Spatial optimization for dispersion of remnant trees in seed-tree cuttings and retention-tree stands of Scots pine

Abstract

In this study, optimal spatial patterns for seed-tree cuttings and green-tree retention in Scots pine stands were investigated. The optimization approach is based on functions that describe the effects of single, retained trees on Scots pine regeneration. Two spatial optimization techniques were applied to this intrastand-level problem. The model approach assumes smooth, non-convex optimization problems with a convex set of feasible solutions. These problems were solved with a deterministic optimization algorithm with 500 initial tree position sets, also taking into account different forest management objectives such as high, homogeneous seed and seedling density. This required the use of multicriteria optimization procedures. The best spatial patterns identified differed significantly according to the objective functions considered. This was demonstrated by aggregation index values of stem maps and from visualization. Thus, the objective functions must be defined carefully to obtain best solutions for the management aims. A small degree of clumping in seed-tree cuttings did not appear detrimental to seedling density objectives. Therefore, short-term retention trees should be selected primarily by phenotype, not solely by a specific distribution scheme.