Calibrating the self-thinning frontier

Calibration of the self-thinning frontier in even-aged monocultures is hampered by scarce data and by subjective decisions about the proximity of data to the frontier. We present a simple model that applies to observations of the full trajectory of stand mean diameter across a range of densities not necessarily close to the frontier. Development of the model is based on a consideration of the slope s = ln(N_t/N_t−1)/ln(D_t/D_t−1) of a log-transformed plot of stocking N_t and mean stem diameter D_t at time t. This avoids the need for subjective decisions about limiting density and allows the use of abundant data further from the self-thinning frontier. The model can be solved analytically and yields equations for the stocking and the stand basal area as an explicit function of stem diameter. It predicts that self-thinning may be regulated by the maximum basal area with a slope of −2. The significance of other predictor variables offers an effective test of competing self-thinning theories such Yoda's −3/2 power rule and Reineke's stand density index.