An Explanation of the Relationships Between

The Mass, Metabolism and Length Explanation (MMLE) was advanced in 1984 to 8 explain the relationship between metabolic rate and body mass for birds and mammals. This 9 paper reports on a modernized version of MMLE. MMLE deterministically predicts the absolute 10 value of Basal Metabolic Rate (BMR) and body mass for individual animals. MMLE is thus 11 distinct from other examinations of these topics that use species-averaged data to estimate the 12 parameters in a statistically best fit power law relationship such as BMR = a(body mass) b . 13 Beginning with the proposition that BMR is proportional to the number of mitochondria in an 14 animal, two primary equations are derived that predict BMR and body mass as functions of an 15 individual animal’s characteristic length and sturdiness factor. The characteristic length is a 16 measureable skeletal length associated with an animal’s means of propulsion. The sturdiness 17 factor expresses how sturdy or gracile an animal is. Eight other parameters occur in the equations 18 that vary little among animals in the same phylogenetic group. The present paper modernizes 19 MMLE by explicitly treating Froude and Strouhal dynamic similarity of mammals’ skeletal 20 musculature, revising the treatment of BMR and using new data to estimate numerical values for 21 the parameters that occur in the equations. A mass and length data set with 575 entries from the 22 orders Rodentia, Chiroptera, Artiodactyla, Carnivora, Perissodactyla and Proboscidae is used. A 23 BMR and mass data set with 436 entries from the orders Rodentia, Chiroptera, Artiodactyla and 24 Carnivora is also used. With the estimated parameter values MMLE can exactly predict every 25 BMR and mass datum from the BMR and mass data set with no error and thus no unexplained 26 variance. Furthermore MMLE can exactly predict every body mass and length datum from the 27 mass and length data set with no error and thus no unexplained variance. Whether or not MMLE 28 can simultaneously exactly predict an individual animal’s BMR and body mass given its 29 characteristic length awaits analysis of a data set that simultaneously reports all three of these 30 items for individual animals. However for many of the addressed phylogenetic homogeneous 31 groups, MMLE can predict the exponent obtained by regression analysis of the BMR and mass 32 data using the exponent obtained by regression analysis of the mass and length data. This argues 33 that MMLE may be able to accurately simultaneously predict BMR and mass for an individual 34 animal. 35 PeerJ PrePrints | http://dx.doi.org/10.7287/peerj.preprints.437v3 | CC-BY 4.0 Open Access | rec: 2 Dec 2014, publ: 2 Dec 2014 P re P rin ts Introduction. Most theoretical treatments of Basal Metabolic Rate (BMR) have focused on the 36 exponent in a relationship of the form BMR = aW b where W is body mass. Two concepts have 37 dominated. One concept is geometric similarity in which the value of the exponent b = 2/3. The 38 theoretical explanations for this value of the exponent generally involve a balance between heat 39 production and its loss through the body surface (Hulbert & Else, 2004; Clarke, Rothery & Isaac, 4