How considering multiple criteria, uncertainty scenarios and biological interactions may influence the optimal silvicultural strategy for a mixed forest

Highlights

• We develop a continuous optimisation approach for multiple criteria at stand-level.

• We consider survival in mixed forests and growth response after partial harvest.

• The model suggests mixed forests for both pure economic and multiple objectives.

• Consideration of biological interactions supports mixed forest.

• Consideration of uncertainty supports continuous cover forestry.

Abstract

Assessing pre-defined strategies remains the status quo for studies supporting silvicultural decision-making for future forest management, yet, such strategies may not fully address decision-makers' preferences and uncertainty attitudes. We develop a continuous stand-level optimisation approach that integrates multiple decision criteria, uncertain input data based on ellipsoidal uncertainty sets and biological interactions. The optimisation aims to derive silvicultural strategies that closely align with the objectives and uncertainty attitudes of decision-makers. The novel approach optimises tree species composition and harvesting regimes simultaneously. In our example, the decision criteria are the soil expectation value (SEV), the volume of timber harvested, the sum of cash flows and the average amount of carbon stored in the forest. We use input data for Norway spruce (Picea abies), Silver fir (Abies alba) and European beech (Fagus sylvatica), and integrate biological stand-level interactions represented by a) enhanced survival of tree species in mixed forests and b) the growth response of trees remaining after partial harvesting. The resulting optimal silvicultural strategies ranged from a clear-cutting system (when maximising SEV and ignoring uncertainty) to continuous cover forestry (maximising SEV and considering uncertainty). Our analyses did not support single species forestry – even the clear-cutting system suggested a mixed rather than pure forest. Silvicultural strategies that consider multiple criteria stored up to 47% more carbon than the clear-cutting system, but their SEVs were up to 39% lower. Biological interactions influence the optimal stand composition and harvesting regime, while establishment costs and the discount rate affect the level achieved for each management criterion. Lower survival due to changes in climate hardly influenced the model results. Our optimisation approach is flexible and may integrate many more and different criteria. It is useful to derive silvicultural strategies to guide science-based recommendations for various forest decision-makers.

Introduction

Paradigms for silvicultural strategies are continuously evolving to reflect stakeholders' current perceptions and needs. For example, forestry in Fennoscandia has mainly built on even-aged stand management and clear-cut silviculture over the last 70 years (Kuuluvainen et al., 2012). Nowadays, a growing number of scientific studies consider continuous cover forestry as a more appropriate alternative (Lundmark et al., 2016; Nieminen et al., 2018; Peura et al., 2018; Seedre et al., 2018). In Germany, pure even-aged coniferous stands have been the dominant forestry strategy of past centuries, but scenario models on future management pathways now assume higher shares of native broadleaves and mixed forests (Schwaiger et al., 2019; Toraño Caicoya et al., 2018). In Great Britain, the often-used notion of “broadleaved woodlands” underlines the importance of native tree species for addressing multiple stakeholders' preferences in modern multifunctional forest management (Burton et al., 2018; Raum and Potter, 2015). This practice is mirrored in Central European forestry more broadly, where extensive conifer stands are transitioning towards multifunctional forests, mainly through admixing European beech (Jandl et al., 2019; Kolář et al., 2017; Pretzsch et al., 2012).

Modelling analyses to support multifunctional forest management commonly build on pre-defined scenarios. Optimising forest management directly based on the (multiple) objectives and uncertainty attitudes of stakeholders remains rare. Optimisation is the process of selecting the best set of actions or of making the best decisions for a given problem or system (Kaya et al., 2016). New optimisation models must provide modelling flexibility to account for variable management preferences in forestry (Heinonen et al., 2020). For example, the preferences of decision-makers and stakeholders will be influenced by their objectives (Aldea et al., 2014), their constraints and their attitudes towards uncertainty (Eyvindson and Kangas, 2016). Ex-post analyses can only partly capture this variation, because they focus on a limited number of scenarios. Such analyses are still the status quo to inform silvicultural management strategies. Examples include Csépányi and Csór (2017), Tarp et al. (2000), Price and Price (2006), Ralston et al. (2004), Andreassen and Øyen (2002), Knoke and Plusczyk (2001) as well as Hanewinkel (2001), who all assessed the economic performance of pre-defined silvicultural strategies. While these studies focus on a single economic criterion, more recent studies have integrated multiple decision criteria in their assessment (Creutzburg et al., 2017; Eggers et al., 2019; Hilmers et al., 2020; Mina et al., 2017; Pardos et al., 2017).

