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Cited by 433Physiological and biochemical adaptationsEvolution and Paleontology StudiesAdipose Tissue and Metabolism

Allometric scaling of mammalian metabolism

Open access
White, Craig R., Seymour, Roger S.·2005·Journal of Experimental Biology
DOI 10.1242/jeb.01501
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Abstract

The importance of size as a determinant of metabolic rate (MR) was first suggested by Sarrus and Rameaux over 160 years ago. Max Rubner's finding of a proportionality between MR and body surface area in dogs (in 1883) was consistent with Sarrus and Rameaux's formulation and suggested a proportionality between MR and body mass (Mb) raised to the power of 2/3. However, interspecific analyses compiled during the first half of the 20th century concluded that mammalian basal MR (BMR, ml O2 h(-1)) was proportional to Mb3/4, a viewpoint that persisted for seven decades, even leading to its common application to non-mammalian groups. Beginning in 1997, the field was re-invigorated by three new theoretical explanations for 3/4-power BMR scaling. However, the debate over which theory accurately explains 3/4-power scaling may be premature, because some authors maintain that there is insufficient evidence to adopt an exponent of 3/4 over 2/3. If progress toward understanding the non-isometric scaling of BMR is ever to be made, it is first essential to know what the relationship actually is. We re-examine previous investigations of BMR scaling by standardising units and recalculating regression statistics. The proportion of large herbivores in a data set is positively correlated both with the scaling exponent (b, where BMR=aMb b) and the coefficient of variation (CV: the standard deviation of ln-ln residuals) of the relationship. Inclusion of large herbivores therefore both inflates b and increases variation around the calculated trendline. This is related to the long fast duration required to achieve the postabsorptive conditions required for determination of BMR, and because peak post-feeding resting MR (RMRpp) scales with an exponent of 0.75+/-0.03 (95% CI). Large herbivores are therefore less likely to be postabsorptive when MR is measured, and are likely to have a relatively high MR if not postabsorptive. The 3/4 power scaling of RMRpp is part of a wider trend where, with the notable exception of cold-induced maximum MR (b=0.65+/-0.05), b is positively correlated with the elevation of the relationship (higher MR values scale more steeply). Thus exercise-induced maximum MR (b=0.87+/-0.05) scales more steeply than RMRpp, field MR (b=0.73+/-0.04), thermoneutral resting MR (RMRt, b=0.712+/-0.013) and BMR. The implication of this observation is that contamination of BMR data with non-basal measurements is likely to increase the BMR scaling exponent even if the contamination is randomly distributed with respect to Mb. Artificially elevated scaling exponents can therefore be accounted for by the inclusion of measurements that fail to satisfy the requirements for basal metabolism, which are strictly defined (adult, non-reproductive, postabsorptive animals resting in a thermoneutral environment during the inactive circadian phase). Similarly, a positive correlation between Mb and body temperature (Tb) and between Tb and mass-independent BMR contributes to elevation of b. While not strictly a defined condition for the measurement of BMR, the normalisation of BMR measurements to a common Tb (36.2 degrees C) to achieve standard metabolic rate (SMR) further reduces the CV of the relationship. Clearly the value of the exponent depends on the conditions under which the data are selected. The exponent for true BMR is 0.686 (+/-0.014), Tb normalised SMR is 0.675 (+/-0.013) and RMRt is 0.712 (+/-0.013).

Integrity signals

Registry

Crossref · 10.1242/jeb.01501

Cites

121 of 121 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

6 of 42 cited sources checked · 3 supported · 1 flagged · accuracy not yet measured

  • Findingcitation
    § Allometric scaling of mammalian metabolism

    With the exclusion of suspected non-basal lineages, BMR scales with an exponent of 0.686±0.014 (95% CI).

    “With the exclusion of these suspected non-basal lineages, White and Seymour (2003) found that BMR scales with an exponent of 0.686±0.014(Fig. •4).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites White and Seymour, 2003 source

      The Results (page not provided) report that, after excluding the specified lineages, the interspecific BMR scaling exponent was 0.68. Our copy does not give the more precise value 0.686 or the stated ±0.014 confidence interval; it also reports an interordinal exponent of 0.65. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
  • Findingcitation

    BMR scaling patterns observed for mammals and birds are not greatly altered by the inclusion of phylogenetic information.

    “Although none of the regressions presented here account for shared descent, BMR scaling patterns observed for mammals and birds are not greatly altered by the inclusion of such information (White and Seymour, 2003;McKechnie and Wolf, 2004).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites White and Seymour, 2003 source
    • cites McKechnie and Wolf, 2004 source
  • Premisecitation

    T_b is positively correlated with body mass.

