Metabolic Theory of Ecology - Theoretical Background

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):

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:

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, these two equations are combined to produce the primary equation of the MTE, where b_o is a normalization constant that is independent of body size or temperature:

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

Hence SMR for large organisms are lower than small organisms.