A comparison of alternative methods for estimating the self-thinning boundary line

The fundamental validity of the self-thinning law has been debated over the last three decades. A long-standing concern centers on how to objectively select data points for fitting the self-thinning line and the most appropriate regression method for estimating the two coefficients. Using data from an even-aged Pinus strobus L. stand as an example, we show that quantile regression (QR), deterministic frontier function (DFF), and stochastic frontier function (SFF) methods have the potential to produce an upper limiting boundary line above all plots for the maximum size-density relationship, without subjectively selecting a subset of data points based on predefined criteria. On the other hand, ordinary least squares (OLS), corrected ordinary least squares (COLS), and reduced major axis (RMA) methods are sensitive to the data selected for model fitting and may produce self-thinning lines with inappropriate slopes. However, statistical inference is very difficult with the DFF and QR methods. Although SFF produces a self-thinning line lower than the upper limiting boundary line because of the nature of the method, it can easily produce the statistics for inference on the model coefficients, given that there are no significant departures from underlying distributional assumptions.