3045 Introduction The problem of the scaling between size and energy metabolism began with the verification, in the late 1800s by Rubner (Hoppeler and Weibel, 2005), that standard metabolic rate does not scale linearly with body mass. This initial evidence came from mammals and the associated exponent of the relationship was 0.67. Subsequently, three authors examined larger data sets and contended that the exponent was 0.75 instead of 0.67 (Kleiber, 1932; Kleiber, 1961) [for Brody in 1945 and Hemmingsen in 1960, see Calder III (Calder, III, 1996), for reference]. From that time to the present day, a series of debates has taken place in the literature concerning the value of and the putative explanation for such an exponent. One can recognize two levels of scientific dispute in this issue. The first level is, broadly, the question of ‘the empirical support to the exponent’. It is related to statistical and data collection matters. To this level of research pertain questions of the type ‘do empirical results reassure the model?’, ‘do the modeled systems fulfill the premises of the model?’ and ‘how robust is the model in the face of empirical deviations from the predicted?’. The second level of the dispute is the question of ‘how to theoretically derive the exponent’. It is related to the adequate choice of parameters and variables that should be taken into account in the modeling itself. At this level we find questions such as: (1) ‘Is the model self-consistent?’ and (2) ‘Is the model correctly stated?’. While at the first level of the argument, the value and even the existence of a characteristic allometric exponent is discussed (e.g. Dodds et al., 2001; Heusner, 1984; McKechnie and Wolf, 2004; McNab, 1983; Riisgärd, 1998; Suarez and Darveau, 2005; Symonds and Elgar, 2002; White and Seymour, 2003; Weibel and Hoppeler, 2005; Wieser, 1984), the second level begins with the assumption that such an exponent is the outcome of a physical burden. Therefore, studies concerning the latter try to demonstrate that a given value of the allometric exponent, usually 0.75, arises naturally from energy minimization principles under geometrical restrictions. One can find examples in the literature discussing elastic energy scale (McMahon, 1973); similarity principles (Günther, 1975); heterogeneous catalytic bioreactor (Sernetz et al., 1985); constructal law (Bejan, 2000); similitude in The exponent of the scaling of metabolic rate with body mass has been the subject of debate for more than a century. The argument is at two levels, one concerning questions of empirical support for the exponent and the other, how to derive it theoretically. At this second level, the exponent is usually treated as the outcome of an underlying physical burden and approached as the search for a natural law emerging within energetic and geometric constraints. Recently, a model relying on fractal geometry was proposed as a general explanation for the phenomenon. In the present study, a reanalysis of the fractal model is performed to verify its validity. All the conditions that allow for the connection between the geometric proposition and the allometric exponent are evaluated, as well as the energy loss minimization procedure put forward in the model. It is demonstrated that the minimization procedure is mathematically incorrect and ill-posed. Also, it is shown that none of the connecting conditions are fulfilled. Therefore, it is concluded that the fractal model lacks self-consistency and correct statement: it relies on strong assumptions of homogeneity in morpho-physiological features among organisms instead of demonstrating them, as claimed by its authors. It is proposed that empiricists and theoreticians should rather evaluate the frameworks for addressing metabolic scaling phenomena. Key words: allometry, fractal geometry, optimization, metabolic rate, body mass. Summary The Journal of Experimental Biology 209, 3045-3054 Published by The Company of Biologists 2006 doi:10.1242/jeb.02362 Commentary A critical understanding of the fractal model of metabolic scaling José Guilherme Chaui-Berlinck Departamento de Fisiologia, Instituto de Biociências, Universidade de São Paulo, Rua do Matão tr. 14, 321, CEP: 05508-900, São Paulo/SP, Brazil e-mail: jgcb@usp.br Accepted 5 June 2006 THEJOURNALOFEXPERIMENTALBIOLOGY THEJOURNALOFEXPERIMENTALBIOLOGY