Carrying capacity

Definition

Carrying capacity is the maximum population size of a species that an environment can sustain indefinitely. It is determined by the availability of resources, space, and other ecological factors.

5 Must Know Facts For Your Next Test

1. Carrying capacity is often represented in logistic growth models using the variable $K$.
2. In a logistic growth equation, $P(t) = \frac{K}{1 + Ae^{-rt}}$, $K$ represents the carrying capacity.
3. Carrying capacity imposes a limit on exponential growth, causing population growth to slow as it approaches $K$.
4. When the population size exceeds carrying capacity, resource depletion causes a decline in population size towards equilibrium.
5. Understanding carrying capacity helps in modeling real-world scenarios such as wildlife management and human resource consumption.

Review Questions

• What does the variable $K$ represent in logistic growth equations?
• How does carrying capacity affect exponential population growth over time?
• What happens when a population exceeds its carrying capacity?

Related terms

Logistic Growth: A type of population growth that starts exponentially but slows as it approaches the carrying capacity due to limited resources.

$r$ (Growth Rate): The rate at which a population increases or decreases. In logistic models, it affects how quickly the population approaches carrying capacity.

$P(t)$ (Population Function): A function representing the population size at time $t$. In logistic models, it adjusts based on growth rate and carrying capacity.