Self-thinning is the natural process whereby numbers of trees per unit area decrease as average tree size increases over time. It is a process intrinsic to all forest and plant communities whose composition and structure are influenced by competition for growing space. Stands follow a relatively predictable course of density-dependent tree mortality as numbers of trees per unit area decrease with increasing average tree size. It is generally assumed that the combined effects of crown expansion and tree mortality are compensatory so that canopy closure is always maintained. In forest management, knowledge of self-thinning point and information about tree density showing a sharp increase of natural mortality is useful to determine the optimal thinning regimes at stand level. Yoda’s self-thinning line and Reineke’s stand density index are useful and widely used in plantation growth models to predict natural mortality and in process-based models; calibrating these relationships is anyway difficult. Self-thinning and size-density relationships in unthinned even-aged Calabrian pine stands in Calabria (Southern Italy) were studied. Four different diameter-density equations were fitted and compared: the Reineke's model (1933), the modification of this model proposed by Zeide (1995), the self-thinning model developed by Tang et al. (1994), the self-thinning frontier adjusted by Vanclay & Sands (2009). Data from ninety untreated or control permanent plots in experimental areas located in artificial stands were used. Reineke's equation for fully stocked stands relates the number of trees of a stand with their square mean diameter. Zeide proposed a modication to Reineke's equation considering that the slope would not be constant, but changing with age. The selfthinning model developed by Tang et al. relates the number of trees with the square mean diameter, and assumes that in a unthinned stand, which has not reached the maximum density, the self-thinning rate increases with stand density index. The model proposed by Vanclay & Sands can be solved analytically and yields equations for the stocking and the stand basal area as an explicit function of stem diameter. It predicts that self-thinning may be regulated by the maximum basal area. Linear regressions were fitted using the REG procedure of SAS for Reineke's and Zeide’s models. For the non-linear regression the Gauss-Newton algorithm from NLIN procedure was performed. Akaike's information criterion, as a measure of the goodness of fit of the four estimated statistical models, was applied. The slope obtained by Reineke’s model (1.580) not is significantly different from the costant value of -1.605 at the 95% confidence level. When height was included in the relationships between number of trees and diameter (modification proposed by Zeide) the adjusted correlation coefficient increased and the squared mean error decreased. The stand density index calculated from Reineke's straight line previously fitted (1283 trees∙ha-1) is lower than the value obtained from the Tang’s model (1919 trees∙ha-1) but these values are not statistically different. The stand self-thinning model proposed by Tang et al., although showing an objective uncertainty due to a relatively wide confidence interval, describes better than other models the relationships between stand density and average diameter in unthinned even-aged Calabrian pine stands in Calabria (Southern Italy)
