Reevaluating the self-thinning boundary line for ponderosa pine (Pinus ponderosa) forests

The self-thinning rule has been used extensively to predict population dynamics under intraspecific and interspecific competition. In forestry, it is an important silvicultural concept for maintaining stand health in the face of climate change and biotic stress, but uncertainty exists because traditional self-thinning limits were set subjectively without regard to site quality. We addressed this by analyzing ponderosa pine (Pinus ponderosa Lawson & C. Lawson) data from 109 research plots measured repeatedly and 59 inventory plots measured once across California. Self-thinning boundaries were fitted to the data with quantile regression and stochastic frontier function (SFF) techniques with and without site index (SI) as a covariate. The models from both methods fitted the data well with either research plots or all plots. Slopes for size-density trajectories were -0.45 with the 0.99 quantile and -0.47 for SFF. Maximum stand density indices (SDI) were 1250 trees per hectare (TPH) with the 0.99 quantile and 1050-1060 TPH with SFF. Mortality occurred when site occupancy from SFF reached 0.75, suggesting a zone of imminent mortality. Curvilinear trends in maximum SDI across SI for both methods indicate that self-thinning varies with site quality. Any management regimes that increase site quality and productivity will increase the self-thinning boundary.