# Inverse relationship between metabolic rate and body size

### Metabolic rate (article) | Khan Academy

metabolic rates are inversely proportional to size of the organism. have a lower surface-to-volume ratio, thus a larger relative heat loss to the a body surface, a small animal must oxidize food at a high rate. Is there a relationship between efficiency of cellular metabolism and warm-blooded-ness?. Why then is there and inverse relationship then between metabolic rate and body size? The answer is easily understood in the case of. The metabolic rate of an organism is condition dependent, and thus should be a relationship between the resting metabolic energy requirement per unit mass of magnitudes of body size and widely differing phylogenetic groups the rates.

While not addressing the entirety of the placental mammals, the orders that are addressed do represent over two-thirds of the species.

This section is a summary of Article S2. Nearly all of the energy flux that is measured as basal metabolic rate BMR is generated by mitochondria. The oxygen is consumed by processes that pump protons across the mitochondrion inner membrane. Heat is produced when some of the protons leak back across the membrane in a controlled fashion as in brown fat or as an uncontrolled basal leak.

Otherwise the protons cause the phosphorylation of adenosine diphosphate ADP to adenosine triphosphate ATP as they return across the inner membrane Jastroch et al.

ATP is the fuel that powers animal tissues. MMLE strives to predict the absolute value of the BMR of an animal rather than the exponent b or the constant a in the relationship aWb. The energy allocated to a tissue type is proportional to the number of mitochondria in the tissue. Thus MMLE tries to count the mitochondria in the tissues that compose an animal and then sum these counts for the entire animal.

It is a signature feature of MMLE theory that the vertebrate body is represented as a combination of masses instead of a single mass. There are at least two masses: The heart, kidneys, liver and brain are the principal non-skeletal muscle tissues. Being a surface, the non-skeletal muscle surface can be mathematically described as the square of a length multiplied by an appropriate constant. Any length could be used as long as the constant is adjusted to make the relationship exact.

For MMLE theory the selected length is one that is related to propulsion dynamics. Go is the non-skeletal muscle constant. Gr is the resting metabolic rate constant.

## How Does an Animal's Size Affect Metabolism?

Gm, Go and Gr are universal constants that should apply to all vertebrates. The fundamental propulsion frequency, f, should be the same function of the characteristic length, l, for all vertebrates that are dynamically similar. The mitochondrion capability coefficient, e, is a constant whose value should be approximately identical for all vertebrates in the same phylogenetic group with the same body temperature.

The characteristic length, l, and the sturdiness factor, s, have unique values for each individual animal. Go is defined so that m is dimensionless with a value of 1. Gm and k were defined so that k is non-dimensional with a value of 1.

Substituting this expression for f in Eq. Strouhal similarity obtains when inertial forces are proportional to oscillatory forces. Reynolds similarity obtains when inertial forces are proportional to viscous forces.

Bats are the only animals examined in the present paper for which viscous drag, and hence Reynolds similarity, might be important. Strouhal similarity does apply to bats. This sort of dependence of the frequency on the characteristic length was not observed. It should be noted, however, that the characteristic length for viscous drag and that for vortex growth and shedding could be different body dimensions. Two animals are geometrically similar if one can be made identical to the other by multiplying all its linear dimensions by the same factor Alexander, However, these central tendencies obscured meaningful taxonomic heterogeneity in scaling exponents.

The primary taxonomic level at which heterogeneity occurred was the order level. Substantial heterogeneity also occurred at the species level, a fact that cannot be revealed by species-averaged data sets used in prior work. Results are interpreted in the light of a variety of existing theories. Our analysis provides the first comprehensive empirical analysis of the scaling relationship between field metabolic rate and body mass in individual birds and mammals. Our data set is a valuable contribution to those interested in theories of the allometry of metabolic rates.

- Metabolic rate
- What is one hypothesis to explain the relationship between body size and metabolic rate?
- The relationship between body mass and field metabolic rate among individual birds and mammals

The authors provide the first comprehensive empirical analysis of the scaling relationship between field metabolic rate and body mass in individual birds and mammals. The analysis reveals the importance of heterogeneity in the scaling exponent, with consequences for biomass and nutrient flow through communities, and the structure and functioning of whole ecosystems. The large majority of past work that has empirically examined the metabolic rate vs.

However, field metabolic rates FMR and individual mass and rate phenotypes are more directly ecologically relevant and are probably more directly subject to selection than resting rates and species-average phenotypes, respectively. BMR measures organism metabolism in a calorimeter, but organisms live and interact in the field. Species-average quantities mask variation on which evolution can act, whereas individual analyses capture this variation.

Researchers who use the scaling of metabolic rate as a component of their models ultimately seek to understand the behaviour of communities and ecosystems in the field.

Individual-level FMR therefore appears to be a more ecologically and evolutionarily relevant measurement to use in the development of ideas about metabolism and its scaling with body size. We therefore compiled the first comprehensive database of measurements of FMR and body mass for individual birds and mammals.

The surface law is based on the ratio of volume to surface area, which affects the rates at which heat is produced and lost to the environment.

More recent studies focussed on whether a single value of b is even appropriate for all clades, and how b varies by clade. Such studies often account for nonindependence in the data resulting from shared evolutionary history. These studies illustrate the volume of research that has examined taxonomic heterogeneity of scaling coefficients, b, for data that has been on basal or resting rates or has been for species averages.

Of the much smaller collection of empirical studies that have investigated body mass dependence of FMR, all but one have used species-averaged data. Nagy 42 reported that FMR scaling was steeper than BMR scaling for both birds and mammals, although the differences were small and not statistically significant. The studies surveyed here serve to illustrate the prior work that has examined mass dependence of FMR, albeit for species-averaged data.

A gap in the existing literature is a comprehensive analysis of individual-level FMR data. 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.

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.

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

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.