Unified Theory of Interspecific Allometric Scaling
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
A general simple theory for the interspecific allometric scaling is developed
in the $d+1$-dimensional space ($d$ biological lengths and a physiological time) of metabolic states of organisms. It is assumed that natural selection shaped the metabolic states in such a way that the mass and energy $d+1$-densities are size-invariant quantities (independent of body mass).
The metabolic rates of animals are controlled by three main transport processes: convection, diffusion and anomalous diffusion.
The different metabolic states, such as basal and maximum, are described
by considering that the biological lengths and the physiological time are related by different transport processes of energy and mass.
Different transport mechanisms are related to different metabolic
states, with its own values for allometric exponents, in agreement with data.
We find that the exponent $b$ of the metabolic rate ($BM^b$) is
$b=5/7$ for the basal case and $b=6/7$ for the aerobic sustained maximum regime.