Despite the valuable insights from studies focusing on pre-defined silvicultural strategies, the comparability of scenarios can be limited, because usually no optimisation has been applied (Rämö and Tahvonen, 2017). Therefore, there is no guarantee that pre-defined scenarios actually include the best option available. Studies by Tahvonen, 2009, Tahvonen, 2015 as well as Tahvonen and Rämö (2016) provide alternative optimisation-based modelling approaches building on mathematical programming. These approaches maximise an economic objective by scheduling individual (or all) trees for harvesting over time. Aspects such as individual tree growth, prices and costs for timber logs, regeneration costs, fixed costs and discount rate affect the number and the selection of the remaining trees for further growth. Depending on the assumed conditions, either even-aged or uneven-aged silvicultural strategies emerge as optimal strategies.

While the rationale for these optimisation-based approaches is very convincing, the models show high non-linearity, are very complex and assume certainty of all input information (e.g. tree growth, survival, prices, costs). Heuristic and metaheuristic algorithms used for optimising such non-linear problems do not guarantee finding the optimal solution, but may come close enough to the optimum. Unfortunately, exact solution procedures are available only for much simpler non-linear problems. For example, Messerer et al. (2020) have applied combinatorial methods to solve low-complexity non-linear forest decision problems, which allowed also considering the influence of uncertainty. On the contrary, for complex non-linear models (e.g., Roessiger et al., 2016; Tahvonen and Rämö, 2016), integrating uncertainty is not practical, as this would exponentiate model complexity. However, uncertainty may have an important impact on decision-making (Bikhchandani et al., 2015), if decision-makers are averse to uncertainty. In land-use decisions, aversion to uncertainty is the rule rather than the exception (Di Falco and Perrings, 2005).

As our main contribution, we develop and present a novel model approach for the forest stand level, seeking a compromise between modelling biological complexity and uncertainty. The approach can consider uncertainty in simulated decision-making and allows for the integration of multiple objectives. We base our model on published empirical growth data and make simple assumptions concerning biological interactions. Biological interactions lead to emergent properties of a forest stand not possessed by its single parts (Lidicker, 1979). Examples for biological interactions in forest stands include mutualism and commensalism, when one or multiple tree species benefit from a mixture with other tree species. Competition among single trees is another example, which depends, inter alia, on stand density. Our model considers two types of biological interactions: the influence of mixing various tree species on the survival of the tree species (Brandl et al., 2020), and the enhanced growth of trees remaining after partial harvest operations (Messerer et al., 2020). We apply a reference point method (Estrella et al., 2014), as developed in Knoke et al. (2020b) for the simulation of tropical deforestation. However, stand level optimisation requires a dynamic approach considering input coefficients that change over time, whereas the mentioned studies only apply static optimisation based on time invariant input coefficients. To develop a novel optimisation approach we build on the analytical framework used by Roessiger et al. (2011). No existing study has coupled Roessiger's stand level approach with a reference point approach to optimise multiple criteria, while considering biological interactions. For example, Roessiger et al. (2013) optimised stand management for a single objective only, using predefined tree species compositions to optimise the schedule of timber harvesting. In a more complex optimisation approach, Roessiger et al. (2016) disregarded uncertainty.

Given this basic setting, we investigate what proportions of a forest stand a manager should allocate to either Norway spruce (Picea abies (L.) H. Karst.), Silver fir (Abies alba Mill.) or European beech (Fagus sylvatica L.). In addition, we simulate the optimal timing and extent of partial harvest operations to establish regeneration in gap cuttings. We define four decision perspectives (explained in the next section), while optimising for: 1) the expected value of a single economic criterion, 2) the robust provision of a single economic criterion, 3) the expected levels for multiple criteria, and 4) the robust levels for multiple criteria. The scenarios building on robust optimisation assume the decision-maker is averse to uncertainty and provide acceptable solutions not only for specific input data, but also for a range of input data. We use “uncertainty” to describe our limited knowledge about the true contribution of management operations to the decision criteria. The alternative term “risk” would require allocating probabilities to our input data (Walker et al., 2016), which is not the case in our robust modelling approach. Decision criteria include the soil expectation value (SEV), the volume of timber harvested, the sum of undiscounted cash flows and the average amount of carbon stored in forest aboveground biomass.

Our main questions are:

• How do silvicultural decision-makers' preferences for specific criteria and concerning uncertainty influence optimal stand composition and stand management?

• How do biological interactions, such as improved survival in mixed stands and growth response after partial harvesting influence the modelling results?

• What is the influence of changes in climate variables, establishment costs and discount rate?

• How do simulation results correspond to silvicultural strategies applied in practice?