# Metabolic theory of ecology

The metabolic theory of ecology (MTE) is an extension of Kleiber's law and posits that the metabolic rate of organisms is the fundamental biological rate that governs most observed patterns in ecology,.[1][2] MTE is part of a larger set of theory known as Metabolic Scaling Theory that attempts to provide a unified theory for the importance of metabolism in driving pattern and process in biology from the level of cells all the way to the biosphere .

MTE is based on an interpretation of the relationships between body size, body temperature, and metabolic rate across all organisms. Small-bodied organisms tend to have higher mass-specific metabolic rates than larger-bodied organisms. Furthermore, organisms that operate at warm temperatures through endothermy or by living in warm environments tend towards higher metabolic rates than organisms that operate at colder temperatures. This pattern is consistent from the unicellular level up to the level of the largest animals and plants on the planet.

In MTE, this relationship is considered to be the single constraint that defines biological processes at all levels of organization (from individual up to ecosystem level), and is a macroecological theory that aims to be universal in scope and application.[2][3]

## Theoretical background

Metabolic rate scales with the mass of an organism of a given species according to Kleiber's law where B is whole organism metabolic rate (in watts or other unit of power), M is organism mass (in kg), and Bo is a mass-independent normalization constant (given in a unit of power divided by a unit of mass. In this case, watts per kilogram):

$B = B_oM ^ {3/4}\,$

At increased temperatures, chemical reactions proceed faster. This relationship is described by the Boltzmann factor, where E is activation energy in electronvolts or joules, t is absolute temperature in kelvins, and k is the Boltzmann constant in eV/K or J/K:

$e^{-\frac{E}{k\,t}}$

While Bo in the previous equation is mass-independent, it is not explicitly independent of temperature. To explain the relationship between body mass and temperature, building on earlier work [4] showing that the effects of both body mass and temperature could be combined multiplicatively in a single equation, the two equations above can be combined to produce the primary equation of the MTE, where bo is a normalization constant that is independent of body size or temperature:

$B = b_oM^{3/4}e^{-\frac{E}{k\,t}}$

According to this relationship, metabolic rate is a function of an organism’s body mass and body temperature. By this equation, large organisms have proportionally higher metabolic rates (in Watts) than small organisms, and organisms at high body temperatures have higher metabolic rates than those that exist at low body temperatures.However specific metabolic rate (SMR, in Watts/kg) is given by

$SMR = (B/M) = b_oM^{-1/4}e^{-\frac{E}{k\,t}}$

Hence SMR for large organisms are lower than small organisms.

## Controversy over exponent

There is disagreement amongst researchers about the most accurate value for use in the power function, and whether the factor is indeed universal.[5] The main disagreement is whether metabolic rate scales to the power of 3/4 or 2/3. The majority view is currently that 3/4 is the correct exponent, but a large minority believe that 2/3 is the more accurate value.[5]

The argument that 2/3 should be the correct scaling factor is based on the assumption that energy dissipation across the surface area of three-dimensional organisms is the key factor driving the relationship between metabolic rate and body size.[5] Smaller organisms tend to have higher surface area to volume ratios, causing them to lose heat energy at a faster rate than large organisms. As a consequence, small organisms must have higher specific metabolic rates to combat this loss of energy over their large surface area to volume ratio.

In contrast, the argument for a 3/4 scaling factor is based on a hydraulic model of energy distribution in organisms, where the primary source of energy dissipation is across the membranes of internal distribution networks.[1] This model is based on the idea that metabolism is essentially the rate at which an organism’s distribution networks (such as circulatory systems in animals or xylem and phloem in plants) deliver nutrients and energy to body tissues.,[1][6] It therefore takes longer for large organisms to distribute nutrients throughout the body and thus they have a slower metabolic rate. The 3/4 factor is then derived from the observation that selection favors a fractal or near-fractal distribution network for space-filling circulatory systems.[6] All fractal networks terminate in identical units (such as capillary beds), and the number of such units in organisms is proportional to a 3/4 power relationship with body size.[6]

Although a rigorous exploration of the controversy over choice of scaling factor is beyond the scope of this article, it is informative to understand the biological justification for the use of either value. It is worth noting that the prediction for the 3/4 scaling exponent from the fractal network model is one specific prediction from the theory. Variation in allometric scaling exponents can be related to a more relaxed versions of the fractal network model. Extensions of the network model shows that additional selection pressures for alternative branching geometries could govern much of the observed variation in biological scaling exponents.[7] Kolokotrones et al. 2010[8] showed that relationship between mass and metabolic rate has a convex curvature on logarithmic scale (see also.[1] The curvature can also explain some of variations in the power law exponent.

