Question

The field of allometry assesses how species traits scale with each other. Given the relationship between metabolic rate and body mass, which one of the following statements is true?

• A. Elephants expend more energy per gram per hour than mice do
• B. Mice expend more energy per gram per hour than humans do
• C. Elephants expend less total energy per day than mice do
• D. Humans and elephants expend similar amounts of total energy per day

Hint:

Kleiber's law gives total metabolic rate as roughly \(M^{0.75}\); dividing by mass shows mass-specific (per gram) metabolic rate falls with size, so smaller animals burn more per gram than larger ones.

Answer 1

The Correct Option is B

Step 1: Understanding the Question.
Allometry studies how a trait such as metabolic rate scales with body size across species. We need to work out which one of the four statements about energy expenditure in mice, humans and elephants matches the known scaling relationship.

Step 2: Key Concept or Approach.
Across a huge range of body sizes, the whole-body (total) metabolic rate \(B\) scales with body mass \(M\) close to
\[ B \propto M^{0.75} \]
This is Kleiber's law. Because the exponent \(0.75\) is less than \(1\), total metabolic rate grows more slowly than mass does. If we divide both sides by \(M\) to get the mass-specific rate, energy used per gram of body per hour, we get
\[ \frac{B}{M} \propto M^{0.75-1}=M^{-0.25} \]
Since the exponent is negative, the per gram metabolic rate falls as body mass rises. In plain words, smaller animals burn more energy for every gram of their body per hour than larger animals do.

Step 3: Detailed Explanation.
Order the three animals by mass: mice are the smallest, humans are much larger than mice, and elephants are far larger still. By the \(M^{-0.25}\) relationship, mass-specific metabolic rate should go mice greater than humans greater than elephants.
Option (A) claims elephants expend more energy per gram per hour than mice do. This is backwards. Being far larger, elephants have a lower per gram rate, not a higher one, so this statement is false.
Option (B) claims mice expend more energy per gram per hour than humans do. Since mice are smaller than humans, this follows directly from the negative scaling of mass-specific rate with size, so this statement is true.
Option (C) claims elephants expend less total energy per day than mice do. This confuses total energy with mass-specific energy. Total metabolic rate rises with mass (as \(M^{0.75}\), a positive power), so an elephant's whole-body energy use per day is far larger than a mouse's, not smaller. This statement is false.
Option (D) claims humans and elephants expend similar total energy per day. Since total metabolic rate scales with mass to the power \(0.75\), and elephants outweigh humans by roughly two orders of magnitude, elephants use total energy several times greater than humans do per day, so the two are not similar. This statement is false.

Step 4: Final Answer.
Smaller animals burn more energy per gram of tissue per hour than larger animals, so mice expend more energy per gram per hour than humans do.
\[ \boxed{\text{Mice expend more energy per gram per hour than humans do}} \]