How to Plot a Bell Curve for K-Selected Species: Understanding Population Growth Graphs

Population growth is a central concept in ecology, and the way we graph it can reveal much about a species’ life history and environment. For K-selected species, which are typically large, long-lived, and have low reproductive rates, population growth follows a pattern known as logistic growth—often represented by an S-shaped curve when population size is plotted over time. However, if we plot population size (N) on the X-axis, we can derive a different, equally informative curve. This article explains what should be plotted on the Y-axis to produce a bell-shaped curve for K-selected species, and why this is important for understanding population dynamics.

Understanding K-Selected Species

K-selected species are adapted to stable environments where resources are limited. They invest heavily in each offspring, producing few young but providing extensive parental care. As a result, their populations grow slowly and are regulated by density-dependent factors such as competition for food, space, and mates. These species tend to stabilize near their environment’s carrying capacity (K), the maximum population size the environment can support.

Population Growth Models

There are two primary models of population growth:

• Exponential growth: Occurs when resources are unlimited, producing a J-shaped curve when population size is plotted over time. This is typical for r-selected species, which are adapted to unstable or unpredictable environments.

• Logistic growth: Occurs when resources are limited, producing an S-shaped (sigmoid) curve. This is typical for K-selected species, as their growth slows and stabilizes near the carrying capacity.

Plotting Population Size (N) on the X-axis

If we plot population size (N) on the X-axis, we are not plotting population size over time, but rather examining how some other variable changes as the population size increases. To understand what to plot on the Y-axis to get a bell-shaped curve for K-selected species, we need to consider how population growth rate changes with population size.

The Logistic Growth Equation

The logistic growth equation is:

dNdt=rN(1−NK)dtdN=rN(1−KN)

where:

• dNdtdtdN = rate of change of population size over time (population growth rate)

• $r$ = intrinsic growth rate

• $N$ = current population size

• $K$ = carrying capacity

This equation shows that the growth rate is highest at intermediate population sizes and decreases as the population approaches the carrying capacity.

Deriving the Bell Curve

If we plot population size (N) on the X-axis and population growth rate (dNdtdtdN) on the Y-axis, the resulting graph for logistic growth is a bell-shaped curve (parabola), not an S-curve.

• At low N: Growth rate is low because there are few individuals to reproduce.

• At intermediate N: Growth rate is highest because there are enough individuals to reproduce rapidly, but not so many that resources are limiting.

• At high N (near K): Growth rate declines as resources become scarce and competition increases, eventually reaching zero at the carrying capacity.

This bell-shaped curve is a hallmark of density-dependent population regulation, which is characteristic of K-selected species.

Evaluating the Options

Let’s consider the options provided:

1. dNdtdtdN:

   • Interpretation: The growth rate of the population.

   • Graph: When plotted against N, this gives a bell-shaped curve for logistic growth.

   • Correct for K-selected species.

2. 1−dNdt1−dtdN:

   • Interpretation: Not a standard measure in population ecology.

3. T:

   • Interpretation: Time. Plotting N vs. T gives the classic S-shaped logistic growth curve, not a bell curve.

4. Nt−1Nt−1:

   • Interpretation: Population size at the previous time step. Not relevant for this type of graph.

Conclusion:
Option (1) dNdtdtdN should be plotted on the Y-axis to get a bell-shaped curve when population size (N) is on the X-axis.

Why Is This Important?

Understanding how to plot and interpret these curves is essential for:

• Predicting population trends: Identifying when a population is growing fastest and when it is approaching its limits.

• Managing wildlife and conservation: Knowing when to intervene to prevent overpopulation or extinction.

• Ecological research: Analyzing the effects of environmental changes on population dynamics.

Real-World Example

Imagine a population of elephants (a classic K-selected species) in a national park. If you plot the number of elephants (N) on the X-axis and the annual population growth rate (dNdtdtdN) on the Y-axis, you would see a bell-shaped curve. The growth rate is highest when the population is moderate, and it declines as the population approaches the park’s carrying capacity.

Common Misconceptions

• Bell curve vs. S-curve:

  • S-curve: Population size over time (logistic growth).

  • Bell curve: Growth rate (dNdtdtdN) vs. population size (N).

• Exponential growth:

  • Produces a straight line (on a log scale) or a J-curve (on a linear scale) when plotting population size over time.

  • Not relevant for K-selected species in the long term.

Summary Table

Conclusion

To obtain a bell-shaped curve for K-selected species when population size (N) is plotted on the X-axis, plot the population growth rate (dNdtdtdN) on the Y-axis. This graph illustrates how growth rate peaks at intermediate population sizes and declines as the population approaches the carrying capacity, reflecting the density-dependent regulation typical of K-selected species.

Correct answer:
(1) dNdtdtdN