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

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 computes 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(bodymass) (b) . Beginning with the proposition that BMR is proportional to the number of mitochondria in an animal, two primary equations are derived that compute BMR and body mass as functions of an individual animal's characteristic length and sturdiness factor. The characteristic length is a measureable 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 Proboscidea 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 calculate characteristic length and sturdiness factor values so that every BMR and mass datum from the BMR and mass data set can be computed exactly. Furthermore MMLE can calculate characteristic length and sturdiness factor values so that every body mass and length datum from the mass and length data set can be computed exactly. Whether or not MMLE can calculate a sturdiness factor value so that an individual animal's BMR and body mass can be simultaneously computed 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 MMLE 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 compute BMR and mass for an individual animal.

Metabolic scaling in animals: methods, empirical results, and theoretical explanations

Life on earth spans a size range of around 21 orders of magnitude across species and can span a range of more than 6 orders of magnitude within species of animal. The effect of size on physiology is, therefore, enormous and is typically expressed by how physiological phenomena scale with mass(b). When b ≠ 1 a trait does not vary in direct proportion to mass and is said to scale allometrically. The study of allometric scaling goes back to at least the time of Galileo Galilei, and published scaling relationships are now available for hundreds of traits. Here, the methods of scaling analysis are reviewed, using examples for a range of traits with an emphasis on those related to metabolism in animals. Where necessary, new relationships have been generated from published data using modern phylogenetically informed techniques. During recent decades one of the most controversial scaling relationships has been that between metabolic rate and body mass and a number of explanations have been proposed for the scaling of this trait. Examples of these mechanistic explanations for metabolic scaling are reviewed, and suggestions made for comparing between them. Finally, the conceptual links between metabolic scaling and ecological patterns are examined, emphasizing the distinction between (1) the hypothesis that size- and temperature-dependent variation among species and individuals in metabolic rate influences ecological processes at levels of organization from individuals to the biosphere and (2) mechanistic explanations for metabolic rate that may explain the size- and temperature-dependence of this trait.