4.Kleiber’s law states that for a number of animal species, the metabolic rate,
scales as the 3/4th power of its mass. Thus, a cat that weighs about 80 times
more than a mouse:
consumes about 27 times the energy of the mouse.
consumes about 1/27 times the energy of the mouse.
consumes as much energy as the mouse.
consumes about 60 times the energy of the mouse.
A cat weighing 80 times more than a mouse consumes about 27 times the energy of the mouse, as per Kleiber’s law, where metabolic rate scales with mass raised to the 3/4 power.
Kleiber’s Law Explanation
Kleiber’s law describes how basal metabolic rate (BMR) in animals relates to body mass M via the equation BMR ∝M3/4. For a mass ratio of 80, the metabolic rate ratio calculates as 803/4≈26.75, which rounds to about 27 times.
Option Analysis
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Consumes about 27 times the energy of the mouse: Correct. 800.75=26.75≈27, matching the 3/4 scaling precisely.
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Consumes about 1/27 times the energy of the mouse: Incorrect. This reverses the relationship; larger animals have higher total metabolic rates, not lower.
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Consumes as much energy as the mouse: Incorrect. Equal energy ignores mass scaling; linear scaling (M1) would predict 80 times, but 3/4 power predicts less.
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Consumes about 60 times the energy of the mouse: Incorrect. 801=80 or even 800.9≈60, but 3/4 power yields ~27, not 60.
Kleiber’s law metabolic rate mass scaling reveals a fundamental biological principle: an animal’s basal metabolic rate scales as the 3/4th power of its body mass. Named after Max Kleiber, this empirical rule applies across species, from mice to elephants. In the classic cat-mouse comparison, a cat weighing 80 times more than a mouse consumes about 27 times the energy, not proportionally more.
Mathematical Basis
The relationship follows BMR =k⋅M3/4, where k is a constant. For mass ratio r=80, energy ratio = r3/4=800.75≈26.75≈27. This sublinear scaling explains why larger animals have lower mass-specific metabolic rates.
Biological Implications
Kleiber’s law metabolic rate mass scaling influences ecology, physiology, and evolution. Smaller animals like mice have higher per-gram energy needs, aiding rapid reproduction. Larger ones like cats allocate energy efficiently for size-related demands. Debates persist on the exact 3/4 exponent, but it holds empirically.
CSIR NET Relevance
For CSIR NET Life Sciences aspirants, Kleiber’s law appears in ecology and physiology sections. Questions test scaling calculations, like the cat-mouse scenario, emphasizing allometry.
