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 Metabolic theory of ecology ： ウィキペディア英語版
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,. 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.〔
== 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 ''B''o is a mass-independent normalization constant (given in a unit of power divided by a unit of mass. In this case, watts per kilogram):
:$B = B_oM ^ \,$
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:
:$e^\right\}$
While ''B''o 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 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 ''b''o is a normalization constant that is independent of body size or temperature:
:$B = b_oM^e^\right\}$
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

$SMR = \left(B/M\right) = b_oM^e^\right\}$
Hence SMR for large organisms are lower than small organisms.

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