References for allometric equations

   A comprehensive review of metabolic scaling (well worth reading):
White CR, Kearney MR (2014)  Metabolic scaling in animals:  Methods, empirical results, and theoretical expectations. Comprehensive Physiology (American Physiological Society) 4: 231-256.

   General references (poikilotherms, homeotherms)
  • Hemmingsen AM (1960) Rep Steno M. Hosp (Copenhagen) 9:1-10

    • Land Arthropods:   Land-dwelling arthropods (insects, spiders, mites, scorpions, etc.) are highly diverse and their resting metabolism shows similar diversity.  According to some analyses, variation in metabolism in these groups is more related to activity levels than to taxonomic affiliation (but see the Chown et al. 2007 paper for an alternate view within insects).  Ticks and scorpions do appear to have low metabolic rates.

    • Lighton and Fielden examined metabolic data from ants, spiders, ticks, and beetles; their results suggest that all non-flying land arthropods -- except ticks -- have similar resting metabolic rates (they note that RMR's of flight-capable species may be considerably higher).

      Lighton JRB, Fielden LJ (1995) Physiological Zoology 68:43-62 and (1996) Journal of Insect Physiology 42:347-357

    • Chown et al. performed an extensive analysis on 391 insect species, including phylogenetic correction.  In contrast to some previous studies, they found no effect of flight on resting metabolism (i.e., insects that fly do not have higher RMR than non-volant forms once phylogeny is taken into account).

       Chown SL, Marais E, Terblanche JS, Klok CJ, Lighton JRB, Blackburn TM (2007) Functional Ecology 21: 282-290

    • Lighton et al. extended their previous data set to include several species of scorpions.  Like ticks, scorpions have very low RMR (they also have a rather high Q10 of nearly 3).

       Lighton JRB, Brownell PH, Joos B, Turner RJ (2000 ) Journal of Experimental Biology 204:607-613

    • Bartholomew and Casey looked at metabolism in tropical beetles and various moth species (note that the moths and many of the beetles were flight-capable, so SMRs may be higher than predicted for non-flying arthropods).

       Bartholomew GA, Casey TM (1977) Journal of Thermal Biology 2:173-176
       Bartholomew GA, Casey TM (1978) Journal of Experimental Biology 76:11-25

      Fish:   Fish metabolism is shown as SMR (inactive or 'resting' fish), 'routine' MR (spontaneous activity in addition to rest), and active MR (forced exercise).   Many fish do not ‘rest’ in the classical sense; they continually swim, in some cases as a matter of necessity for ventilating their gills.  The ‘routine’ and ‘active MR’ categories include a wide range of exercise intensities and are intended to provide rough estimates only.   There is no apparent difference in active MR of different classes of fish, but SMR is about 2-fold higher in Teleosts than in Agnathans, with Elasmobranchs intermediate.

    • White et al. performed a broad-scale phylogenetically aware analysis of vertebrate taxa, including fish.

      White CR, Phillips NF, Seymour RS (2006), Biology Letters 2006(2): 125-127

    • Data from which the equations for different orders were derived largely came from the FishBase data set.   Note that in many cases the size range is small (especially for Agnathans); and in other cases there is a sampling bias towards small individuals (particularly for Elasmobranchs).   This lends some doubt about the validity of MR predictions, particularly for large specimens.

      FishBase (2000) Froese, R. and D. Pauly, Editors
      World Wide Web electronic publication,

      Amphibians:   Amphibian metabolic rates are not as widely studied as those of other vertebrate classes.

    • Feder examined the effects of lunglessness on metabolism in salamanders.

       Feder ME (1976), Physiological Zoology 49:398-406

    • Hutchison et al. examined the effects of size and surface area on metabolism in frogs.

      Hutchinson VH, Whitford WG, Kohl M (1968), Physiological Zoology 41:68-85

    • White et al. performed a broad-scale phylogenetically aware analysis of vertebrate taxa, including amphibians.

       White CR, Phillips NF, Seymour RS (2006), Biology Letters 2006(2): 125-127

      Reptiles:   The various groups of reptiles -- particularly lizards -- have been extensively studied.

    • Bennett and Dawson compiled literature data and produced allometries for several reptile orders at different temperatures.

       Bennett AF, Dawson WR (1976), "Metabolism" in C. Gans and WR Dawson (eds.) Biology of the Reptilia, vol. 5, Physiology. Academic Press, New York

    • White et al. performed a broad-scale phylogenetically aware analysis of vertebrate taxa, including reptiles.

