Carrying capacity
= Carrying capacity
{title2=$K$}
A <carrying capacity> is an abundance scale at which a specified environment's net population growth vanishes. In the <logistic growth equation>, positive unharvested populations approach $K$. It depends on the species, resources and environment rather than being an immutable universal population <limit>.
The useful distinction is between a growth rate and a sustainable abundance. In a <logistic differential equation>, $r$ controls how quickly a population responds, while the <carrying capacity> $K$ sets the positive <equilibrium point>. Increasing $r$ with $K$ fixed accelerates approach without raising that <equilibrium>. Increasing $K$ changes the destination. The <logistic differential equation> diagrams show populations approaching the same <carrying capacity> from below and above.
In ecological use, the <carrying capacity> describes what a particular environment can support under specified conditions. Nutrient supply, available space, and accumulated waste can change those conditions; it is not a permanent property of a <species> alone. A population temporarily above a <carrying capacity> is possible. In the simplest constant-$K$ <logistic growth equation>, its net growth becomes negative; real <population dynamics> can include delays, seasonal variation, and changing resources that the basic <mathematical model> omits. https://openstax.org/books/biology-2e/pages/45-3-environmental-limits-to-population-growth[Clark, Douglas and Choi, Biology 2e, §45.3: carrying capacity and environmental limitations]{ref}.