# 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):

${\displaystyle B=B_{o}M^{3/4}\,}$

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:

${\displaystyle e^{-{\frac {E}{k\,T}}}}$

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:

${\displaystyle B=b_{o}M^{3/4}e^{-{\frac {E}{k\,T}}}}$

According to this relationship, metabolic rate is a function of an organism's body mass and body temperature. By this equation, large organisms have 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

${\displaystyle SMR=(B/M)=b_{o}M^{-1/4}e^{-{\frac {E}{k\,T}}}}$

Hence SMR for large organisms are lower than small organisms.

## Controversy over mechanisms and the allometric constant

Researchers disagree about the two main aspects of this theory, the pattern and the mechanism. The primary pattern in question is whether metabolic rate scales to the power of ​34 or ​23w, or whether either of these can even be considered a universal constant.[5][6] The majority view is currently that ​34 is the correct exponent, but a large minority believe that ​23 is the more accurate value. In addition to disagreeing about the pattern, researchers also disagree about mechanism. Various authors have proposed at least eight different types of mechanisms that predict an allometric scaling exponent of either ​23 or ​34. Some of these models make a large number of testable predictions while others are less comprehensive.[5]

Much of the current debate focuses on two particular types of mechanisms.[6] One of these assumes energy or resource transport across the external surface area of three-dimensional organisms is the key factor driving the relationship between metabolic rate and body size. The surface area in question may be skin, lungs, intestines, or, in the case of unicellular organisms, cell membranes. In general, the surface area (SA) of a three dimensional object scales with its volume (V) as SA = cV23, where c is a proportionality constant. The Dynamic Energy Budget model is currently the most promising version of these, and it predicts exponents that vary between ​23 – 1, depending on the organism's developmental stage, basic body plan and resource density [7][8] Smaller organisms tend to have higher surface area to volume ratios, causing them to gain resources at a proportionally higher rate than large organisms. As a consequence, small organisms can have higher volume-specific metabolic rates.

In contrast, the arguments for a ​34 scaling factor are based on resource transport network models,[6] where the limiting resources are distributed via some optimized network to all resource consuming cells or organelles.[1][9] These models are based on the assumption that metabolism is proportional to 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][10][11] Larger organisms are necessarily less efficient because more resource is in transport at any one time than in smaller organisms: size of the organism and length of the network imposes an inefficiency due to size. It therefore takes somewhat longer for large organisms to distribute nutrients throughout the body and thus they have a slower mass-specific metabolic rate. An organism that is twice as large cannot metabolize twice the energy—it simply has to run more slowly because more energy and resources are wasted being in transport, rather than being processed. Nonetheless, natural selection appears to have minimized this inefficiency by favoring resource transport networks that maximize rate of delivery of resources to the end points such as cells and organelles.[9][10] This selection to maximize metabolic rate and energy dissipation results in the allometric exponent that tends to D/(D+1), where D is the primary dimension of the system. A three dimensional system, such as an individual, tends to scale to the 3/4 power, whereas a two dimensional network, such as a river network in a landscape,tends to scale to the 2/3 power.[9][11][12]

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. While different underlying mechanisms[1][8] make somewhat different predictions, the following provides an example of some of the implications of the metabolism of individuals.

### Organism level

Small animals tend to grow fast, breed early, and die young.[13] According to MTE, these patterns in life history traits are constrained by metabolism.[14] 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.[15] 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.[13] Classically, species are thought of as being either r selected (where populations tend to grow exponentially, and are ultimately limited by extrinsic factors) or K selected (where population size is limited by density-dependence and 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,[16] and in fact has been shown to scale to M−1/4 across taxonomic groups.[13] 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.[17] 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.[18] In contrast, MTE explains this pattern as being driven by the kinetic constraints imposed by temperature on metabolism.[19] The rate of molecular evolution scales with metabolic rate,[20] 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).[21] 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 account for differences in diversity gradients by including feedbacks between ecological interactions (size-dependent competition and predation) and evolutionary rates (speciation and extinction) [22]