Despite the controversy over the value of the exponent, the implications of this theory might remain true regardless of its precise numerical value.

## Implications of the theory

The metabolic theory of ecology’s main implication is that metabolic rate, and the influence of body size and temperature on metabolic rate, provide the fundamental constraints by which ecological processes are governed. If this holds true from the level of the individual up to ecosystem level processes, then life history attributes, population dynamics, and ecosystem processes could be explained by the relationship between metabolic rate, body size, and body temperature.

### Organism level

Small animals tend to grow fast, breed early, and die young.[9] According to MTE, these patterns in life history traits are constrained by metabolism.[10] An organism's metabolic rate determines its rate of food consumption, which in turn determines its rate of growth. This increased growth rate produces trade-offs that accelerate senescence. For example, metabolic processes produce free radicals as a by-product of energy production.[11] These in turn cause damage at the cellular level, which promotes senescence and ultimately death. Selection favors organisms which best propagate given these constraints. As a result, smaller, shorter lived organisms tend to reproduce earlier in their life histories.

### Population and community level

MTE has profound implications for the interpretation of population growth and community diversity.[9] Classically, species are thought of as being either r selected (where population size is limited by the exponential rate of population growth) or K selected (where population size is limited by carrying capacity). MTE explains this diversity of reproductive strategies as a consequence of the metabolic constraints of organisms. Small organisms and organisms that exist at high body temperatures tend to be r selected, which fits with the prediction that r selection is a consequence of metabolic rate.[2] Conversely, larger and cooler bodied animals tend to be K selected. The relationship between body size and rate of population growth has been demonstrated empirically,[12] and in fact has been shown to scale to M−1/4 across taxonomic groups.[9] The optimal population growth rate for a species is therefore thought to be determined by the allometric constraints outlined by the MTE, rather than strictly as a life history trait that is selected for based on environmental conditions.

Observed patterns of diversity can be similarly explained by MTE. It has long been observed that there are more small species than large species.[13] In addition, there are more species in the tropics than at higher latitudes.[2] Classically, the latitudinal gradient in species diversity has been explained by factors such as higher productivity or reduced seasonality.[14] In contrast, MTE explains this pattern as being driven by the kinetic constraints imposed by temperature on metabolism.[15] The rate of molecular evolution scales with metabolic rate,[16] such that organisms with higher metabolic rates show a higher rate of change at the molecular level.[2] If a higher rate of molecular evolution causes increased speciation rates, then adaptation and ultimately speciation may occur more quickly in warm environments and in small bodied species, ultimately explaining observed patterns of diversity across body size and latitude.

MTE’s ability to explain patterns of diversity remains controversial. For example, researchers analyzed patterns of diversity of New World coral snakes to see whether the geographical distribution of species fit within the predictions of MTE (i.e. more species in warmer areas).[17] They found that the observed pattern of diversity could not be explained by temperature alone, and that other spatial factors such as primary productivity, topographic heterogeneity, and habitat factors better predicted the observed pattern. Extensions of metabolic theory to diversity that include eco-evolutionary theory show that an elaborated metabolic theory can accounts for differences in diversity gradients by including feedbacks between ecological interactions (size-dependent competition and predation) and evolutionary rates (speciation and extinction) [18]

### Ecosystem processes

At the ecosystem level, MTE explains the relationship between temperature and production of total biomass.[19] The average production to biomass ratio of organisms is higher in small organisms than large ones.[20] This relationship is further regulated by temperature, and the rate of production increases with temperature.[21] As production consistently scales with body mass, MTE provides a framework to assess the relative importance of organismal size, temperature, functional traits, soil and climate on variation in rates of production within and across ecosystems.[19] Metabolic theory shows that variation in ecosystem production is characterized by a common scaling relationship, suggesting that global change models can incorporate the mechanisms governing this relationship to improve predictions of future ecosystem function.

## References

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