Does Body Size Optimization Result in Skewed Body Size Distribution on a Logarithmic Scale?

Abstract

Kozlowski and Weiner (1997) challenged the idea that interspecific allometries reflect unitary functional relationships between parameters that are shared by all of the species within a set. They suggested that these allometries might also be produced as a by-product of underlying intraspecific processes. In the course of their argument, Kozlowski and Weiner developed a model for the optimal adult body size and found a striking result, which is that optimizing body size produces a distribution of sizes within a taxon that is skewed to the right, even when examined on a logarithmic scale. In this note, we point out that while this result was based on a limited range of parameters, it is actually a very general outcome of optimizing body size in their model. Kozlowski and Weiner’s (1997) new model is based on the assumptions that assimilation and respiration are allometric functions of body size, aw and hw , respectively; that the production rate, P(w), is the difference between assimilation and respiration, that is, ; b b P(w) 5 aw 2 hw that the mortality rate, m(w), can be described by ; and that the optimal adult body size can l m(wx) 5 2gw be found as a solution of