### Ecosystem processes

At the ecosystem level, MTE explains the relationship between temperature and production of total biomass.[23] The average production to biomass ratio of organisms is higher in small organisms than large ones.[24] This relationship is further regulated by temperature, and the rate of production increases with temperature.[25] 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.[23] 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

1. ^ a b c d West, G. B., Brown, J. H., & Enquist, B. J. (1997). "A general model for the origin of allometric scaling laws in biology". Science. 276 (7): 122–126. doi:10.1126/science.276.5309.122. PMID 9082983.CS1 maint: multiple names: authors list (link)
2. Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M., & G. B. West (2004). "Toward a metabolic theory of ecology". Ecology. 85 (7): 1771–89. doi:10.1890/03-9000.CS1 maint: multiple names: authors list (link)
3. ^ Enquist, B. J., Economo, E. P., Huxman, T. E., Allen, A. P., Ignace, D. D., & Gillooly, J. F. (2003). "Scaling metabolism from organisms to ecosystems". Nature. 423 (6940): 639–642. Bibcode:2003Natur.423..639E. doi:10.1038/nature01671.CS1 maint: multiple names: authors list (link)
4. ^ Robinson, W. R., Peters, R. H., & Zimmermann, J. (1983). "The effects of body size and temperature on metabolic rate of organisms". Canadian Journal of Zoology. 61 (2): 281–288. doi:10.1139/z83-037.CS1 maint: multiple names: authors list (link)
5. ^ a b Agutter, P.S., Wheatley, D.N. (2004). "Metabolic scaling: consensus or controversy?". Theoretical Biology and Medical Modelling. 1: 1–13. doi:10.1186/1742-4682-1-13. PMC 539293. PMID 15546492.CS1 maint: multiple names: authors list (link)
6. ^ a b c Hirst, A. G., Glazier, D. S., & Atkinson, D. (2014). "Body shape shifting during growth permits tests that distinguish between competing geometric theories of metabolic scaling". Ecology Letters. 17 (10): 1274–1281. doi:10.1111/ele.12334. PMID 25060740.CS1 maint: multiple names: authors list (link)
7. ^ Kooijman, S. A. L. M. "Energy budgets can explain body size relations". Journal of Theoretical Biology. 121 (3): 269–282. doi:10.1016/S0022-5193 (inactive 2019-08-20).
8. ^ a b Kooijman, S. A. L. M. (2010). "Dynamic energy budget theory for metabolic organisation". Cambridge University Press, Cambridge. Cite journal requires |journal= (help)
9. ^ a b c Banavar, J. R., Maritan, A., & Rinaldo, A. (1999). "Size and form in efficient transportation networks". Nature. 399 (6732): 130–132. Bibcode:1999Natur.399..130B. doi:10.1038/20144. PMID 10335841.CS1 maint: multiple names: authors list (link)
10. ^ a b West, G.B., Brown, J.H., & Enquist, B.J. (1999). "The fourth dimension of life: Fractal geometry and allometric scaling of organisms". Science. 284 (5420): 1677–9. Bibcode:1999Sci...284.1677W. doi:10.1126/science.284.5420.1677. PMID 10356399.CS1 maint: multiple names: authors list (link)
11. ^ a b Banavar, J. R., Damuth, J., Maritan, A., & Rinaldo, A. (2002). "Supply-demand balance and metabolic scaling". Proceedings of the National Academy of Sciences. 99 (16): 10506–10509. Bibcode:2002PNAS...9910506B. doi:10.1073/pnas.162216899. PMC 124956. PMID 12149461.CS1 maint: multiple names: authors list (link)
12. ^ Rinaldo, A., Rigon, R., Banavar, J. R., Maritan, A., & Rodriguez-Iturbe, I. (2014). "Evolution and selection of river networks: Statics, dynamics, and complexity". Proceedings of the National Academy of Sciences. 111 (7): 2417–2424. Bibcode:2014PNAS..111.2417R. doi:10.1073/pnas.1322700111. PMC 3932906. PMID 24550264.CS1 maint: multiple names: authors list (link)
