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

  title={Beyond the ‘3/4‐power law’: variation in the intra‐and interspecific scaling of metabolic rate in animals},
  author={Douglas Stewart Glazier},
  journal={Biological Reviews},
In this review I show that the ‘3/4‐power scaling law’ of metabolic rate is not universal, either within or among animal species. Significant variation in the scaling of metabolic rate with body mass is described mainly for animals, but also for unicells and plants. Much of this variation, which can be related to taxonomic, physiological, and/or environmental differences, is not adequately explained by existing theoretical models, which are also reviewed. As a result, synthetic explanatory… 

The 3/4-Power Law Is Not Universal: Evolution of Isometric, Ontogenetic Metabolic Scaling in Pelagic Animals

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Effects of metabolic level on the body size scaling of metabolic rate in birds and mammals

  • D. S. Glazier
  • Biology, Environmental Science
    Proceedings of the Royal Society B: Biological Sciences
  • 2008
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  • D. S. Glazier
  • Biology
    Biological reviews of the Cambridge Philosophical Society
  • 2010
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The methods of scaling analysis are reviewed, using examples for a range of traits with an emphasis on those related to metabolism in animals, and mechanistic explanations for metabolic rate that may explain the size- and temperature-dependence of this trait are proposed.

Phylogeny and metabolic scaling in mammals.

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The intraspecific scaling of metabolic rate with body mass in fishes depends on lifestyle and temperature.

A new model postulates that the metabolic scaling exponent (b) varies between 2/3 and 1, and is inversely related to the elevation of the intraspecific scaling relationship (metabolic level, L), which in turn varies systematically among species in response to various ecological factors.

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Variation in scaling relationships, which occurred at different hierarchical levels and across time as the fish aged, may have implications for bioenergetics and ecosystem modelling, and for individual ecological and physiological studies where body mass adjustments are made using specific scaling exponents to compare traits of interest between different-sized individuals.

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This heuristic attempt at building a unifying theory of metabolic scaling will not only stimulate further testing of all of the various subtheories composing it, but also foster an appreciation that many current models are, at least in part, complementary or even synergistic, rather than antagonistic.



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’’.

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.

No foundation of a “3/4 power scaling law” for respiration in biology

It is shown that young and fast growing stages show higher weight specific respiration rates than older and adult stages, and this implies that the b values tend to be higher: b∼ 1 in small (young) organisms falling to b = 0.6–0.7 in larger (older) stages.

Physiology (communication arising): Why does metabolic rate scale with body size?

A multiple-cause model for mammalian metabolic rate is proposed as the “sum of multiple contributors”, Bi, which is assumed to scale as Bi = aiMML:Mbi, and it is argued that this scaling equation is based on technical, theoretical and conceptual errors, including misrepresentations of the published results.

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

Supply–demand balance and metabolic scaling

It is shown that the ubiquitous 3/4 power law for interspecific metabolic scaling arises from simple, general geometric properties of transportation networks constrained to function in biological organisms.

Mammalian basal metabolic rate is proportional to body mass2/3

  • C. R. WhiteR. Seymour
  • Biology
    Proceedings of the National Academy of Sciences of the United States of America
  • 2003
A new analysis of the allometry of mammalian BMR that accounts for variation associated with body temperature, digestive state, and phylogeny finds no support for a metabolic scaling exponent of 3/4.

Complications Inherent in Scaling the Basal Rate of Metabolism in Mammals

  • B. McNab
  • Environmental Science
    The Quarterly Review of Biology
  • 1988
The scaling of the basal rate of metabolism in mammals is reexamined and suggests that insight into the significance of scaling relations can be obtained by examining the residual variation around a scaling function as well as by examining conformation to the function.

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

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 = 3/4.