for calculating efficiency scores for the silvicultural systems.

CCF provided more ecosystem services than RFM, and CCF was more efficient than RFM and AAF in the production of ecosystem services. Multi-objective management provided more ecosystem services (except harvested timber) than single-objective management that maximized economic profitability. The use of low discount rate (resulting in low cutting level and high growing stock volume) led to better supply of most ecosystems services than the use of high discount rate. RFM where NPV was maximized with high discount rate led to particularly poor provision of most ecosystem services. In CCF the provision of ecosystem services was less sensitive to changes in discount rate and management objective than in RFM.

In economically optimal management,trees that are removed in a thinning treatment should be selected on the basis of their value,relative value increment and the effect of removal on the growth of remaining trees. Large valuable trees with decreased value increment should be removed,especially when they overtop smaller trees.

This study optimized the tree selection rule in the thinning treatments of continuous cover management when the aim is to maximize the profitability of forest management. The weights of three criteria (stem value,relative value increment and effect of removal on the competition of remaining trees) were optimized together with thinning intervals.

The results confirmed the hypothesis that optimal thinning involves removing predominantly large trees. Increasing stumpage value,decreasing relative value increment,and increasing competitive influence increased the likelihood that removal is optimal decision. However,if the spatial distribution of trees is irregular,it is optimal to leave large trees in sparse places and remove somewhat smaller trees from dense places. However,the benefit of optimal thinning,as compared to diameter limit cutting is not usually large in pure one-species stands. On the contrary,removing the smallest trees from the stand may lead to significant (30-40 %) reductions in the net present value of harvest incomes.

Decisions on forest management are made under risk and uncertainty because the stand development cannot be predicted exactly and future timber prices are unknown. Deterministic calculations may lead to biased advice on optimal forest management. The study optimized continuous cover management of boreal forest in a situation where tree growth, regeneration, and timber prices include uncertainty.

Both anticipatory and adaptive optimization approaches were used. The adaptive approach optimized the reservation price function instead of fixed cutting years. The future prices of different timber assortments were described by cross-correlated auto-regressive models. The high variation around ingrowth model was simulated using a model that describes the cross- and autocorrelations of the regeneration results of different species and years. Tree growth was predicted with individual tree models, the predictions of which were adjusted on the basis of a climate-induced growth trend, which was stochastic. Residuals of the deterministic diameter growth model were also simulated. They consisted of random tree factors and cross- and autocorrelated temporal terms.

Of the analyzed factors, timber price caused most uncertainty in the calculation of the net present value of a certain management schedule. Ingrowth and climate trend were less significant sources of risk and uncertainty than tree growth. Stochastic anticipatory optimization led to more diverse post-cutting stand structures than obtained in deterministic optimization. Cutting interval was shorter when risk and uncertainty were included in the analyses.

Adaptive optimization and management led to 6%–14% higher net present values than obtained in management that was based on anticipatory optimization. Increasing risk aversion of the forest landowner led to earlier cuttings in a mature stand. The effect of risk attitude on optimization results was small.

The minimum set of sub-models for simulating stand dynamics on an individual-tree basis consists of tree-level models for diameter increment and survival. Ingrowth model is a necessary third component in uneven-aged management. The development of this type of model set needs data from permanent plots, in which all trees have been numbered and measured at regular intervals for diameter and survival. New trees passing the ingrowth limit should also be numbered and measured. Unfortunately, few datasets meet all these requirements. The trees may not have numbers or the length of the measurement interval varies. Ingrowth trees may not have been measured, or the number tags may have disappeared causing errors in tree identification.

This article discussed and demonstrated the use of an optimization-based approach to individual-tree growth modelling, which makes it possible to utilize data sets having one or several of the above deficiencies. The idea is to estimate all parameters of the sub-models of a growth simulator simultaneously in such a way that, when simulation begins from the diameter distribution at the first measurement occasion, it yields a similar ending diameter distribution as measured in the second measurement occasion. The method was applied to Pinus patula permanent sample plot data from Kenya. In this dataset, trees were correctly numbered and identified but measurement interval varied from 1 to 13 years. Two simple regression approaches were used and compared to the optimization-based model recovery approach.

The optimization-based approach resulted in far more accurate simulations of stand basal area and number of surviving trees than the equations fitted through regression analysis.

The optimization-based modelling approach can be recommended for growth modelling when the modelling data have been collected at irregular measurement intervals.

The Siberian moth (Dendrolimus sibiricus) (SM) defoliates several tree species from the genera Larix, Picea and Abies in northern Asia, east of the Urals. The SM is a potential invasive forest pest in Europe because Europe has several suitable host species and climatic conditions of central and northern Europe are favourable for the SM.

This study developed a grid-based spatio-temporal model for simulating the spread of the SM in case it enters Europe from Russia via border stations. The spread rate was modeled as a function of the spatial distribution of host species, climatic suitability of different locations for the SM, human population density, transportation of moth-carrying material, and flying of moths from tree to tree.

The simulations showed that the SM is most likely to spread in the forests of northeast Belarus, the Baltic countries, and southern and central Finland. Climatic conditions affected the occurrence of the SM more than human population density and the coverage of suitable host species.

Studies on optimal stand management often make simplifications or restrict the choice of treatments. Examples of simplifications are neglecting natural regeneration that appears on a plantation site, omitting advance regeneration in simulations, or restricting thinning treatments to low thinning (thinning from below).

This study analyzed the impacts of simplifications on the optimization results for Fennoscandian boreal forests. Management of pine and spruce plantations was optimized by gradually reducing the number of simplifying assumptions.

Forced low thinning, cleaning the plantation from the natural regeneration of mixed species and ignoring advance regeneration all had a major impact on optimization results. High thinning (thinning from above) resulted in higher NPV and longer rotation length than thinning from below. It was profitable to leave a mixed stand in the tending treatment of young plantation. When advance regeneration was taken into account, it was profitable to increase the number of thinnings and postpone final felling. In the optimal management, both pine and spruce plantation was gradually converted into uneven-aged mixture of spruce and birch.

The results suggest that, with the current management costs and timber price level, it may be profitable to switch to continuous cover management on medium growing sites of Fennoscandian boreal forests.