Logistic Growth

This equation says a population grows fastest when it is small relative to the environment, but its growth slows as resources, space, disease, or other limits become important. The factor rN gives the familiar exponential tendency: more individuals produce more new individuals, so growth increases with population size. The term (1 - N/K) reduces that growth as N approaches the carrying capacity K, making the net growth rate fall to zero when the population is near the maximum the environment can support.

Use this model when population increase is initially rapid but then levels off because of resource limitation, such as bacteria in a closed culture, animals in a bounded habitat, or cells in a finite growth medium. It is also useful for fitting data to estimate carrying capacity and intrinsic growth rate.

• Treating K as the current population instead of the long-term upper limit
• Forgetting that the growth rate depends on N, so the rate changes over time
• Assuming the population grows exponentially for all N, even when N is close to K