The problem with running up against the limits is that it isn't always pretty. I've heard it said that "all exponential functions are really S-curves" which in this situation would correspond to a civilisation gracefully decreasing its growth as it approached the limits.
However, other curves are possible too. Overshoot and collapse can also occur.
The S-curve scenario can only happen under the following circumstances.
a) the limits are recognised by us
b) they are responded to immediately with no delay.
Another scenario, called "overshoot and oscillation" occurs when:
a) there is a delay in the response
b) AND the the limits that we have exceeded recover quickly. i.e. the limits are no erodable.
"Overshoot and collapse" occurs when we erode some resource that does not recover quickly. Unfortunately, I can think of many resources that are very erodable. The most obvious being fossil fuels which take millions of years to replace themselves. Top-soil and biodiversity are also examples of highly erodable resources.
However, other curves are possible too. Overshoot and collapse can also occur.
The S-curve scenario can only happen under the following circumstances. a) the limits are recognised by us b) they are responded to immediately with no delay.
Another scenario, called "overshoot and oscillation" occurs when: a) there is a delay in the response b) AND the the limits that we have exceeded recover quickly. i.e. the limits are no erodable.
"Overshoot and collapse" occurs when we erode some resource that does not recover quickly. Unfortunately, I can think of many resources that are very erodable. The most obvious being fossil fuels which take millions of years to replace themselves. Top-soil and biodiversity are also examples of highly erodable resources.