Density-dependent mortality models for mono- and multi-species uneven-aged stands: The role of species mixture

The self-thinning law describes the progressive mortality of growing trees in crowded even-aged stands because of competition. In uneven-aged stands, however, density-dependent mortality is relatively poorly known. We developed density-dependent self-thinning models for mono-species and multi-species uneven-aged stands. Three models for mono-species Picea abies, Abies alba and Fagus sylvatica stands, four models for mixed conifer/ broadleaf stands and a model for single tree selection stands as a specific type of uneven-aged forest were parametrized by Quantile Regression (QR) and Stochastic Frontier Analysis (SFA) using data from n = 31,612 forest inventory plots in Slovenia. The average slope of the self-thinning line in uneven-aged stands of-1.422 was statistically significantly lower than Reineke's slope. Maximum stand density was higher in mono-species stands than in multi-species stands. The higher the proportion of beech in a stand, the higher the intercept and slope of the maximum stand density line. In single tree selection stands, the intercept and the slope of the maximum stand density line were highest and statistically different from all other types of uneven-aged forests. Species mixture had an impact on the slope and intercept of the self-thinning line. The slopes of the self-thinning lines differed between the studied types by up to 36% and 69% in the SFA and QR models, respectively, while the intercepts differed by up to 13% and 24%, respectively. However, maximum stand densities differed significantly only between compositionally very dissimilar stand types, such as Fagus sylvatica-or Picea abies-dominated mixtures versus other broadleaf mixtures (e.g., Quercus petraea, Carpinus betulus). The SFA predictions of maximum stand densities were systematically lower and less varying than the QR predictions, but not statistically different. The models can be used to constrain individual tree growth models in uneven-aged forests and to estimate the onset of inter-tree competition in irregular stands.