Abstract:

Aims The self-thinning boundary line represents the upper boundary of possible yield-density combinations in crowded stands. Our aim was to elucidate how to objectively select data points and the most appropriate regression method for estimating the self-thinning boundary line.

Methods We compare alternatives for selecting data points and fitting coefficients that have been or can be used to estimate the self-thinning boundary line. The selecting data point methods include visualized inspection, mortality criterion, equal intervals method and relative density method; the fitting coefficients methods include ordinary least squares regression, reduced major axis method, quantile regression and stochastic frontier function. We used data from an even-aged Cunninghamia lanceolata stand as example.

Important findings Visualized inspection is subjective. Mortality criterion can precisely determine onset of the self-thinning without the independent-density stand. The equal intervals method has the potential to reduce independent-density mortality effect and the selected data points may adequately reflect stand self-thinning dynamics. The relative density method can avoid influence of independent-density mortality and ensure stand density threshold value. Stand self-thinning span is a limiting factor with equal intervals and relative density. The slope and intercept estimates used in ordinary least squares regression and reduced major axis differ from the stand self-thinning upper boundary line. Both the quantile regression technique and stochastic frontier function produce the self-thinning boundary line because the method can easily perform that there are no significant departures based on the adequate selection of quantile value and residual converge to zero with underlying distributional assumptions.

Key words: Cunninghamia lanceolata, fitting coefficients methods, selection of data points, self-thinning boundary line