Logistic Growth, explained.
Logistic growth describes a population or quantity that grows quickly when resources are abundant, then slows as it approaches a carrying capacity.
Why it happens
The growth term combines the amount already present with the remaining fraction of capacity. Per-capita growth declines as crowding rises. In the continuous model, total growth is largest around half of capacity, rather than at the final plateau.
Growth proportional to both current size and remaining room creates an S-shaped path.
Read the result
Compare the growth rate with the level. A curve that keeps rising can still be growing more slowly. The carrying capacity is an assumption of this model, not a measured permanent limit for every real system.
A worked example
A bounded population
A habitat has an illustrative carrying capacity of 100, and begins with a population of five.
Growth accelerates as the population expands, then slows as it approaches the assumed limit.
The leveling curve reflects resource constraints. A higher capacity would change the eventual level, not merely the speed of reaching it.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Starting from 5, each period adds rN(1−N/K), with r=growth/100 and K=capacity, for 50 periods.
Where this idea is useful
A practical use
Sketch adoption or population growth when space and resources constrain expansion.
A common misconception
“Slower growth means the population is shrinking.”
A positive but decreasing growth rate still raises the population. Decline requires the change itself to become negative.
What this explanation leaves out
- Capacity and growth rate are fixed; real ecosystems and markets can shift abruptly.
Can carrying capacity change?
Yes. Resources, technology, competition, and environmental conditions can change it. A fixed capacity is a teaching simplification.
Are you comparing total size, growth per period, or growth per participant?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.