13. ^ a b c Savage V.M.; Gillooly J.F.; Brown J.H.; West G.B.; Charnov E.L. (2004). "Effects of body size and temperature on population growth". American Naturalist. 163 (3): 429–441. doi:10.1086/381872. PMID 15026978.
14. ^ Enquist, B. J., West, G. B., Charnov, E. L., & Brown, J. H. (1999). "Allometric scaling of production and life-history variation in vascular plants". Nature. 401 (6756): 907–911. Bibcode:1999Natur.401..907E. doi:10.1038/44819.CS1 maint: multiple names: authors list (link)
15. ^ Enrique Cadenas; Lester Packer, eds. (1999). Understanding the process of ages : the roles of mitochondria, free radicals, and antioxidants. New York: Marcel Dekker. ISBN 0-8247-1723-6.
16. ^ Denney N.H., Jennings S. & Reynolds J.D. (2002). "Life history correlates of maximum population growth rates in marine fishes". Proceedings of the Royal Society of London B. 269 (1506): 2229–37. doi:10.1098/rspb.2002.2138. PMC 1691154. PMID 12427316.
17. ^ Hutchinson, G., MacArthur, R. (1959). "A theoretical ecological model of size distributions among species of animals". Am. Nat. 93 (869): 117–125. doi:10.1086/282063.CS1 maint: multiple names: authors list (link)
18. ^ Rohde, K. (1992). "Latitudinal gradients in species-diversity: the search for the primary cause". Oikos. 65 (3): 514–527. doi:10.2307/3545569. JSTOR 3545569.
19. ^ Allen A.P., Brown J.H. & Gillooly J.F. (2002). "Global biodiversity, biochemical kinetics, and the energetic-equivalence rule". Science. 297 (5586): 1545–8. Bibcode:2002Sci...297.1545A. doi:10.1126/science.1072380. PMID 12202828.
20. ^ Gillooly, J.F., Allen, A.P., West, G.B., & Brown, J.H. (2005). "The rate of DNA evolution: Effects of body size and temperature on the molecular clock". Proc Natl Acad Sci U S A. 102 (1): 140–5. Bibcode:2005PNAS..102..140G. doi:10.1073/pnas.0407735101. PMC 544068. PMID 15618408.CS1 maint: multiple names: authors list (link)
21. ^ Terribile, L.C., & Diniz-Filho, J.A.F. (2009). "Spatial patterns of species richness in New World coral snakes and the metabolic theory of ecology". Acta Oecologica. 35 (2): 163–173. Bibcode:2009AcO....35..163T. doi:10.1016/j.actao.2008.09.006.CS1 maint: multiple names: authors list (link)
22. ^ Stegen, J. C., Enquist, B. J., & Ferriere, R. (2009). "Advancing the metabolic theory of biodiversity". Ecology Letters. 12 (10): 1001–1015. doi:10.1111/j.1461-0248.2009.01358.x. PMID 19747180.CS1 maint: multiple names: authors list (link)
23. ^ a b Michaletz, S. T., Cheng, D., Kerkhoff, A. J., & Enquist, B. J. (2014). "Convergence of terrestrial plant production across global climate gradients". Nature. 512 (39): 39–44. Bibcode:2014Natur.512...39M. doi:10.1038/nature13470. PMID 25043056.CS1 maint: multiple names: authors list (link)
24. ^ Banse K. & Mosher S. (1980). "Adult body mass and annual production/biomass relationships of field populations". Ecol. Monogr. 50 (3): 355–379. doi:10.2307/2937256. JSTOR 2937256.
25. ^ Ernest S.K.M.; Enquist B.J.; Brown J.H.; Charnov E.L.; Gillooly J.F.; Savage V.M.; White E.P.; Smith F.A.; Hadly E.A.; Haskell J.P.; Lyons S.K.; Maurer B.A.; Niklas K.J.; Tiffney B. (2003). "Thermodynamic and metabolic effects on the scaling of production and population energy use". Ecology Letters. 6 (11): 990–5. doi:10.1046/j.1461-0248.2003.00526.x.