1. INTRODUCTION All biological activities thus understanding wh fundamental importanc bolic rate is body size typically scales with b power function R=ai
1. INTRODUCTION All biological activities thus understanding wh fundamental importanc bolic rate is body size typically scales with b power function R=ai
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter19: Temperature, Thermal Expansion And Gas Laws
Section: Chapter Questions
Problem 71PQ
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This is in ecology please help me identify what the variables in this equation mean R=aM^b
![1. INTRODUCTION
All biological activities depend on metabolic energy, and
thus understanding why rates of metabolism vary is of
fundamental importance. A major factor affecting meta-
bolic rate is body size. Respiratory metabolic rate (R)
typically scales with body mass (M) according to the
power function R=aM, where a is a normalization
constant (antilog of the intercept in a log-log plot) and b
is the scaling exponent (slope in a log-log plot). Rubner
(1883) observed that the scaling exponent b was 2/3 in
dogs of different size, which he explained using the theory
of Sarrus & Rameaux (1839: cited in McNab 2002).
According to this theory, to maintain a constant body
temperature, endothermic animals must metabolically
produce enough body heat to exactly balance the amount
of heat lost through their body surface. Therefore, since
body surface scales as M, so should metabolic rate.
However, in broader comparisons of different species of
mammals, Kleiber (1932) found that b was closer to 3/4
than 2/3. Since that time, it has been commonly assumed
that b is typically 3/4, a generalization known as 'Kleiber's
h
e
law' or the 3/4-power law' (Brody 1945; Hemmingsen](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feceb8058-c7a9-4ec1-9952-bafa6949c626%2F71883b4a-092e-4dee-95a4-5f52a5aaf8a5%2F453u3yt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. INTRODUCTION
All biological activities depend on metabolic energy, and
thus understanding why rates of metabolism vary is of
fundamental importance. A major factor affecting meta-
bolic rate is body size. Respiratory metabolic rate (R)
typically scales with body mass (M) according to the
power function R=aM, where a is a normalization
constant (antilog of the intercept in a log-log plot) and b
is the scaling exponent (slope in a log-log plot). Rubner
(1883) observed that the scaling exponent b was 2/3 in
dogs of different size, which he explained using the theory
of Sarrus & Rameaux (1839: cited in McNab 2002).
According to this theory, to maintain a constant body
temperature, endothermic animals must metabolically
produce enough body heat to exactly balance the amount
of heat lost through their body surface. Therefore, since
body surface scales as M, so should metabolic rate.
However, in broader comparisons of different species of
mammals, Kleiber (1932) found that b was closer to 3/4
than 2/3. Since that time, it has been commonly assumed
that b is typically 3/4, a generalization known as 'Kleiber's
h
e
law' or the 3/4-power law' (Brody 1945; Hemmingsen
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