# Metabolic rate and body mass relationship

### BBC Bitesize - Higher Biology - Metabolic rate - Revision 1

The Mass, Metabolism and Length Explanation (MMLE) was advanced in to explain the relationship between metabolic rate and body. Metabolic rate is traditionally assumed to scale with body mass to the relationships should vary between 2/3 and 1, in a systematic way with. () proposes that the scaling of metabolic rate with body mass will vary from 2 /3 to 1 among different taxa, depending on the degree to which increasing body.

Within-species scaling of FMR is of interest in its own right, but incorporating this variation into scaling models across species is also likely to be more robust than if it were simply treated as error variance, as in conventional analyses. We compiled the first comprehensive database of measurements of FMR and body mass for individual birds and mammals.

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We here publish our data and use it to answer four questions. First, what is the magnitude of variation in the exponent b among taxa, and at what taxonomic level does variation primarily occur when intraspecific variation is considered alongside variation among species and higher taxa? Second, after accounting for such variation, what are the mean scaling exponents for birds and mammals? Finally, what are the implications of our data for existing theory on metabolic rate scaling?

These questions have been important in debates centred on species-averaged BMR data, but have not been systematically addressed for individual-level FMR data. More broadly than testing some of the existing theories, this study provides the first comprehensive data set and systematic description of the individual-level FMR-vs. We considered only data resolved to individual level; other criteria for study inclusion are in Appendix S1.

In cases where an individual was measured more than once, we computed M and FMR means to get single values for each individual. M was converted to kg and FMR to. The main set of models We fitted linear mixed-effects models to the -vs. Log transformation is standard e. When equ 1 is fitted to log-transformed data, a is the antilog of the intercept and b is the slope.

This changes estimates of regression intercepts, but does not affect slopes, which are the subject of this study. All mixed-effects models included fixed effects of taxonomic class Aves or Mammalia on both intercept and slope. Class was used as a fixed effect on slope because we are interested in the differences, if any, in slope between birds and mammals. This modelling strategy allowed the variation in slope at each taxonomic rank to be estimated and accounted for the unbalanced nature of the data and nonindependence that results from shared evolutionary history.

Random effects at each of the taxonomic ranks of order, family and species were allowed to be either i no random effect, ii random effect on intercept or iii random effect on both slope and intercept, possibly correlated. Thus, there were three options for random effects at three hierarchical levels, giving combinations of random effects.

### The relationship between body mass and field metabolic rate among individual birds and mammals

Random effects at genus level were not considered because many families are represented by few genera or one genus in our database, so the data were not sufficient to parameterize models with random effects at that level; this modelling choice is consistent with the recommendations of Bolker et al.

Some studies presented FMR data for more than one species, and data for some species came from more than one study. To allow for variation in the doubly labelled water protocol Butler et al. Models are described using mathematical notation in Appendix S2.

We fitted all 27 mixed-effects models to the data. The Akaike weight, w, was computed for each model. These weights indicate the weight of evidence in favour of each model.

Random effects are characterized by standard deviations. We computed model-averaged standard deviations of random effects on b at the order, family and species level. These values indicated the relative importance of heterogeneity of slope at the taxonomic levels. The absence of a random effect at a given taxonomic level in a model implied a zero standard deviation for that random effect.

When model averaging random-effect standard deviations, we therefore used a value of zero for random effects that were not included in models. Supporting analyses We here describe two supporting analyses: Ordinary linear regression models have historically been used to examine eqn 1 Nagy 42 ; Riek 50 and through comparison with the main models allow a test for a universal exponent. We fitted four simple linear regression models, all without random effects. These models had fixed effects of taxonomic class on intercept and had respectively: An assumption of the main set of models is that there are class-specific effects of M on FMR, with random variation around these means at lower taxonomic levels.

## The relationship between body mass and field metabolic rate among individual birds and mammals

This is the same as saying that deviations of individual mass from species mean mass have the same effect on FMR as do deviations of species means from family means and deviations of family means from order means. The models are described using mathematical notation in Appendix S3. Each model had a random-effect structure comparable to one of the main models. How does metabolic rate scale with size? Reader Mode When one arrives at biology from its sister disciplines of physics or engineering there is a strong temptation to search for consistent quantitative trends and general rules.

One such pursuit centers on the power consumption of different organisms, the so-called metabolic energy consumption rate. This example illustrates how scaling arguments work. For many inanimate systems the energy produced has to be removed through the bounding surface area, and each unit of area allows a constant energy flux.

At the same time the volume, V, scales as R3. Assuming constant density this will also be the scaling of the total mass, M. According to our assumption above, the energy is removed through the surface at a constant rate, and thus the total energy produced should be proportional to A, i.

Does this simple scaling result based on simple considerations of energy transfer also hold for biological systems? The resting energy demand of organisms has recently been compared among more than different organisms spanning over 20 orders of magnitude in mass! In contrast to the Kleiber law prediction, this recent work found a relatively small range of variation with the vast majority of organisms having power requirements lying between 0. Further evidence for breaking of Kleiber scaling was provided recently for protists and prokaryotes J.

The metabolic rate of an organism is condition dependent, and thus should be strictly defined if one wants to make an honest comparison across organisms.