Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025
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
Carrying capacity is often represented in logistic growth models using the variable $K$.
In a logistic growth equation, $P(t) = \frac{K}{1 + Ae^{-rt}}$, $K$ represents the carrying capacity.
Carrying capacity imposes a limit on exponential growth, causing population growth to slow as it approaches $K$.
When the population size exceeds carrying capacity, resource depletion causes a decline in population size towards equilibrium.
Understanding carrying capacity helps in modeling real-world scenarios such as wildlife management and human resource consumption.
Review Questions
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.