Question

A log-log graph is plotted of total surface area of organisms versus their body weight. The best fit line will have a slope of

• A. $1/2$
• B. $2/3$
• C. $3/4$
• D. 1

Hint:

Biological scaling = 3/4 (Kleiber's Law); Geometric scaling = 2/3.

Answer 1

The Correct Option is C

Step 1: Concept
This relationship is a classic example of allometric scaling in biology, where physiological variables are related to body mass.

Step 2: Meaning
For many biological parameters, the relationship follows the power law equation $Y = aM^b$, where $M$ is body mass and $b$ is the scaling exponent.

Step 3: Analysis
While simple geometric scaling (surface area to volume) suggests a slope of $2/3$, Kleiber's Law and subsequent metabolic theories established that biological scaling for surface-related exchanges often follows a $3/4$ power.

Step 4: Conclusion
On a log-log plot, the exponent $b$ becomes the slope of the line, which is approximately $3/4$ for these biological organisms. Final Answer: (C)