Significant differences and curvilinearity in the self-thinning relationships of 11 temperate tree species assessed from forest inventory data

Introduction In pure and even-aged stands, the allometry between mean tree size and maximum stand density-or self-thinning relationship-has long been considered a constant among tree species. Although the self-thinning allometric coefficient has been shown to be species-dependent, estimates available for a given species also differ. Whether this coefficient truly varies across species thus remains an open issue. A potential cause of variation in the coefficient may lie in a departure from the allometric assumption in the self-thinning relationship. Methods We analysed the species dependence of the self-thinning relationship for 11 temperate and Mediterranean tree species growing in pure and even-aged stands in France based on the French National Forest Inventory (NFI) data. Self-thinning relationships were fitted using a 'stochastic frontier' technique. Pairwise comparison tests of the self-thinning allometric coefficients were implemented. We also investigated the allometric nature of the relationship by testing a linear and a curvilinear model of log density against the log quadratic mean diameter. Results Self-thinning relationships were clearly evidenced from the NFI data and displayed significant differences between species. The curvilinear model was significantly more accurate for 7 out of 11 species and depicted a concave relationship, suggesting a decrease in self-tolerance over ontogeny. Conclusion As a major finding, the self-thinning relationship significantly varies across species. We emphasise the need to consider a high number of species to show such specific variations in the self-thinning relationship. Another important outcome is that the self-tolerance depends on the developmental stage.