Logistic Growth

This equation says that a population grows fastest when it is small enough that resources are plentiful, but the growth rate gradually weakens as crowding, competition, or limited food and space become important. The factor (1 - N/K) measures how much unused capacity remains: when N is tiny, it is close to 1, so growth is nearly exponential; when N approaches K, it shrinks toward 0, so the population levels off. It comes from the idea that per-capita growth cannot stay constant in a finite environment, so the environment itself suppresses further increase.

Use this model when a population is constrained by a finite resource base, such as bacteria in a closed culture, animals in a restricted habitat, or an invasive species spreading into a limited region. It is especially useful when data show rapid early growth followed by slowing and stabilization near an upper limit.

• Treating K as the current population size instead of the long-term upper limit
• Forgetting that the growth rate must be reduced by the factor (1 - N/K) when the population is large
• Using the model when population limits are not density-dependent, such as short-term growth with no crowding effects