    “which is also positively correlated with body mass (Withers et al., 2000;White and Seymour, 2003).”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Withers et al., 2000 source
    • cites White and Seymour, 2003 source
  • Findingcitation

    T_b is significantly correlated (r≈0.55) with the residual variation in mammalian BMR.

    “T b is significantly correlated (r≈0.55) with the residual variation in mammalian BMR (White and Seymour, 2003)”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites White and Seymour, 2003 source
  • Findingnone given

    In herbivorous mammals, mean retention time (MRT) scales positively with an exponent of 0.17±0.05 (95% CI), regardless of whether the main site of fermentation is the foregut, hindgut or caecum.

    “In herbivorous mammals, MRT scales positively with an exponent of 0.17±0.05(95% CI), regardless of whether the main site of fermentation is the foregut, hindgut or caecum (Fig. •2).”
    Quote in the paperSubstantial claim
  • May combine two claims. 21
  • Classified as probably not a substantial claim. 3

  • May combine two claims.

    Findingown data

    Contrary to Kleiber's finding, the exclusion of large herbivores from recent data sets decreases the scaling exponent and decreases variation around the regression line.

    “Contrary to Kleiber's finding (Kleiber, 1932), the exclusion of large herbivores from recent data sets does decrease the scaling exponent and also decreases variation around the regression line (Fig. •1).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Kleiber, 1932 source

      The Table 1 discussion (p. 8) reports that excluding ruminants lowered the best-fitting exponent from 0.74 to 0.73 and could lower the coefficient of variability from ±7.6% to ±5.6%. Kleiber’s reported direction of change therefore agrees with, rather than runs contrary to, the trend the citing sentence describes. (LLM, conf=0.88)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured

  • May combine two claims.

    Premisecitation

    Kleiber (1932, 1961) found that metabolic rate was proportional to body mass raised to an exponent significantly greater than 2/3, and a value of 3/4 was subsequently adopted.

    “Kleiber (1932Kleiber ( , 1961) ) found that metabolic rate was proportional to body mass raised to an exponent significantly greater than 2/3, and a value of 3/4 was subsequently adopted.”
    Quote in the paperSubstantial claim1 of 2 sources checked
    • cites Kleiber, 1932 source

      Table 1 (p. 8) reports that 0.74 was the best-fitting exponent for the thirteen animal groups. But the same section says the data were inadequate to decide conclusively between exponents near 2/3 and 3/4, so it does not establish an exponent significantly greater than 2/3. Application of Results (p. 24) says further investigation might favor a unit other than W³/⁴; this 1932 paper does not document its subsequent adoption. (LLM, conf=0.88)

      Experimental — accuracy not yet measured
    • cites Kleiber, 1961

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Findingcitation

    Inclusion of large herbivores in recent BMR scaling studies increases the coefficient of variation of the relationship and increases the scaling exponent.

    “A comparison of recent BMR scaling studies (since 1984) reveals that the inclusion of large herbivores both increases the coefficient of variation of the relationship (the standard deviation of ln-ln residuals; Garland, 1984) and increases the scaling exponent (Fig. •1).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Garland, 1984 source

  • May combine two claims.

    Findingcitation

    Large herbivores (Artiodactyla, Perissodactyla, Proboscidea) represent only 5% of Mammalia but comprise 28-39% of the data in seminal BMR scaling analyses.

    “Whereas these groups (henceforth referred to as 'large herbivores') represent only 5% of Mammalia (Nowak, 1999), they comprise 28-39% of the data in these seminal analyses (Table •1).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Nowak, 1999 source

  • May combine two claims.

    Findingreasoning

    The SMR scaling exponent for hibernating mammals (b=0.87; 95% CI, 0.79-0.94) is significantly different to that of euthermic (b=0.675; 95% CI, 0.663-0.688) and torpid ones (b=0.67; 95% CI, 0.56-0.77).

    “As such, the SMR scaling exponent for hibernating mammals (b=0.87;95% CI, 0.79-0.94) is significantly different to that of euthermic (b=0.675;95% CI, 0.663-0.688)and torpid ones (b=0.67;95% CI, 0.56-0.77;Fig. •5).”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The Q10 for euthermic mammals (2.8; 95% CI, 2.4-3.2) is not significantly different to that found for hibernating (Q10=2.2; 95% CI, 1.7-2.8) or torpid ones (Q10=2.4; 95% CI, 1.6-3.5).

    “Interestingly, the Q 10 for euthermic mammals (2.8; 95% CI, 2.4-3.2) is not significantly different to that found for hibernating (Q 10 =2.2; 95% CI, 1.7-2.8)or torpid ones (Q 10 =2.4; 95% CI, 1.6-3.5),although the exact values for hibernating and torpid animals are quite uncertain.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingcitation

    When normalised to a common T_b according to the Q10 principle, the BMR values of birds and mammals do not differ in allometric coefficient or exponent, nor do the BMR values of eutherians and marsupials.

