The inter-specific body mass allometries describe the traits of organisms as power functions of body mass, i.e., as t=w^a where t is the trait, w the body mass, and a the exponent. For life-history traits like the metabolic rate, life-span, life-time reproduction, and the population growth rate the exponents have been estimated to 3/4, 1/4, 0, and -1/4 for terrestrial organisms, while the exponents for ecological traits like the homerange area and the population density have been estimated to 1 and -3/4 (Calder, 1984; Peters, 1983).

Until recently there was no general explanation for the exponents of the body mass allometries (LaBarbera, 1986). But in Malthusian Relativity the above mentioned exponents have been deduced from the ecological constraints on the foraging process in mobile organisms (Witting, 1995). The deduction suggests that the characteristic values of ±1/4 and ±3/4 apply only to organisms that forage in two spatial dimensions, while the corresponding values for organisms that forage in three spatial dimensions are ±1/6 and ±5/6. This prediction has been confirmed empirically: the lifespan exponent is 0.25 ±0.04 among 195 species of terrestrial mammals, while it is 0.16 ±0.02 among 40 species of pelagic mammals (terrestrial mammals normally forage in two dimensions, while pelagic mammals are likely to forage in three dimensions).

More recently West et al. (1997) have proposed that the 3/4 exponent for the metabolic rate reflects the constraints associated with the branching of vascular systems. Unlike Witting's proposal the latter model does not explain the exponents of other ecological allometries, and nor does it explain why the 3/4 exponent apparently applies only to organisms that forage in two dimensions, while the metabolic exponent appears to be 5/6 among organisms that forage in three dimensions [see Gates and Gittleman (1998) and Witting (1998) for discussion].

References

• Calder, W. A. I. (1984). Size, function, and life history. Cambridge: Harvard University Press.
• Gates, S. E. & Gittleman, J. L. (1998). Reply from S. E. Gates and J. L. Gittleman. Trends in Evolution and Ecology 13, 25.
• LaBarbera, M. (1986). The evolution and ecology of body size. In: Patterns and processes in the history of life (Raup, D. M. & Jablonski, D., eds) pp. 69--98. Berlin: Springer-Verlag.
• Peters, R. H. (1983). The ecological implication of body size. Cambridge: Cambridge University Press.
• West, G. B., Brown, J. H., & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science 276, 122--126.
• Witting, L. (1995). The body mass allometries as evolutionarily determined by the foraging of mobile organisms. Journal of Theoretical Biology 177, 129--137.
• Witting, L. (1998). Body mass allometries caused by physiological or ecological constraints? Trends in Evolution and Ecology 13, 25.