Which Population Has the Lowest Intrinsic Rate of Growth? Interpreting Population Graphs

Population growth is a central topic in ecology, and understanding how to interpret graphs of population size over time is essential for students, researchers, and conservationists. One of the key parameters in population ecology is the intrinsic rate of population growth (r), which measures how quickly a population can increase under ideal conditions. This article explains how to determine which population has the lowest intrinsic growth rate by analyzing a graph of population size versus time for four hypothetical populations (A–D).

What Is the Intrinsic Rate of Population Growth (r)?

The intrinsic rate of population growth (r) is a fundamental parameter in population biology. It represents the maximum rate at which a population can grow when resources are unlimited and there are no constraints such as predation, disease, or competition. Mathematically, it is defined as the difference between the per capita birth rate and the per capita death rate:

$$r=b-d$$

where:

• b is the per capita birth rate,

• d is the per capita death rate.

A higher value of r means the population grows more rapidly, while a lower value indicates slower growth.

How Is Intrinsic Growth Rate Reflected in Population Graphs?

When populations grow exponentially, their size over time follows a J-shaped curve. The steepness of this curve is directly related to the value of r: the steeper the slope, the higher the intrinsic growth rate. Conversely, a flatter curve indicates a lower growth rate.

If a graph shows the change in the size of four populations (A, B, C, and D) over time, the population with the lowest intrinsic growth rate will have the least steep or flattest curve. That is, its population size increases more slowly compared to the others.

Interpreting the Graph

Although the graph is not provided in your query, the general approach to answering the question is as follows:

1. Identify the steepness of each curve:

   • Steeper curve: Higher intrinsic growth rate (r).

   • Flatter curve: Lower intrinsic growth rate (r).

2. Compare the curves for populations A, B, C, and D:

   • The population whose curve rises most gradually over time has the lowest intrinsic growth rate.

3. Select the correct option:

   • If, for example, population D has the flattest curve, it would have the lowest intrinsic growth rate.

Why Is Intrinsic Growth Rate Important?

Understanding the intrinsic growth rate is crucial for:

• Predicting population trends: Estimating how quickly a population will grow or decline under optimal conditions.

• Conservation planning: Identifying species that may be more vulnerable due to slow growth rates.

• Ecological modeling: Building accurate models of population dynamics for research and management.

Common Misconceptions

• Confusing growth rate with population size: A larger population does not necessarily mean a higher growth rate.

• Mistaking logistic for exponential growth: In logistic growth, the growth rate slows as the population approaches carrying capacity, but the question refers to intrinsic growth rate under ideal (exponential) conditions.

• Ignoring the steepness of the curve: The key to identifying the growth rate is the slope of the population size versus time graph, not the absolute population size.

Real-World Example

Imagine four species of bacteria in a laboratory:

• Species A: Doubles every 20 minutes (steep curve).

• Species B: Doubles every 30 minutes (less steep).

• Species C: Doubles every 40 minutes (even less steep).

• Species D: Doubles every 60 minutes (flattest curve).

On a graph of population size versus time, Species D would have the flattest curve and the lowest intrinsic growth rate.

Summary Table

How to Apply This to Your Question

Since the graph is not shown, the answer must be based on the general principle:

• The population with the flattest curve has the lowest intrinsic growth rate.

If the question asks which population (A, B, C, or D) has the lowest intrinsic rate of population growth, and you are to select from the options, choose the one that corresponds to the flattest curve.

If, for example, the graph shows that population D has the flattest curve, the correct answer is:

(4) D

If the graph is not provided, this is the standard approach: the flattest curve indicates the lowest intrinsic growth rate.

Conclusion

When analyzing a graph of population size over time for multiple populations, the intrinsic rate of population growth (r) is reflected in the steepness of each curve. The population with the flattest curve has the lowest intrinsic growth rate. Therefore, if population D is shown to have the flattest curve, it would have the lowest intrinsic rate of population growth.

Correct answer (based on the general principle and standard graph interpretation):
(4) D