3.4 Carrying Capacity

What is carrying capacity?

Carrying capacity (K) is the maximum population size an environment can sustain indefinitely given available resources like food, water, space, and shelter. Populations near K experience slower growth due to limiting factors. Exceeding K causes resource depletion, leading to a population decline back toward a sustainable level.

Logistic growth model

Logistic growth produces an S-shaped curve: populations grow exponentially when small, then slow as they approach K due to density-dependent factors (competition, disease, predation) that intensify as population density rises. Growth rate is highest at K/2, where resources are still plentiful but population size is growing fastest.

Overshoot and carrying capacity changes

Overshoot occurs when a population exceeds K, often followed by a population crash as resources become scarce. Carrying capacity isn't fixed — it can shift with environmental changes (climate, resource availability, technology, or human impact), so K should be viewed as dynamic rather than constant.

Key terms

Carrying capacity (K)

The maximum population size an environment can sustain indefinitely given its resources.

Logistic growth

Population growth that slows as it approaches carrying capacity, producing an S-shaped curve.

Density-dependent factors

Limiting factors (e.g., competition, disease, predation) whose effects intensify as population density increases.

Overshoot

When a population exceeds its carrying capacity, often leading to a population crash.

K/2

The population size at which growth rate is typically highest in the logistic growth model.

Try an AP-style question

What does this show?

1. Logistic growth leveling off at K
2. Density-independent growth only
3. A stable population at equilibrium
4. Overshoot, then die-off