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

@article{Dodds2001ReexaminationOT, title={Re-examination of the "3/4-law" of metabolism.}, author={P. Dodds and D. Rothman and J. Weitz}, journal={Journal of theoretical biology}, year={2001}, volume={209 1}, pages={ 9-27 } }

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… Expand

#### Figures, Tables, and Topics from this paper

#### Paper Mentions

#### 500 Citations

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

- Biology, Medicine
- Journal of theoretical biology
- 2003

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’’. Expand

The predominance of quarter-power scaling in biology

- Biology
- 2004

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. Expand

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

- Mathematics, Physics
- 2015

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. Expand

Curvature in metabolic scaling

- Medicine, Physics
- Nature
- 2010

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. Expand

On the thermodynamic origin of metabolic scaling

- Mathematics, Medicine
- Scientific Reports
- 2018

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. Expand

Is there a Universal Temperature Dependence of metabolism

- Biology
- 2004

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. Expand

Revisiting the evolutionary origin of allometric metabolic scaling in biology

- Biology
- 2008

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. Expand

Allometric scaling of mammalian metabolism

- Mathematics, Medicine
- Journal of Experimental Biology
- 2005

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. Expand

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

- Mathematics, Medicine
- Journal of Experimental Biology
- 2008

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. Expand

Lack of Evidence for 3/4 Scaling of Metabolism in Terrestrial Plants

- Mathematics
- 2005

Scaling, as the translation of information across spatial, temporal, and organizational scales, is essential to predictions and understanding in all sciences and has become a central issue in… Expand

#### References

SHOWING 1-10 OF 88 REFERENCES

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

- Mathematics, Medicine
- Respiration physiology
- 1983

It is demonstrated that there is both experimental and theoretical justification for the use of both exponents in describing the variation of basal energy metabolism among animals of different size and species. Expand

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

- Biology
- 1967

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. Expand

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

- Biology, Medicine
- Comparative biochemistry and physiology. A, Comparative physiology
- 1986

The database used by Hemmingsen (1960) to compute energy metabolism in unicellular organisms was reassembled and submitted to linear (log-log) analysis, concluding that the case for a three-quarters power rule expressing energy metabolism as a function of size in un icellular organisms generally is not at all persuasive. Expand

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

- Mathematics, Medicine
- Journal of theoretical biology
- 1990

A model of "elastic similarity" was developed and this model predicts an interspecific scaling exponent of 0-75 directly, and an alternative approach (Blum, 1977) also predicts the 0·75 exponent directly. Expand

Energy metabolism and body size. I. Is the 0.75 mass exponent of Kleiber's equation a statistical artifact?

- Biology, Medicine
- Respiration physiology
- 1982

This study shows that the 0.75 interspecific mass exponent in Kleiber's equation is a statistical artifact and suggests that the data from literature are consistent with the theory of biological similitude of Lambert and Teissier. Expand

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

- Medicine
- Science
- 1997

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. Expand

Energy metabolism and body size. II. Dimensional analysis and energetic non-similarity.

- Biology, Medicine
- Respiration physiology
- 1982

The allometric equation P = aMb (P: standard metabolism, M: body mass, a: mass coefficient, and b: mass exponent) can be theoretically derived from the following relations: l/L = t/T = lambda, m/M =… Expand

Dimensional analysis and theory of biological similarity.

- Medicine
- Physiological reviews
- 1975

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. Expand

Size and Scaling in Primate Biology

- Biology
- Advances in Primatology
- 1985

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. Expand

On the allometric mass exponent, when it exists.

- Mathematics, Medicine
- 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. Expand