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/Nt-1)/ln(D-t/Dt-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. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.