An explanation of the relationship between mass, metabolic rate and characteristic length for placental mammals

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Abstract
The Mass, Metabolism and Length Explanation (MMLE) was advanced in 1984 to explain the relationship between metabolic rate and body mass for birds and mammals. This paper reports on a modernized version of MMLE. MMLE deterministically predicts the absolute value of Basal Metabolic Rate (BMR) and body mass for individual animals. MMLE is thus distinct from other examinations of these topics that use species-averaged data to estimate the parameters in a statistically best fit power law relationship such as BMR = a(body mass)b. Beginning with the proposition that BMR is proportional to the number of mitochondria in an animal, two primary equations are derived that predict BMR and body mass as functions of an individual animal’s characteristic length and sturdiness factor. The characteristic length is a measurable skeletal length associated with an animal’s means of propulsion. The sturdiness factor expresses how sturdy or gracile an animal is. Eight other parameters occur in the equations that vary little among animals in the same phylogenetic group. The present paper modernizes MMLE by explicitly treating Froude and Strouhal dynamic similarity of mammals’ skeletal musculature, revising the treatment of BMR and using new data to estimate numerical values for the parameters that occur in the equations. A mass and length data set with 575 entries from the orders Rodentia, Chiroptera, Artiodactyla, Carnivora, Perissodactyla and Proboscidae is used. A BMR and mass data set with 436 entries from the orders Rodentia, Chiroptera, Artiodactyla and Carnivora is also used. With the estimated parameter values MMLE can exactly predict every BMR and mass datum from the BMR and mass data set with no error and thus no unexplained variance. Furthermore MMLE can exactly predict every body mass and length datum from the mass and length data set with no error and thus no unexplained variance. Whether or not MMLE can simultaneously exactly predict an individual animal’s BMR and body mass given its characteristic length awaits analysis of a data set that simultaneously reports all three of these items for individual animals. However for many of the addressed phylogenetic homogeneous groups, MMLE can predict the exponent obtained by regression analysis of the BMR and mass data using the exponent obtained by regression analysis of the mass and length data. This argues that MMLE may be able to accurately simultaneously predict BMR and mass for an individual animal.

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