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1、3045TheJournalofExperimentalBiology209,3045-3054PublishedbyTheCompanyofBiologists2006doi:10.1242/jeb.02362CommentaryAcriticalunderstandingofthefractalmodelofmetabolicscalingJoséGuilhermeChaui-BerlinckDepartamentodeFisiologia,InstitutodeBiociências,UniversidadedeS?oPaulo,RuadoMat?otr.14,321,CEP:05
2、508-900,S?oPaulo/SP,Brazile-mail:jgcb@usp.brAccepted5June2006SummaryTheexponentofthescalingofmetabolicratewithbodyprocedureputforwardinthemodel.Itisdemonstratedmasshasbeenthesubjectofdebateformorethanathattheminimizationprocedureismathematicallycentury.Theargumentisattwolevels,oneconcerningincorr
3、ectandill-posed.Also,itisshownthatnoneofthequestionsofempiricalsupportfortheexponentandtheconnectingconditionsareful?lled.Therefore,itisother,howtoderiveittheoretically.Atthissecondlevel,concludedthatthefractalmodellacksself-consistencyandtheexponentisusuallytreatedastheoutcomeofancorrectstatemen
4、t:itreliesonstrongassumptionsofunderlyingphysicalburdenandapproachedasthesearchhomogeneityinmorpho-physiologicalfeaturesamongforanaturallawemergingwithinenergeticandgeometricorganismsinsteadofdemonstratingthem,asclaimedconstraints.Recently,amodelrelyingonfractalgeometrybyitsauthors.Itisproposedth
5、atempiricistsandwasproposedasageneralexplanationforthetheoreticiansshouldratherevaluatetheframeworksforphenomenon.Inthepresentstudy,areanalysisoftheaddressingmetabolicscalingphenomena.fractalmodelisperformedtoverifyitsvalidity.Alltheconditionsthatallowfortheconnectionbetweenthegeometricpropositio
6、nandtheallometricexponentareKeywords:allometry,fractalgeometry,optimization,metabolicrate,evaluated,aswellastheenergylossminimizationbodymass.IntroductionThesecondlevelofthedisputeisthequestionof‘howtoTheproblemofthescalingbetweensizeandenergytheoreticallyderivetheexponent’.Itisrelatedtotheadequa
7、temetabolismbeganwiththeveri?cation,inthelate1800sbychoiceofparametersandvariablesthatshouldbetakenintoRubner(HoppelerandWeibel,2005),thatstandardmetabolicaccountinthemodelingitself.Atthislevelwe?ndquestionsratedoesnot
