Sources of Variation in the Self-Thinning Boundary Line for Three Species with Varying Levels of Shade Tolerance
The species self-thinning boundary line has been widely analyzed with a variety of statistical techniques. Most previous studies in the forestry literature have reported that the relationship does not differ across a range of stand and site factors, but these studies have primarily used statistical techniques that make model fitting subjective or interpretation of covariate significance difficult. There is growing evidence that the use of stochastic frontier analysis is an effective statistical means for objectively fitting the species self-thinning boundary line, offering the opportunity to test the influence of additional covariates. Using extensive even-aged coastal Douglas-fir (Pseudotsuga menziesii var. menziesii [Mirb.] Franco), western hemlock (Tsuga heterophylla), and red alder (Alnus rubra Bong.) data sets in the Pacific Northwest, we examined the assumption that the intercept and slope of the species self-thinning boundary line are insensitive to stand and site factors. Likelihood ratio tests indicated that site index, stand origin (natural versus planted), and purity (proportion of basal area in the primary species) significantly influenced the species self-thinning boundary line intercept for each of the species examined in this study. In Douglas-fir and western hemlock, the slope of the self-thinning boundary was also dependent on stand origin as well as site index in the case of Douglas-fir. Fertilization did not significantly influence the intercept or slope of the species self-thinning line for Douglas-fir and western hemlock. In addition, the inclusion of site aspect and dryness index marginally improved the red alder model of self-thinning, but neither site soil nor climatic variables improved the models for western hemlock and Douglas-fir. Thus, the species self-thinning boundary line can vary significantly among stands, and its variation is driven by several distinct factors; stochastic frontier analysis is an effective tool for identifying these factors.