Do competition-density rule and self-thinning rule agree?

Abstract

Competition-density relationships and self-thinning are major principles in forest growth. They are combined, describing self-thinning as a marginal case of the competition-density relationship. Robust estimation techniques allow parameterizing of both from national forest inventory data even for minor species. The competition-density principle, which can mathematically be described by the competition-density rule, is an important principle in plant ecology. The border line relationship is the self-thinning rule. Despite the importance of both rules for forest management, they have been fit for few species. The aim of this study is to compare competition-density rule and self-thinning rule in particular with respect to potential density for 15 species from the Austrian National Forest Inventory (ANFI). The self-thinning line was estimated using quantile regression. The competition-density rule was fit as four- and as three-parameter model, where the fourth parameter was substituted (a) with a specific slope from the self-thinning line estimated from the ANFI and (b) Reineke’s slope (−1.605). Potential density was highest for Austrian pine and Norway spruce, followed by silver fir and Scots pine; it was considerably lower for European larch, stone pine and broadleaf species. Species-specific slopes of the self-thinning line ranged between −1.5 and −2.0 and were significantly different from Reineke’s slope for Norway spruce, European larch and European beech. Using robust estimation techniques, both competition-density rule and self-thinning line can also be fit for minor species, providing an important guide for practical forest management.