Mathematician William Basener talks in interesting detail about his new paper modelling the collapse of civilisation on Easter Island.   Introductory blog entry . Actual interview .
The point is that the mathematics enables us to describe the process very precisely, allows us to determine if a given civilization is headed for a collapse. It helps us to determine the long-term sustainability of resource use. One of the interesting results is that a collapse due to environmental overuse can be extremely sudden; consequently a civilization can be headed for a collapse even when the population appears to be growing steadily. This is evident in the graphs in our paper.

He answers a few questions about method and the usefulness of models too.
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Comments
  • cam . # .
    James Lovelock found something similar: while modeling climate change. Complex systems seem to self-dampen until the point of collapse. Lovelock found that a climate would stay within finite bounds, despite being a lost cause, then suddenly would fly wildly out of control, unleashing extreme weather, before re-aligning itself to a new equilibrium.

    IIRC his warning was that it would find a new equilibrium, just that the new complex system might not include humanity, or be inhabitable. Sounds like this modeling of environmental collapse gives a similar warning.

    cam