Density Frontiers for Even-Aged Douglas-fir and Western Hemlock Stands in Coastal British Columbia
Douglas-fir (Pseudotsuga menziesii [Mirb.] Franco var. menziesii) and western hemlock (Tsuga heterophylla [Raf.] Sarg.) are the two most common and commercially important species on the coast of British Columbia, Canada. Our research focused on determining the relationship between maximum density and top height for pure stands of these species. These relationships can be used to provide a constraint on mortality functions in individual-tree growth and yield models for even-aged stands. Our data consist of density and top height from experimental plots established along the coast of British Columbia, Washington, and Oregon. These experiments yielded 2,930 observations from 628 plots. We fit stochastic frontier functions to the density/top height data. Stochastic frontier functions have a stochastic component that allows data points to lie on either side of the frontier. The fitting of the frontier functions using maximum likelihood estimation resulted in maximum density lines as an exponential function of top height for both species. The fitted model is based loosely on the −3/2 power thinning law. Our analysis shows that these relationships hold across sites with differing quality. The maximum density line is greater for western hemlock than for Douglas-fir up to a height of about 35 m, at which point they are almost the same. The higher maximum density of western hemlock is likely related to its greater shade tolerance. We used the growth-and-yield model Table Interpolation Program for Stand Yields (TIPSY) to simulate the growth of high-density stands of Douglas-fir and western hemlock. These simulations gave similar results to our fitted density frontier line.