Three interpretations of the self-thinning rule

The self-thinning rule states that w, the mean biomass per plant in a dense monospecific stand, is related to p, the number of plants in a unit area of that stand, by the power law relationship w = Kp−λ, where λ is approximately three-halves. The support for this rule, theoretical as well as experimental, has thus far been largely empirical. In an effort to provide a firmer theoretical basis for it, three different and somewhat independent theoretical models are propounded and shown to lead to power law relationships with characteristic exponents in the vicinity of three-halves.