A note on metabolic rate dependence on body size in plants and animals (Q2177122)

This paper discusses the biophysical basis of allometric scaling. The base metabolic rate \(B\) of an organism is often taken to scale with a power law in organismal mass \(M\), \(B \sim M^\alpha\) across a wide range of masses and phyla, but there is an ongoing empirical debate about the value of the exponent \(\alpha\). The ``textbook'' value for the exponent \(\alpha\) is \(3/4\), in contrast to the value of \(2/3\) that would be expected from a simple square-cube scaling and elementary physics. Previous work by West, Brown \& Enquist attempted to explain and justify an \(\alpha = 3/4\) scaling through considerations of fluid transport in plants. The main result of this paper is a derivation of an allometric scaling law from considerations of energy uptake and metabolic requirements. They argue that the limiting factor in determining factor in base metabolic rates is not energy transport within the organism, but energy uptake through its boundary. As energy uptake scales with area, and metabolic requirements with mass, these results support an allometric scaling of \(\alpha = 2/3\). They thus claim to refute the approach of West, Brown \& Enquist. They study plants in-depth as upper limits on energy uptake can be related to total leaf area. They also derive a law relating leaf area index to altitude that shows reasonable agreement with experimental data. Their results should be qualified by their attempt to extend it to describe animals. The same framework suggests there may be a departure from \(\alpha = 2/3\) in very large mammals. This paper is primarily of interest to biophysicists interested in allometry and physiology. Botanists and ecologists may be interested in predictions of leaf area index at altitude.