Summary
Growth that slows as a population nears carrying capacity, forming an S-shaped curve.
In depth
dN/dt = rN(K-N)/K. Growth is fastest at K/2 and zero at K. Real populations may overshoot and oscillate around K, especially with time lags.
Phases: lag, exponential, deceleration and plateau.
The logistic model assumes constant K and no time lags. Real populations may oscillate. Harvesting is most sustainable at about K/2, where growth is maximal.
Example: fisheries use this concept in setting maximum sustainable yield.
The S-shaped curve has a lag, exponential rise, deceleration and plateau near K. Gause grew Paramecium in test tubes and found logistic increase. Time lags in density dependence can cause oscillations, and a high r value in the discrete model can lead to chaos (May, 1976). The maximum sustainable yield is at K/2, where growth is fastest, which is important in fisheries but risky because of uncertainty.
Real populations also fluctuate with weather and food. Some, such as lemmings, show cycles and many show stable fluctuations. The logistic equation is the basis for more complex models including competition and predation.
Example: reindeer introduced to St. Matthew Island in 1944 grew from 29 to about 6000 by 1963, then crashed to 42 after exceeding the food supply, an overshoot of K.
Frequently asked questions
What is Logistic Growth?
Growth that slows as a population nears carrying capacity, forming an S-shaped curve.
Which area of biology covers Logistic Growth, and how advanced is it?
Logistic Growth is one of the 54 topics in Ecology. It is rated Intermediate, so it suits learners who already know the core vocabulary. Related topics in this area include Lotka-Volterra Models, Carrying Capacity, Limiting Factors.
Can you give an example of Logistic Growth?
Yeast in a closed container follows an S-shaped curve until nutrients run out or alcohol accumulates.
What should I learn before Logistic Growth?
Work through the Beginner topics in Ecology first, such as Ecology, Ecosystem, Biotic and Abiotic Factors, then return to Logistic Growth. Intermediate topics assume the Beginner vocabulary.
What topics are related to Logistic Growth?
The closest topics to Logistic Growth are Lotka-Volterra Models, Carrying Capacity, Limiting Factors, Exponential Growth. Comparing them side by side is a good way to see how the ideas connect.
How can I check that I understand Logistic Growth?
Read the summary and the in-depth section, then use the quick check on the interactive lesson for Logistic Growth. To practise the whole of Ecology, use the Ecology quiz.
How is Logistic Growth different from Lotka-Volterra Models?
Logistic Growth: Growth that slows as a population nears carrying capacity, forming an S-shaped curve. Lotka-Volterra Models: Differential equations describing oscillating predator and prey populations. Read both side by side and note what each one explains.
How should I study Logistic Growth step by step?
First, read the summary and write the definition in your own words. Second, read the in-depth section and note any example. Third, compare it with Lotka-Volterra Models and explain the difference aloud. Finally, take the Ecology quiz and come back to this page for any question you miss.