Allometric scaling of metabolic rate

An apparent power-law relationship between standard metabolic rate and body mass obtains for many if not all groups of organisms. Explanations have proved elusive and current ideas are controversial. In collaboration with Lloyd Demetrius and his colleagues (Harvard University, Boston, MA and Max Planck Institute, Berlin), we are developing an account of metabolic allometry based on quantum metabolism and directionality theory. The key references are as follows.

Agutter, P. S. & Wheatley, D. N. (2004) Metabolic scaling: consensus or controversy? Theor. Biol. Med. Mod. 1:13. PMID: 15546492

Abstract: Background - The relationship between body mass (M) and standard metabolic rate (B) among living organisms remains controversial, though it is widely accepted that in many cases B is approximately proportional to the three-quarters power of M. Results - The biological significance of the straight-line plots obtained over wide ranges of species when B is plotted against log M remains a matter of debate. In this article we review the values ascribed to the gradients of such graphs (typically 0.75, according to the majority view), and we assess various attempts to explain the allometric power-law phenomenon, placing emphasis on the most recent publications. Conclusion -

Although many of the models that have been advanced have significant attractions, none can be accepted without serious reservations, and the possibility that no one model can fit all cases has to be more seriously entertained.

Demetrius, L. (2006) The origin of allometric scaling laws in biology. J. Theor. Biol. 233, 455-467. PMID: 16989867

Abstract: The empirical rules relating metabolic rate and body size are described in terms of (i) a scaling exponent, which refers to the ratio of the fractional change in metabolic rate to a change in body size, (ii) a proportionality constant, which describes the rate of energy expenditure in an organism of unit mass. This article integrates the chemiosmotic theory of energy transduction with the methods of quantum statistics to propose a molecular mechanism which, in sharp contrast to competing models, explains both the variation in scaling exponents and the taxon specific differences in proportionality constants. The new model is universal in the sense that it applies to unicellular organisms, plants and animals.

Demetrius, L. & Ziehe, M. (2007) Darwinian fitness. Theor. Popul. Biol. 72, 323-345. PMID: 17804030

Abstract: The term Darwinian fitness refers to the capacity of a variant type to invade and displace the resident population in competition for available resources. Classical models of this dynamical process claim that competitive outcome is a deterministic event which is regulated by the population growth rate, called the Malthusian parameter.

Recent analytic studies of the dynamics of competition in terms of diffusion processes show that growth rate predicts invasion success only in populations of infinite size. In populations of finite size, competitive outcome is a stochastic process--contingent on resource constraints--which is determined by the rate at which a population returns to its steady state condition after a random perturbation in the individual birth and death rates.

This return rate, a measure of robustness or population stability, is analytically characterized by the demographic parameter, evolutionary entropy, a measure of the uncertainty in the age of the mother of a randomly chosen newborn. This article appeals to computational and numerical methods to contrast the predictive power of the Malthusian and the entropic principles.

The computational analysis rejects the Malthusian model and is consistent with of the entropic principle. These studies thus provide support for the general claim that entropy is the appropriate measure of Darwinian fitness and constitutes an evolutionary parameter with broad predictive and explanatory powers.

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