Final answer:
The carrying capacity, represented by the letter K, is the maximum population size that an environment can sustain without resource depletion or environmental harm. It is central to the logistic growth model in population ecology.
Step-by-step explanation:
The maximum population size that a given environment can sustain is called the carrying capacity and is represented with the letter K. Carrying capacity refers to the largest number of individuals of a species that can be supported by the limited resources of a habitat without depleting those resources or harming the environment. This concept is essential in understanding population dynamics and environmental limits.
In population ecology, the carrying capacity is crucial for the logistic growth model where the population growth rate slows as the population size approaches the K value, eventually plateauing. The carrying capacity can change due to variations in resources, environmental conditions, and other factors influencing an ecosystem's ability to support a population. Species that typically reach this capacity are known as K-selected species, and they often exhibit traits such as fewer offspring with higher survival rates, contrasting with r-selected species which grow rapidly but are far less stable.