    “when normalised to a common T b according to the Q 10 principle, the BMR values of birds and mammals do not differ in allometric coefficient or exponent, nor do the BMR values of eutherians and marsupials (White and Seymour, in press).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites White and Seymour, in press

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Findingreasoning

    Once normalised to a euthermic T_b (36.2°C), the metabolic rate of torpid mammals is equivalent to that of euthermic mammals, whilst small hibernating mammals show an additional suppression of metabolic rate.

    “Once normalised to a euthermic T b (36.2°C), the metabolic rate of torpid mammals is equivalent to that of euthermic mammals, whilst small hibernating mammals show an additional suppression of metabolic rate.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    MMR_e scales with an exponent greater than RMR_pp, FMR, RMR_t, BMR, and SMR.

    “MMR e (b=0.87±0.05;Fig. •6A) scales with an exponent greater than RMR pp (b=0.75±0.03;Fig. •3), FMR (b=0.73±0.04;Nagy et al., 1999), RMR t (b=0.712±0.013;Savage et al., 2004), BMR (b=0.686±0.014;Fig. •4) and SMR (b=0.675±0.013;Fig. •5).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Nagy et al., 1999 source
    • cites Savage et al., 2004 source

  • May combine two claims.

    Findingcitation

    The percentage of large herbivores in a BMR data set is significantly correlated with the coefficient of variation and scaling exponent of the allometric relationship between BMR and body mass.

    “Relationship between the percentage of large herbivores in a basal metabolic rate (BMR) data set and the coefficient of variation (CV, the standard deviation of residuals from a ln-ln allometric relationship;Garland, 1984) and scaling exponent (shown ±95% CI) of the allometric relationship between BMR and body mass.Both correlations are significant (CV: r=0.92,P<0.0001; scaling exponent: r=0.85,P=”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Garland, 1984 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Ruminants may require 7 days to arrive at a postabsorptive state, although such a state may in fact be unachievable.

    “However, ruminants may require 7 days to arrive at a postabsorptive state (Blaxter, 1962), although such a state may in fact be unachievable (McNab, 1997).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Blaxter, 1962

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites McNab, 1997 source

  • May combine two claims.

    Premisecitation

    OLS regression assumes M_b is independent of the variable of interest and measured without error, which may not be the case.

    “Secondly, OLS regression assumes that M b is independent of the variable of interest and measured without error, which may not be the case.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Sokal and Rohlf, 1995

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning

    Given that large herbivores are typically fasted for no more than 72 h, if at all, prior to determination of metabolic rate, it is likely that such measurements fail to satisfy the conditions required for determination of BMR.

    “Given that large herbivores are typically fasted for no more than 72•h, if at all, prior to determination of metabolic rate, it seems likely that such measurements fail to satisfy the conditions required for determination of BMR.”
    Quote in the paperSubstantial claim
    • Rests on an assumption: Large herbivores are typically fasted for no more than 72 h, if at all, prior to determination of metabolic rate.

  • May combine two claims.

    Interpretationcitation

    For species that are difficult to obtain or measure, BMR can be estimated only from M_b, because M_b alone accounts for 94% of the variation in BMR.

    “For species that are difficult to obtain or measure, BMR can be estimated only from M b , because M b alone accounts for 94% of the variation in BMR (White and Seymour, 2003).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites White and Seymour, 2003 source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Body mass and temperature are primary determinants of metabolic rate.

    “Body mass and temperature are primary determinants of metabolic rate (Gillooly et al., 2001).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Gillooly et al., 2001 source

  • May combine two claims.

    Premisecitation
    § Allometric scaling of mammalian metabolism

    Macropods and lagomorphs are excluded because they have microbial fermentation in the stomach or hindgut, while shrews (Soricidae) are excluded because resting and postabsorptive conditions may be mutually exclusive.

    “Macropods and lagomorphs are excluded because they have microbial fermentation in the stomach or hindgut (Stevens and Hume, 1995), while shrews (Soricidae) are excluded because resting and postabsorptive conditions may be mutually exclusive (Speakman et al., 1993).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Stevens and Hume, 1995
    • cites Speakman et al., 1993 source

  • May combine two claims.

    Interpretationreasoning

    A MRT of 12 h is predicted for a 20 g herbivore, compared to nearly 3 days for a 500 kg one.

    “A MRT of 12•h is therefore predicted for a 20•g herbivore, compared to nearly 3 days for a 500•kg one.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation

    The final appearance of faeces following feeding can take 4 times longer than the MRT, suggesting that MRT may approximate only the minimum time required to achieve a postabsorptive condition.

