Metabolic rate scales as 3/4 power of body size, and its relationship with temperature is described by the Van't Hoff-Arrhenius equation over the range of 0 to 40 °C.
[8] In order to survive and maintain metabolism, an organism must be able to obtain crucial elements and excrete waste products.
Past debated have focused on the question whether metabolic rate scales to the power of 3⁄4 or 2⁄3w, or whether either of these can even be considered a universal exponent.
[16] 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.
The Dynamic Energy Budget model predicts exponents that vary between 2⁄3 – 1, depending on the organism's developmental stage, basic body plan and resource density.
[21] DEB also provides a basis for population, community and ecosystem level processes to be studied based on energetics of the constituent organisms.
In this theory, the biomass of the organism is separated into structure (what is built during growth) and reserve (a pool of polymers generated by assimilation).
[2][23] 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.
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.
[23][24] 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.
The relationship between body size and rate of population growth has been demonstrated empirically,[30] and in fact has been shown to scale to M−1/4 across taxonomic groups.
[27] 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.
Regarding density, MTE predicts carrying capacity of populations to scale as M-3/4, and to exponentially decrease with increasing temperature.
The fact that larger organisms reach carrying capacity sooner than smaller one is intuitive, however, temperature can also decrease carrying capacity due to the fact that in warmer environments, higher metabolic rate of organisms demands a higher rate of supply.
[31] Empirical evidence in terrestrial plants, also suggests that density scales as -3/4 power of the body size.
[1] Classically, the latitudinal gradient in species diversity has been explained by factors such as higher productivity or reduced seasonality.
[34] In contrast, MTE explains this pattern as being driven by the kinetic constraints imposed by temperature on metabolism.
[1] 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.