The Limits to Growth Archetype demonstrates the manner in which initial growth may be slowed over time by a limiting factor. There is also a video for this model which is a component of the Systems Archetypes Course.
The Limits to Growth Archetype begins with the basic reinforcing loop where the [action] is intended to grow [result] which influences more of the same [action].
The [result] interacts with a [limiting factor] to create a [slowing action]. Typically the [limiting factor] is of a nature where it doesn't come into play until the [result] has reached a certain amount. A bathtub doesn't run over till the water level gets to the overflow protection, which is probably a bad example because filling a bathtub is not a growth structure.
The [limiting factor] is the goal of a balancing loop which is using the [slowing action] in an attempt to bring a balance between [result] and [limiting factor]. Remember balancing structures always have goals.
In this stock & flow version of the causal loop diagram we run into the first apparent limitation of causal loops. The causal structure doesn't give any specifics about how the limit is effected.
The limit might be a hard limit as in the overflow level of the bathtub. It might be a soft limit where it makes progress more difficult though there still is some, or it might actually limit the action which produces the results. With stock & flow simulation models you can't get a way with hand waving or smoke & mirrors. Everything is explicit.
Two simulations that follow will demonstrate the soft and hard limit behavior of the structure.
With [factor] = 0.3, [results] = 1, [limiting factor] = 20 and [hard limit] = 0 the simulation shows that once the [limiting factor] is reached growth begins to slow. Eventually the slowing builds to a point where [results] no longer increases.
If we change to [hard limit] = 1 the behavior of [results] is quite different. The [limiting factor] becomes the limit. The transition spike is because the Time Step for the model is set too large. You can experiment with this later to get a sense of the implication of changing its values.
Strategy: All growth structures sooner or later run into limits. It's just the nature of the beast. If you are attempting to promote growth you should seek out and attempt to deal with limits before you reach them. The alternative is to figure out how to disconnect the limiting factor or the slowing action from the results.
Change the sliders to run the model with various parameters to see how they impact the behavior of the model. Also change the Simulation Time Step in Settings to .5, .25, and .125 to see how this affects the nature of the graphs.