Controversy Over Exponent
There is disagreement amongst researchers about the most accurate value for use in the power function, and whether the factor is indeed universal. The main disagreement is whether metabolic rate scales to the power of 3/4 or 2/3. The majority view is currently that 3/4 is the correct exponent, but a large minority believe that 2/3 is the more accurate value. Although a rigorous exploration of the controversy over choice of scaling factor is beyond the scope of this article, it is informative to understand the biological justification for the use of either value.
The argument that 2/3 should be the correct scaling factor is based on the assumption that energy dissipation across the surface area of three dimensional organisms is the key factor driving the relationship between metabolic rate and body size. Smaller organisms tend to have higher surface area to volume ratios, causing them to lose heat energy at a faster rate than large organisms. As a consequence, small organisms must have higher specific metabolic rates to combat this loss of energy over their large surface area to volume ratio.
In contrast, the argument for a 3/4 scaling factor is based on a hydraulic model of energy distribution in organisms, where the primary source of energy dissipation is across the membranes of internal distribution networks. This model is based on the idea that metabolism is essentially 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 longer for large organisms to distribute nutrients throughout the body and thus they have a slower metabolic rate. The 3/4 factor is then derived from the observation that selection favors a fractal or near-fractal distribution network for space-filling circulatory systems. All fractal networks terminate in identical units (such as capillary beds), and the number of such units in organisms is proportional to a 3/4 power relationship with body size.
Kolokotrones et al. 2010 showed that relationship between mass and metabolic rate has a convex curvature on logarithmic scale. The curvature explains the variations in the power law exponent.
Despite the controversy over the value of the exponent, the implications of this theory might remain true regardless of its precise numerical value.
Read more about this topic: Metabolic Theory Of Ecology
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