The allometric interpretation of the self-thinning rule

Plant populations growing at high densities undergo density-dependent mortality or self-thinning. The density of survivors ({ρ}) is related to their mean biomass (w) by the power equation w = K_ρ^?a, where a is $\text{3}\text{2}$. This is known as the “self-thinning rule”. This relationship is very general for plant populations and represents both an asymptotic time-trajectory for a particular population and a boundary line for juxtaposed joint values of w and p of separate populations. The traditional allometric derivation of the rule is outlined and shown to be unrealistic. An attempt to reformulate the self-thinning rule, based on the traditional allometric derivation, is shown to be unsatisfactory and an alternative allometric derivation is presented. The rule in its traditional statement $\text{w = K}{}_{\mathrm{\rho }}{}^{\mathrm{?3}}\text{2}$ is still its best expression. The nature of the constant K is discussed with particular reference to its dimensionality.