Abstract
Introduction The self-thinning relationship established by Reineke in 1933 assumes a relationship between the number of stems and the quadratic mean diameter in fully stocked pure stands. This rule is extensively used for management purposes, but it has been initially calibrated for pure, even-aged stands for relatively few species. Objectives Here, we extend this relationship to mixed-species and mixed-size forests through a generalized modeling approach. Reineke's rule can be seen as a particular case of this generalized approach. Resource sharing is taken as a starting point; thus, both site fertility and diameter heterogeneity are taken into account. Discussion Calibration on actual inventories is made on a dataset of 82 French stands. The theoretical relationship is successfully adjusted for species in which enough data were available, namely, common beech (Fagus sylvatica L.), oak (Quercus petraea [Mattuschka] Liebl and Quercus robur L.), and Norway spruce (Picea abies [L.] Karst). Conclusion Self-thinning exponents obtained for beech and oak (1.86 and 1.76, respectively) can be used in the mixed-species equation that we developed. These results encourage calibrating the parameters for other species if appropriate data are available. Resource sharing is taken as a starting point; thus, both site fertility and diameter heterogeneity are taken into account. Discussion Calibration on actual inventories is made on a dataset of 82 French stands. The theoretical relationship is successfully adjusted for species in which enough data were available, namely, common beech ( Fagus sylvatica L.), oak ( Quercus petraea [Mattuschka] Liebl and Quercus robur L.), and Norway spruce ( Picea abies [L.] Karst). Conclusion: Self-thinning exponents obtained for beech and oak (1.86 and 1.76, respectively) can be used in the mixed-species equation that we developed. These results encourage calibrating the parameters for other species if appropriate data are available