Self-thinning of plant populations from a dynamic viewpoint

1. In this paper a new formulation of the self-thinning law for plant populations is presented, based on dynamical principles. The basis of the new approach is explicitly to separate the equation of state (total = mean × number) from the change in state (δtotal = mean × δnumber + number × δmean). 2. Using the dynamical approach, an analytical expression for the self-thinning exponent is derived which shows that the self-thinning exponent follows a trajectory, but whenever the total is constant the self-thinning exponent must, by definition, = -1. Conversely, whenever the total varies the self-thinning exponent must, by definition, differ from -1. The underlying general principles of self-thinning trajectories are deduced. 3. The new dynamic interpretations are general because they are independent of the details about how the changes in the number and mean occurred. 4. The theory is demonstrated using a typical self-thinning experiment.