The Importance of Using Permanent Plots Data to Fit the Self-Thinning Line: An Example for Maritime Pine Stands in Portugal

Abstract

Density-dependent mortality occurs in the evolution of even-aged populations when these approach crown closure age. This density-dependent mortality is regulated by the so-called “3/2 power law of self-thinning” that assumes a constant slope for the line relating the log of stand density with the log of the average tree size, the self-thinning line or maximum size–density relationship, MSDR. A good estimate of the self-thinning line is therefore an essential component to any forest growth model. Two concepts for the MSDR have emerged: (1) a static upper limit for the species; and (2) a dynamic self-thinning line influenced by several factors (e.g., management techniques, site quality and/or genetics). The objective of this study was to estimate a new static self-thinning line based on the quadratic mean diameter at breast height (Reineke’s self-thinning line) for the generalized use in maritime pine growth models in Portugal. Data from 41 observations obtained in nine long-term permanent experimental trials of maritime pine species were carefully selected from a data set of 186 plots as being under self-thinning. Two methods were used: OLS and mixed linear models. An exploratory analysis on the impact of each environmental variable on the slope and intercept of the self-thinning line led to the selection of a subset of environmental variables later used in an all possible regressions algorithm to find the subsets leading to the lowest values of Akaike information criterion (AIC). The OLS procedure showed that the differences between the plots could be explained by site index, by climate variables (e.g., evaporation or climatic indices) and the use of more than one covariable slightly improved the fit. Nevertheless, the best MSDR line fitted with mixed linear models (ln N = 12.97158 − 1.83926 ln dg) having the plot random effect in the intercept, largely outperformed the best OLS model and is therefore recommended for generalized use in forest growth models.