Comment on 'A critical understanding of the fractal model of metabolic scaling'.

Chaui-Berlinck recently published a paper in which he claims that the original West, Brown and Enquist (WBE) model for metabolic scaling (West et al., 1997) is fundamentally flawed (Chaui-Berlinck, 2006). In particular, Chaui-Berlinck asserted that 'the minimization procedure [of the original WBE model] is mathematically incorrect and ill-posed' and that the model 'lacks self-consistency and correct statement'. These are strong accusations and should, therefore, be closely scrutinized. Unfortunately, Chaui-Berlinck's conclusions are incorrect because of rudimentary mathematical mistakes, and, even worse, these false conclusions are now being perpetuated in the literature. For example, Muller-Landau (Muller-Landau, 2007), in a review for Faculty of 1000, recently drew attention to Chaui-Berlinck's paper by stating that 'This article carefully dissects West, Brown and Enquist's (1997) derivation of allometric scaling of metabolism. It illuminates important logical inconsistencies and mathematical problems with the argument'. We note that none of the original authors nor the extended scaling community associated with the WBE model were asked to review Chaui-Berlinck's manuscript. As we show below, the entire basis of Chaui-Berlinck's paper stems from fundamental mathematical mistakes. In short, the conclusions of Chaui-Berlinck (and, subsequently, Muller-Landau) are completely incorrect. We conclude that Chaui-Berlinck's paper (Chaui-Berlinck, 2006) should be retracted. The most egregious errors of Chaui-Berlinck are seen in his equation·5a. Specifically, Chaui-Berlinck makes two mistakes. He first mis-transcribes the original equation from WBE (West et al., 1997) and then makes a fundamental error in his calculus. In his equation·5a, Chaui-Berlinck insists that he is carefully analyzing the mathematics of the WBE model. He obtains the quotient 0/0 in several equations and then concludes that, because of his analysis, the results of WBE are meaningless. However, Chaui-Berlinck's results of 0/0 only demonstrate both a misreading of the WBE paper and a basic mathematical error. The first mistake stems from Chaui-Berlinck incorrectly writing equation·9 from WBE as: but the correct expression, as given in WBE, is: Notice that he swaps two ␤ < for ␤ > in the first term inside the parentheses. For the second mistake, he then goes on to evaluate equation·9 from WBE in a regime where the equation does not hold. Thus, Eqn·1b (above) contains expressions for geometric sums that hold only for values of ␤ < , ␤ > , n and ␥ such that n␤ 2 < ␥ϭ1 and n␤ 2 > ␥ϭ1. These expressions are not stated explicitly in WBE because they are apparent from basic …