    “However, the final appearance of faeces following feeding can take 4 times longer than the MRT (Blaxter, 1989), suggesting that MRT may approximate only the minimum time required to achieve a postabsorptive condition.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Blaxter, 1989

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Premisereasoning

    Because of shared phylogenetic descent, species data are likely not to represent statistically independent points, resulting in overestimation of degrees of freedom and increased Type I error rate.

    “Firstly, because of shared phylogenetic descent, species data are likely not to represent statistically independent points.This results in overestimation of degrees of freedom and an increased Type I error rate.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites Felsenstein, 1985 source
    • cites Harvey and Pagel, 1991 source
    • cites Garland et al., 1992 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given

    Three-quarter power scaling of mammalian BMR is a central paradigm of comparative physiology that has been accepted for over 70 years and remains in widespread use.

    “Three-quarter power scaling of mammalian BMR is a central paradigm of comparative physiology that has been accepted for over 70 years and remains in widespread use.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Premisenone given

    MMR_c is measured under conditions that maximise heat loss.

    “This might be expected given that MMR c is measured under conditions that maximise heat loss.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites Rosenmann and Morrison, 1974 source
    • cites Thomas et al., 1998 source

  • May combine two claims.

    Premisecitation

    Hemmingsen (1960) included unicellular organisms and poikilothermic vertebrates, expanding the range of body masses to 18 orders of magnitude, and also supported an exponent of 3/4.

    “Hemmingsen (1960) included unicellular organisms and poikilothermic vertebrates, thereby expanding the range of body masses to 18 orders of magnitude, and also supported an exponent of 3/4 (a similar approach with a similar result was recently presented by Gillooly et al., 2001).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Hemmingsen, 1960

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites Gillooly et al., 2001 source
22 of 22

  • The paper relies on this without support.

    Large herbivores are typically fasted for no more than 72 h, if at all, prior to determination of metabolic rate.

    “Given that large herbivores are typically fasted for no more than 72•h, if at all, prior to determination of metabolic rate, it seems likely that such measurements fail to satisfy the conditions required for determination of BMR.”

  • The paper relies on this without support.

    There is no functional link in endotherms between metabolic rate and T_b within the thermal neutral zone, where BMR is measured.

    “Although there is no functional link in endotherms between metabolic rate and T b within the thermal neutral zone, where BMR is measured, repeated attempts have been made to explain the BMR differences between birds and mammals, and eutherians and marsupials, in terms of differences in T b (Hemmingsen, 1960;Dawson and Hulbert, 1970;White and Seymour, in press).”
2 of 2

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Kleiber's monograph is assigned two publication years

    Minor

    The paper dates Kleiber's monograph to 1938 in one passage but to 1932 elsewhere; its reference list also gives 1932 for the monograph.

1 of 1

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Related

Authors
White, C. R., & Seymour, R. S.
Affiliations
The University of Adelaide (AU)
Corresponding author
White, Craig R.
ORCID
Venue
Journal of Experimental Biology
Publisher
The Company of Biologists
Published
2005-05-01
Volume
208
Issue
9
Pages
1611-1619
ISSN
  • 0022-0949 (ISSN-L)
  • 1477-9145
DOI
10.1242/jeb.01501
OpenAlex
W2096114109
Cited by
433
References
124
Citations by year
2026: 15 · 2025: 17 · 2024: 17 · 2023: 28 · 2022: 9 · 2021: 14 · 2020: 19 · 2019: 9 · 2018: 11 · 2017: 19 · 2016: 25 · 2015: 21 · 2014: 20 · 2013: 20 · 2012: 22
FWCI
2.43
Type
journal article
Language
en
Open access
Locations
  • Journal of Experimental Biology (publishedVersion)
  • PubMed (publishedVersion)
  • Adelaide Research & Scholarship (AR&S) (University of Adelaide) (submittedVersion)
  • HighWire Press Open Archive (submittedVersion)
Topics
  • Physical Sciences › Environmental Science › Ecology › Physiological and biochemical adaptations
  • Physical Sciences › Earth and Planetary Sciences › Paleontology › Evolution and Paleontology Studies
  • Health Sciences › Medicine › Physiology › Adipose Tissue and Metabolism
Keywords
allometric scaling, basal metabolic rate, resting metabolic rate, 3/4 power law, 2/3 power law, scaling exponents, mammalian metabolism, body mass, large herbivores, coefficient of variation, field metabolic rate, interspecific variation, oxygen consumption
MeSH terms
Animals, Basal Metabolism, Body Temperature, Energy Metabolism, Mammals, Models, Biological, Regression Analysis, Body Size

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