64. What parameter, plotted on Y-axis against generationtime, would yield the curve shown in the figure?

(1) Survivorship (2) Body size
(3) Lifespan (4) Intrinsic rate of growth

Introduction

In population ecology, understanding the relationship between generation time and other life-history parameters is crucial for predicting how populations grow, recover, or decline. When examining a curve with generation time on the X-axis, the choice of what to plot on the Y-axis can reveal key biological insights. Among the options—survivorship, body size, lifespan, and intrinsic rate of growth—only one produces the classic inverse relationship seen in population studies.

The Key Relationship: Generation Time vs. Intrinsic Rate of Growth

What Is Generation Time?

Generation time is the average period between the birth of an individual and the birth of its offspring. It’s a fundamental measure of how quickly a population can turn over generations.

What Is Intrinsic Rate of Growth (r)?

The intrinsic rate of growth (r) is the maximum potential rate at which a population can increase under ideal conditions. It reflects how rapidly a species can multiply if resources are unlimited.

The Mathematical Connection

Ecologists have established a strong inverse relationship between generation time and intrinsic rate of growth. The mathematical expression is:

r=ln⁡R0Gr=GlnR0

• $r$: Intrinsic rate of growth

• R0R0: Net reproductive rate

• $G$: Generation time

As generation time increases, the intrinsic rate of growth decreases. This produces a downward-sloping, hyperbolic curve when r (Y-axis) is plotted against generation time (X-axis).

Why Not Other Parameters?

• Survivorship: Typically plotted against age to create survivorship curves, not generation time.

• Body Size: While often positively correlated with generation time, the relationship is not typically hyperbolic or inverse.

• Lifespan: Also tends to increase with generation time, but does not produce the classic inverse curve.

Real-World Example

• Bacteria: Species with very short generation times, like E. coli, have high intrinsic rates of growth and can rapidly increase in number.

• Large Mammals: Elephants and whales have long generation times and low intrinsic rates of growth, making population recovery slow.

Importance in Ecology

Understanding this relationship helps ecologists:

• Predict how quickly populations can rebound from declines

• Assess extinction risks for slow-growing species

• Inform conservation and management strategies

Conclusion

When plotting generation time on the X-axis, the parameter that yields a classic inverse curve on the Y-axis is the intrinsic rate of growth (r). This relationship is foundational in population ecology and highlights why fast-reproducing species can recover quickly, while those with long generation times are more vulnerable to environmental changes.

The correct answer is: Intrinsic rate of growth