I know what a J-curve is but unsure about S-curve.
In: Mathematics
Population starts. It grows exponentially, so long as the ecosystem can sustain the growth. When the ecosystem can’t anymore, the growth slows and finally stops where it reaches the maximum amount of population the ecosystem can sustain.
Assuming you are talking about population/Logistic growth:
The environment only contains enough of a resource (food shelter, maters, etc…) to keep a certain number of individuals in a population alive. The s shape is caused by the population reaching number close to this maximum size limit (called carry capacity). As the population gets larger than can be supported, the population crashes (extra death) and then more births bring the total population back close to the carrying capacity.
S curve is your J curve that has hit the carrying capacity. Exponential growth has stopped.
An S-shaped curve [1] has the same rough shape as [this curve](https://en.wikipedia.org/wiki/File:Logistic-curve.svg).
In ecology, an S curve is usually used as a mathematical model of how population grows over time in a favorable but resource limited environment.
A small population placed into an environment where it can thrive will grow exponentially over time, growing faster and faster, but once the population gets large enough, it will start running into resource limits like space or food/prey, which means the growth will slow down again.
[1] “Sigmoid curve” is a fancy term for S-shaped curve
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