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(Nt/Nt−1)/ln(Dt/Dt−1) of a log-transformed plot of stocking Nt and mean stem diameter Dt 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.