On the conceptual basis of the self‐thinning rule

Abstract

We show a widely accepted proof of the self‐thinning rule offered by Enquist et al. to be mathematically incomplete, as it does not identify the plant mass distributions that satisfy a condition implicitly used in the proof. We propose a method to guide the search for such mass distributions, based on a requirement of maximum mass diversity under the appropriate constraints. This generic method allows construction of a probability density that incorporates the available information on a given stochastic variable, and we illustrate its use through the calculation of a continuous mass distribution for the self‐thinning rule that satisfies the implicit condition mentioned above. We suggest a biological justification of maximum mass diversity, as a corollary to the random and unbiased nature of the source of diversity in Darwin's principle.

Scaling and power-laws in ecological systems

“…Recent work on scaling relationships has pointed out to the effect of data aggregation in the estimation of scaling relationships in ecology (Torres et al, 2001;Savage, 2004c;Cohen et al, 2005). This is an important methodological point that should be borne in mind when working with scaling relationships in general.…”

Self‐thinning of plant populations from a dynamic viewpoint

“…1995; Adler 1996; Franco & Kelly 1998; Li, Wu & Zou 2000). Recently it has been argued that the −3/2 law really should be a −4/3 law (Enquist, Brown & West 1998; Niklas, Midgley & Enquist 2003; but see Torres et al . 2001 for an alternative view) based on the proposition that the metabolic rate of individuals scales as the 3/4 power of body mass (West, Brown & Enquist 1997; but see Bejan 2000, 2001 for an alternative view about the origin of 3/4 power scaling).…”

On the relationship between mass and diameter distributions in tree communities

“…Because the observed form of the diameter distribution in tree communities is not consistent with an ISD of the form , the published metabolic theory explanation for the form of the ISD (Enquist & Niklas 2001) is not supported by empirical data. Therefore, metabolic theory has yet to provide a mechanistic explanation for ISDs within forests (see also Torres et al. 2001; Coomes 2006; Muller‐Landau et al.…”

“…Because the observed form of the diameter distribution in tree communities is not consistent with an ISD of the form f M ðM Þ / M À3=4 , the published metabolic theory explanation for the form of the ISD is not supported by empirical data. Therefore, metabolic theory has yet to provide a mechanistic explanation for ISDs within forests (see also Torres et al 2001;Coomes 2006;Muller-Landau et al 2006b). In addition, the two studies in animal communities that have offered support for the predicted )3 ⁄ 4 form of the individual mass distribution (Ackerman et al 2004;Meehan 2006) did so using incorrect statistical methods (see White et al 2008 for a detailed explanation).…”