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

Frasier CC - PeerJ (2015)

Bottom Line: The characteristic length is a measureable skeletal length associated with an animal's means of propulsion.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.This argues that MMLE may be able to accurately simultaneously compute BMR and mass for an individual animal.

View Article: PubMed Central - HTML - PubMed

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 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.

No MeSH data available.


Related in: MedlinePlus

Log body mass as a function of log shoulder height for running/walking Artiodactyla and Carnivora.Data are from Nowak (1999). The upper and lower slanted solid lines are MMLE sturdiness factor boundaries for y = 2/3. The upper boundary was generated with a sturdiness factor, s, of the square root of 3, (3)0.5. The lower boundary was generated with s = (3)−0.5. The middle slanted line was generated with s = 1.0. The slanted lines are for Froude–Strouhal dynamic similarity. The Artiodactyla mass and shoulder height data are marked by open squares. The Carnivora mass and shoulder height data are marked by open triangles. Excluding Hippopatamus amphibus marked by crossed Xes and domestic cattle marked by Xes, . The solid vertical lines demark the AVG method first set of cohorts. The dashed vertical lines demark the second set of cohorts.
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fig-1: Log body mass as a function of log shoulder height for running/walking Artiodactyla and Carnivora.Data are from Nowak (1999). The upper and lower slanted solid lines are MMLE sturdiness factor boundaries for y = 2/3. The upper boundary was generated with a sturdiness factor, s, of the square root of 3, (3)0.5. The lower boundary was generated with s = (3)−0.5. The middle slanted line was generated with s = 1.0. The slanted lines are for Froude–Strouhal dynamic similarity. The Artiodactyla mass and shoulder height data are marked by open squares. The Carnivora mass and shoulder height data are marked by open triangles. Excluding Hippopatamus amphibus marked by crossed Xes and domestic cattle marked by Xes, . The solid vertical lines demark the AVG method first set of cohorts. The dashed vertical lines demark the second set of cohorts.

Mentions: The sturdiness factor is best understood by looking at Fig. 1. Figure 1 plots 314 samples of log body mass versus log shoulder height for running/walking mammals from the orders Artiocactyla and Carnivora obtained from (Nowak, 1999). Shoulder height is a good surrogate for characteristic length for running/walking mammals. The data in Fig. 1 spread over an area in the two dimensional log shoulder height, log body mass space. It was found in the original paper that most of the area over which the data spreads would be bounded by an upper line computed using Eq. (3) with the sturdiness factor set to the square root of 3, (3)0.5, and a lower line computed with the sturdiness factor set to (3)−0.5. These boundaries are plotted as the upper and lower slanting lines in Fig. 1. Excluding Hippopotamus amphibius and domestic cattle, over 97% of the data plotted in Fig. 1 are contained between these boundary lines.


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

Frasier CC - PeerJ (2015)

Log body mass as a function of log shoulder height for running/walking Artiodactyla and Carnivora.Data are from Nowak (1999). The upper and lower slanted solid lines are MMLE sturdiness factor boundaries for y = 2/3. The upper boundary was generated with a sturdiness factor, s, of the square root of 3, (3)0.5. The lower boundary was generated with s = (3)−0.5. The middle slanted line was generated with s = 1.0. The slanted lines are for Froude–Strouhal dynamic similarity. The Artiodactyla mass and shoulder height data are marked by open squares. The Carnivora mass and shoulder height data are marked by open triangles. Excluding Hippopatamus amphibus marked by crossed Xes and domestic cattle marked by Xes, . The solid vertical lines demark the AVG method first set of cohorts. The dashed vertical lines demark the second set of cohorts.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4562252&req=5

fig-1: Log body mass as a function of log shoulder height for running/walking Artiodactyla and Carnivora.Data are from Nowak (1999). The upper and lower slanted solid lines are MMLE sturdiness factor boundaries for y = 2/3. The upper boundary was generated with a sturdiness factor, s, of the square root of 3, (3)0.5. The lower boundary was generated with s = (3)−0.5. The middle slanted line was generated with s = 1.0. The slanted lines are for Froude–Strouhal dynamic similarity. The Artiodactyla mass and shoulder height data are marked by open squares. The Carnivora mass and shoulder height data are marked by open triangles. Excluding Hippopatamus amphibus marked by crossed Xes and domestic cattle marked by Xes, . The solid vertical lines demark the AVG method first set of cohorts. The dashed vertical lines demark the second set of cohorts.
Mentions: The sturdiness factor is best understood by looking at Fig. 1. Figure 1 plots 314 samples of log body mass versus log shoulder height for running/walking mammals from the orders Artiocactyla and Carnivora obtained from (Nowak, 1999). Shoulder height is a good surrogate for characteristic length for running/walking mammals. The data in Fig. 1 spread over an area in the two dimensional log shoulder height, log body mass space. It was found in the original paper that most of the area over which the data spreads would be bounded by an upper line computed using Eq. (3) with the sturdiness factor set to the square root of 3, (3)0.5, and a lower line computed with the sturdiness factor set to (3)−0.5. These boundaries are plotted as the upper and lower slanting lines in Fig. 1. Excluding Hippopotamus amphibius and domestic cattle, over 97% of the data plotted in Fig. 1 are contained between these boundary lines.

Bottom Line: The characteristic length is a measureable skeletal length associated with an animal's means of propulsion.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.This argues that MMLE may be able to accurately simultaneously compute BMR and mass for an individual animal.

View Article: PubMed Central - HTML - PubMed

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 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.

No MeSH data available.


Related in: MedlinePlus