A spatial yield model for optimizing the thinning regime of mixed stands of <i>Pinus sylvestris</i> and <i>Picea abies</i>

Abstract

This paper presents a distance‐dependent yield model for a mixed stand of Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies (L.) Karst.) that accounts for the possible mixture effects separately for each tree and can be numerically optimized. The model consists of distance‐dependent single‐tree growth models, distance‐independent height models, distance‐dependent mortality models, and a distance‐dependent thinning algorithm. The thinning algorithm is controlled by the stand basal areas that trigger thinnings, and the relative removals from different tree species and diameter classes. The role of the thinning algorithm is to specify the trees to be harvested; this information is not contained in the decision variables. The algorithm removes trees starting with those individuals that face the most competition. The usage of the yield model together with a nonlinear optimization algorithm was illustrated by an example; the optimal thinning regime was determined for a mixed stand in which the age of pine and spruce was the same. Maximization of soil expectation value called for late and heavy first thinning and shorter rotation than applied in normally practiced forestry. In the one‐thinning regime, spruces were harvested from above and pines from all size classes. When two thinnings were applied, small and large pines are removed in both thinnings, whereas spruces are thinned from below in the first thinning and from above in the second thinning.