Re-examination of the "3/4-law" of metabolism.

  title={Re-examination of the "3/4-law" of metabolism.},
  author={Peter Sheridan Dodds and Daniel H. Rothman and Joshua S. Weitz},
  journal={Journal of theoretical biology},
  volume={209 1},
We examine the scaling law B is proportional to M(alpha)which connects organismal resting metabolic rate B with organismal mass M, where alpha is commonly held to be 3/4. Since simple dimensional analysis suggests alpha = 2/3, we consider this to be a null hypothesis testable by empirical studies. We re-analyse data sets for mammals and birds compiled by Heusner, Bennett and Harvey, Bartels, Hemmingsen, Brody, and Kleiber, and find little evidence for rejecting alpha = 2/3 in favor of alpha = 3… 

The predominance of quarter-power scaling in biology

It is shown that interspecific variation in BMR, as well as field metabolic rates of mammals, and basal or standard metabolic rates for many other organisms, including vertebrates, invertebrates, protists and plants, all scale with exponents whose confidence intervals include 3 / 4 and exclude 2 / 3.

A note on metabolic rate dependence on body size in plants and animals.

The agreement about the ubiquity of a1⁄4 3/4 in the living world has recently been seriously challenged by extensive analyses of data unavailable at the time of adopting the ‘‘3/4 rule’’.

A common origin for 3/4- and 2/3-power rules in metabolic scaling

This model proves that both the 3/4- and 2/3-exponents are phenomenological approximations of the same scaling rule within their applicable mass ranges, and that the 2/ 3-rule does not originate from the classical surface law.

Curvature in metabolic scaling

It is shown that the relationship between mass and metabolic rate has convex curvature on a logarithmic scale, and is therefore not a pure power law, even after accounting for body temperature.

On the thermodynamic origin of metabolic scaling

A conceptually simple thermodynamic framework, where the dependence of metabolic rate with body mass emerges from a trade-off between the energy dissipated as heat and the energy efficiently used by the organism to maintain its metabolism, to reconcile previously inconsistent empirical evidence in mammals, birds, insects and even plants.

Is there a Universal Temperature Dependence of metabolism

The assumptions underlying the formulation of the Universal Temperature Dependence (UTD) of metabolism are examined, and the relationship with a carefully assembled data set for teleost fish is tested.

Revisiting the evolutionary origin of allometric metabolic scaling in biology

It is concluded that the West-Brown-Enquist model cannot account for the observed universal metabolic scaling relation, and Kleiber's law is still as theoretically unexplained as ecologically important.

Allometric scaling of mammalian metabolism

The 3/4 power scaling of RMRpp is part of a wider trend where, with the notable exception of cold-induced maximum MR, large herbivores are therefore less likely to be postabsorptive when MR is measured, and are likely to have a relatively high MR if not post absorptionptive.

Traditional allometric analysis fails to provide a valid predictive model for mammalian metabolic rates

The concept of 3/4-power scaling of metabolic rate to body mass is not well supported because the underlying statistical model does not apply to mammalian species spanning the full range in body size.

Beyond the ‘3/4‐power law’: variation in the intra‐and interspecific scaling of metabolic rate in animals

  • D. S. Glazier
  • Biology
    Biological reviews of the Cambridge Philosophical Society
  • 2005
It is shown that the ‘3/4‐power scaling law’ of metabolic rate is not universal, either within or among animal species, and appears to be the more complex result of diverse adaptations evolved in the context of both physico‐chemical and ecological constraints.



The 3/4 mass exponent for energy metabolism is not a statistical artifact.

A Re-Examination of the Relation between Standard Metabolic Rate and Body Weight in Birds

King and Farner (1961) discuss the possibility that the avian relationship may be curvilinear in the lower ranges of body weight, since small birds have higher metabolic rates than predicted by their equation, and re-analyzed the relationship using more rigorous criteria for including data in their computations.

Scaling of energy metabolism in unicellular organisms: a re-analysis.

  • J. Prothero
  • Environmental Science
    Comparative biochemistry and physiology. A, Comparative physiology
  • 1986

On Blum's four-dimensional geometric explanation for the 0.75 exponent in metabolic allometry.

A General Model for the Origin of Allometric Scaling Laws in Biology

The model provides a complete analysis of scaling relations for mammalian circulatory systems that are in agreement with data and predicts structural and functional properties of vertebrate cardiovascular and respiratory systems, plant vascular systems, insect tracheal tubes, and other distribution networks.

Dimensional analysis and theory of biological similarity.

The body weight of an organism is an adequate reference index for the correlation of morphological and physiological characteristics and the statistical analysis of the experimental data can be represented conveniently by means of the logarithmic equivalent of Huxley's allometric equation.

Size and Scaling in Primate Biology

Although the subject matter and specific details of the issues considered in the 20 chapters that follow are very diversified, all topics share the same fundamental and unifying biological theme: body size variation in primates and its implications for behavior and ecology, anatomy and physiology, and evolution.

On the allometric mass exponent, when it exists.

  • H. Feldman
  • Biology
    Journal of theoretical biology
  • 1995
An axiomatic basis for establishing the existence of a power law is proposed and a formula for calculating the theoretical mass exponent b is derived and it is shown that the value of b, when it exists, depends not only on the physical dimensions of q but also on biological assumptions about the class of animals under consideration.