       White CR, Phillips NF, Seymour RS (2006), Biology Letters 2006(2): 125-127

      Birds:   Birds have been intensively studied and there are a number of widely-used allometric equations for avian BMR.  Recently there has been some controversy over the correct statistical and phylogenetic approaches, and McKechnie & Wolf pointed out that some allometries may have included data that do not fit the stringent criteria for true BMR.

    • McKechnie and Wolf carefully analyzed several hundred published values of BMR, selecting only 67 species for which measurement conditions unambiguously fit the criteria for BMR.  They found no difference between passerines and non-passerines after phylogentic corrections.  Note: their phylogenetically independent equation is used here.

       McKechnie AE, Wolf BO (2004), Physiological and Biochemical Zoology 77:502-521

    • Londoño et al. analysed a very large dataset (almost 500 species) using phylogenetic statistics based on the Hackett et al. (2008) avian tree.   Unlike other recent phylogenetic studies based on smaller datasets and older phylogenies, Londoño et al. found significant differences between passerines and non-passerines.   However, this was largely due to higher regression slope (mass exponent) and lower scaling coefficient ('a' value) in non-passerines (thus at different body masses, passerine metabolism may be higher than that of non-passerines, or vice versa).

       Londoño GA, Chappell MA, Casteñada MR, Jankowski JE, Robinson SK (2014) Functional Ecology 29: 338-346.

    • Bennett and Harvey used phylogenetic analysis of mean values for avian families to generate their equation.

       Bennett PM, Harvey PH (1987), Journal of Zoology (London) 213: 327-363

    • Lasiewski and Dawson produced an early but much-cited paper that provides separate equations for passerine and non-passerine species.

       Lasiewski RD, Dawson WR (1967), Condor 69:13-23

    • Aschoff and Pohl, in another much-cited paper, showed differences between the active (alpha, usually daylight) phase and the inactive (rho, usually night) phase.  The paper is based on a relatively small number of passerine species.

       Aschoff J, Pohl JH (1970), Journal für Ornithologie 111:38-47

    • Reynolds and Lee re-analyzed existing BMR data using phylogenetic techniques and found no differences between passerines and non-passerines.

       Reynolds PS, Lee RM (1996), American Naturalist 147:735-759

    • White and Seymour surveyed an extensive literature on both avian and mammalian BMR.  They concluded there were no differences in BMR between birds and mammals if differences in body temperature were accounted for.

      White CR, Seymour RS (2004), Physiological and Biochemical Zoology 77:926-941

    • Weathers and Siegel examined the resting metabolism of nestlings, using data from 27 species (passerines and non-passerines).

       Weathers WW, Siegel RB (1994), Ibis 137:532-542

      Mammals:   Mammal metabolic rates have been extensively studied for more than a century.   Although generalized equations are available, detailed analyses of mammalian BMR should account for subclass affiliations.  Additionally, specific regression lines are available for some orders, and should be used when possible.   Note that some work by Jack Hayes and others suggests that metabolism scales to mass.667 in mammals (i.e., to the 2/3 power of mass) once mass-related differences in body temperature are accounted for.

    • Brody, Kleiber, and Stahl did classical early work on eutherian BMR that is still frequently cited.

       Brody S (1945), Bioenergetics and Growth. New York: Hafner
       Kleiber M (1961), The Fire of Life. New York: John Wiley
       Stahl WR (1967), Journal of Applied Physiology 22:453-460

    • Dawson and Hulbert's 1970 paper showed that marsupial BMR is lower than that of eutherians, but this is due primarily to the Q10 effect of a lower body temperature in marsupials.

      Dawson TJ, Hulbert AJ (1970), American Journal of Physiology 218:1233-1238

    • MacMillen and Nelson described the metabolic allometry of a major group of marsupials, the Dasyurids.

      MacMillen RE, Nelson JE (1969), American Journal of Physiology 217:1246-1251

    • Elgar and Harvey compiled data from a wide variety of mammals and demonstrated that much of the variance in BMR derives from taxonomic affiliation (instead of ecological factors such as diet, etc.) and is best examined at the level of orders.

      Elgar MA, Harvey PH (1987), Functional Ecology 1:25-36

    • Bozinovic described the metabolic allometry of rodents (he also showed that across a range of body sizes, mass-corrected maximum aerobic metabolism was correlated to BMR).

      Bozinovic F (1992), Physiological Zoology 65:921-932

    • White and Seymour surveyed more than 600 species of mammals and carefully analyzed the effects of size, phylogeny, zoogeography, etc. Among other findings, they concluded there were no differences in BMR between eutherians and marsupials if differences in body temperature were accounted for (similarly, mammals and birds did not differ after compensation for body temperature).

      White CR, Seymour RS (2004), Physiological and Biochemical Zoology 77:926-941

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