Topic 8.4 Notes – Effect of Density on Populations

1. Population Density and Resource Availability

Population density is the number of individuals per unit area or volume (for example, 200 trees per hectare).

As density increases, resources per individual decrease. The total amount of food, water, space, nesting sites, or light in an environment is finite. When more individuals share the same space:

• Each one gets a smaller share of resources
• Competition becomes more intense
• Stress and territorial conflicts increase
• Disease spreads more easily (closer contact)
• Birth rates often decrease
• Death rates often increase

If population size exceeds available resources, overpopulation occurs. Resources are used faster than they can be replaced. Individuals become weaker or die, and the population eventually declines.

Here’s the key systems idea:

• Resource availability limits population size.
• Population density affects how quickly resources are used.

They regulate each other.

2. Carrying Capacity K

Carrying capacity (K) is the maximum sustainable population size an ecosystem can support over the long term.

This does not mean the absolute highest number ever recorded. It means the number that can be maintained without degrading the environment.

At or near K:

• Birth rate ≈ death rate
• Net population growth ≈ 0
• Resources are used at about the rate they are replenished

If the population exceeds K:

• Resources decline
• Mortality rises
• The population drops back toward K

K depends on limiting factors such as:

• Food supply
• Water availability
• Shelter or nesting sites
• Light or nutrients (for plants)

K can change. Drought, pollution, habitat loss, or climate shifts can lower it. Improved resources can raise it.

On exams, students sometimes treat K as fixed. It is not. It depends on environmental conditions.

3. Density-Dependent vs Density-Independent Factors

Environmental factors regulate population size. Some depend on density. Some do not.

Density-Dependent Factors

These become stronger as population density increases. They push populations toward carrying capacity.

Examples:

• Competition for food, water, or space
• Predation (more prey can support more predators)
• Disease transmission (spreads faster in crowded populations)
• Waste accumulation
• Territorial behavior

As N increases, these factors intensify. Growth slows.

Density-Independent Factors

These affect populations regardless of size.

Examples:

• Hurricanes, floods, wildfires
• Extreme heat or freezing events
• Drought
• Human disturbances like pollution or habitat destruction

They can reduce population size suddenly. They may also shift K itself.

Here’s a quick comparison:

A common AP-style question gives you a scenario and asks which type of factor is operating. If the effect becomes worse as population increases, it is density-dependent.

4. Logistic Growth Model

When limits to growth are imposed, populations typically follow logistic growth.

The equation is:

$$\frac{dN}{dt} = r_{\text{max}} N \left(\frac{K - N}{K}\right)$$

Where:

• $N$ = population size
• $\frac{dN}{dt}$ = change in population over time
• $r_{\text{max}}$ = maximum per capita growth rate
• $K$ = carrying capacity

Break it into two parts:

• $r_{\text{max}}N$ → exponential growth potential
• $\left(\frac{K - N}{K}\right)$ → environmental resistance: the unused fraction of carrying capacity (same thing as $1 - \frac{N}{K}$)

Now look at what happens:

1. When $N$ is very small
   • $N/K$ is near 0
   • Growth is almost exponential
2. As $N$ approaches $K$
   • $N/K$ approaches 1
   • Growth slows
3. When $N = K$
   • Growth = 0
4. If $N > K$
   • Growth becomes negative
   • Population declines

Here’s what that looks like on a graph. Focus on the right-hand panel, which shows logistic growth.

Exponential vs. logistic population growth

Notice the S-shape of the logistic curve:

• Rapid growth
• Slowing growth
• Plateau at K, the carrying capacity

In real ecosystems, populations often oscillate around K instead of staying perfectly flat.

When you see data with rapid increase that levels off, think logistic growth. When it keeps increasing without slowing, think exponential.

5. How Density Shapes Population Stability

Low density means weak competition and rapid growth. High density strengthens density-dependent limits and stabilizes the population.

Density-independent events can suddenly disrupt this balance.

This is a systems interaction. Resource limits, competition, and environmental disturbances all feed back into population size. The logistic model captures that feedback mathematically.