65. Three important biological parameters— generationtime, population growth rate (r) and metabolic rate per gram body weight are a function of the organism’s body size.
    
    Which of the curves (a) or (b) represents the correct relation of each of the parameters to body size?
    (1) Generation time — (a); population growth rate — (b); metabolic rate/g bw — (a)
    (2) Generation time — (a); population growth rate — (b); metabolic rate/g bw — (b)
    (3) Generation time — (b); population growth rate — (a); metabolic rate/g bw — (a)
    (4) Generation time — (b); population growth rate — (b), metabolic rate rate/g bw — (a)

Introduction

Body size is one of the most influential factors shaping the biology of animals. It affects how fast they grow, how long they live, and how much energy they use. Three key biological parameters—generation time, population growth rate (r), and metabolic rate per gram body weight—are all functions of body size, but each follows a distinct scaling relationship. Understanding which curve best represents each parameter is fundamental in ecology, physiology, and evolutionary biology.

Allometric Scaling: The Basics

Allometry describes how biological traits scale with body size. These relationships often follow power laws, where the trait of interest changes in a predictable way as body size increases. The general form is:

Y=aMbY=aMb

• Y: trait of interest (e.g., generation time, metabolic rate)

• M: body mass (body size)

• a: scaling coefficient

• b: scaling exponent

The shape of the curve (whether it increases, decreases, or stays constant) depends on the value of b.

How Each Parameter Relates to Body Size

1. Generation Time

Relationship: Generation time increases with body size.

• Explanation: Larger animals mature more slowly and have longer intervals between generations.

• Curve Shape: Positive relationship—as body size increases, generation time increases, typically following a curve that rises with body size.

2. Population Growth Rate (r)

Relationship: Population growth rate decreases with increasing body size.

• Explanation: Small animals reproduce quickly and have high intrinsic rates of increase, while large animals reproduce slowly.

• Curve Shape: Negative relationship—as body size increases, the intrinsic rate of growth decreases, producing a downward-sloping curve.

3. Metabolic Rate per Gram Body Weight

Relationship: Mass-specific metabolic rate decreases as body size increases.

• Explanation: While total metabolic rate increases with size, the rate per gram of tissue is much higher in small animals than in large ones. This is a classic finding in allometric studies, known as Kleiber’s law.

• Curve Shape: Negative relationship—as body size increases, metabolic rate per gram decreases, following a downward curve.

Assigning Curves (a) and (b)

• Curve (a): Represents a positive relationship—parameter increases with body size.

• Curve (b): Represents a negative relationship—parameter decreases with body size.

Based on the biological relationships:

• Generation time — (a) (increases with body size)

• Population growth rate — (b) (decreases with body size)

• Metabolic rate per gram body weight — (b) (decreases with body size)

Correct Answer

Option (2):

• Generation time — (a)

• Population growth rate — (b)

• Metabolic rate per gram body weight — (b)

Why This Matters

Understanding these scaling relationships helps explain why:

• Mice live fast and die young, while elephants grow slowly and live long.

• Small animals have high energy demands per gram, while large animals are more energy-efficient.

• Conservation and management strategies must account for differences in life history and metabolism across species.

Conclusion

Generation time increases with body size, while both population growth rate and metabolic rate per gram body weight decrease with increasing body size. These patterns are foundational in allometric biology and are best represented by assigning curve (a) to generation time and curve (b) to both population growth rate and metabolic rate per gram body weight.