## Curvature in Metabolic Scaling

Tom Kolokotrones, Van M. Savage, Eric J. Deeds and Walter Fontana **Curvature in Metabolic Scaling **Nature* ***464**:753-756, 2010. Nature page

This paper is not about evolution, but it is short, recent, published in Nature and comes from Fontana Lab, so there is definitely no harm in reviewing it. It deals with metabolic scaling, that is the relationship between an organism’s metabolic rate and its body mass. Experimental measurements seem to indicate that the metabolic rate is proportional to the body mass raised to a fixed power. The actual value of the exponent was first thought to be 2/3, and then 3/4; the latter was also derived by West et. al. from an involved theoretical model of vascular system [1].

Kolokotrones et. al. took a large dataset and showed that instead of a simple power law a more complex expression involving two exponents is a much better fit. When plotted on a log-log scale, the graph of this function is a slightly convex curve, rather than the straight line resulting from a pure power law; hence the title of the paper. Of course by introducing a new degree of freedom you will always get a better fit, but the improvement in this case is considerable, and, crucially, the curve can be approximated in different regions by pure power laws with the well-established exponents. This shows that essentially both the 2/3 and 3/4 hypotheses were correct.

A mechanistic explanation for the 3/4 theory was provided by West’s model, and so the authors set out to modify it to get a two-exponent formula instead. Apparently it is possible by postulating a different moment of transition between the pulsatile and smooth blood flow dynamics. More details can be found in Supplementary Information, if you’re interested (I am not).

Now, it is possible that the curved fit does not represent any underlying biological principle. As mentioned above, the curve can be approximated by two or more power laws acting on different parts of the data. It is conceivable that the relationship is in fact a pure power law, but evolutionary distant families of mammals (the study is on mammals) evolved—for whatever reasons—different exponents. Through phylogenetic analysis, Kolokotrones et.al. show that this is not the case, and that curvature is observed in subsets of data corresponding to closely related species. Other factors, such as habitat and food type were also excluded, suggesting that there is an underlying mechanistic principle at work.

[1] West, G. B., Brown, J. H. & Enquist, B. J. *A general model for the origin of allometric scaling laws in biology.* Science 276, 122–126 (1997).

Written by evopapers

April 7, 2010 at 17:44

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