There aren't many problems in biology that have remained unsolved for over a century. Yet one of these problems, the scaling of resting metabolic rates in animals with their body mass, has not only evaded solution but has even evaded description! The problem is simple, how does the amount of energy an animal uses at rest change with its size? The answer may seem obvious - a resting mouse uses less metabolic energy than an elephant because the mouse has a smaller body. But is there a single relationship that can describe the way metabolic rate changes with changing body mass?

The first evidence for a universal scaling law came in 1883 when Max Rubner suggested that the resting metabolic rate (RMR) was proportional to body mass(Mb) to the power of 2/3 or RMR ∝ Mb2/3. This suggests that, although a mouse uses less energy in real terms than an elephant, relative to its body mass it uses more. One explanation for this scaling was that as animals increase in body mass their surface area doesn't increase as quickly as their volume, so large animals have a lower surface area to volume ratio and lose relatively less heat than their smaller counterparts. And if Rubner's result had remained uncontested then the surface area to volume ratio would have been a convenient explanation, but a more thorough analysis by Max Kleiber 49 years later didn't produce the same result. Instead, he found that RMR was closer to being proportional to Mb3/4. This posed a problem -the surface area to volume ratio explanation cannot account for the Mb3/4 scaling. And despite 65 years of research, there was no explanation for the Mb3/4 scaling. Then, in 1997, Geoffrey West and colleagues controversially proposed that the branching patterns of transport systems such as lungs, blood vessels and tracheoles can account for the scaling of RMR with Mb3/4.

Since 1997, several studies have suggested that the available data don't support Kleiber's Mb3/4 scaling (and therefore West et al.'s explanation for it), favouring Rubner's original Mb2/3 scaling, whilst others have claimed that they have found different explanations for the Mb3/4 scaling. So, it's not surprising then that the April 2004 issue of Functional Ecology is devoted to this contentious issue. One study by Folmer Bokma adds new evidence to the debate.

Bokma studied the scaling of RMR with body mass in 113 species of fish. Most previous studies have analysed RMRs in mammals and birds but a universal law should apply to all animals. Bokma also extracted data from 217 measurements of RMR that were already available in the literature and plotted all of the measurements against Mb. Over all of the species of fish analysed, the RMR scaled with Mb0.715. The problem with this relationship is that it falls midway between the two scaling relationships that were proposed by Rubner and Kleiber and doesn't support either one. Even more worryingly though for advocates of a universal scaling is that when Bokma analysed the scaling of RMR with Mb in individual species, it was clear that there was substantial variation in the scaling exponents. For instance,measurements of RMR were available over a wide range of body masses (0.1-600 g) for the trout Salmo trutta trutta and yielded a reliable scaling exponent of 0.86 - different again from the proposed Mb2/3 or Mb3/4scaling.

Bokma is quite clear on his interpretation of these results - a universal law for the scaling of RMR with Mb may not exist. Certainly, the study emphasises that far more data and analysis are required,and possibly studies that supported universal scaling may also need to be reassessed as they may not explain much of the variation observed experimentally. One thing is certain, however; the scaling of RMR with Mb seems set to continue to elude explanation for many years to come.

Bokma, F. (
2004
). Evidence against universal metabolic allometry.
Funct. Ecol.
18
,
184
-187.