Is there a Universal Temperature Dependence of metabolism?
In a challenging and provocative paper Gillooly et al. (2001) have proposed that the metabolism of all organisms can be described by a single equation,
* Q = b0M3/4e−E/kT,
where Q = metabolic rate, M = body mass, E = the activation energy of metabolism (defined as the average activation energy for the rate-limiting enzyme catalysed biochemical reactions of metabolism), T = absolute temperature, k = Boltzmann's constant and b0 is a normalization constant independent of M and T. In deriving this equation Gillooly et al. (2001) start from the premise that metabolic rate scales with body mass as Q ∝ M3/4, based on the fractal-like design of exchange surfaces and distribution networks in plants and animals (West, Brown & Enquist 1997, 1999a,b). These arguments have stimulated some criticism (see for example Dodds, Rothman & Weitz 2001) but here I will concentrate on the derivation of the second part of the equation, namely the temperature dependence term.
Gillooly et al. (2001) called the temperature dependence term of this equation the Universal Temperature Dependence (UTD) of metabolism. Although there have been many statistical descriptions of the relationship between size, temperature and metabolism since the classic work of Hemmingsen (1950, 1960) and Kleiber (1950, 1961), the UTD differs from these in being explicitly derived from first principles, in the sense that the formulation of the temperature dependence term is derived from classical statistical thermodynamics. The UTD has subsequently been incorporated into explanations of developmental time in all organisms, and macroecological patterns including global-scale analyses of diversity and population density (Allen, Brown & Gillooly 2002; Belgrano et al. 2002; Gillooly et al. 2002).
Here I examine the assumptions underlying the formulation of the UTD, and test the relationship with a carefully assembled data set for teleost fish. In doing so I have distinguished between two philosophically different forms of the UTD, both of which are discussed but not explicitly distinguished by Gillooly et al. (2002). The first is where metabolic rate is determined mechanistically by temperature alone; this might be termed the hard UTD hypothesis. In the second form the UTD is simply a parameter-sparse statistical model describing the relationship between temperature and metabolic rate; this is the soft UTD hypothesis.