Just to add to this discussion - the case of Rapa Nui is disputed - see e.g. Rainbird (2002) "A message for our future? The Rapa Nui (Easter Island) ecodisaster and Pacific island environments" - there's actually very little convincing evidence that Rapa Nui society collapsed as a result of environmental destruction, although the native palm tree did become extinct sometime after or around the time at which people arrived: the people seem to have adapted with rock-gardens to grow crops, in the absence of being able to fish in the deep ocean. What is very clear is that the Europeans very effectively destroyed Rapa Nui society with the 200 or so years after they encountered it.
Edmund's model, on the other hand, seems to align well with the standard Hardin tragedy of the commons scenario - if there is no collective pressure on agents to not consume all resource (and they have no foresight), and they gain a temporary benefit from locally exhausting it, then what would prevent its destruction? Agents able to capture all resource rapidly at the expense of others you might think would even be favoured. My experience of small ecosystem models of this type is that they tend to be quite tricky to get to survive in the long term, since even a relatively slow degradation of the environmental resource can lead to its long-term collapse (and stochastic noise + oscillations leading to extinction doesn't help) - however, at continental scale perhaps it is quite difficult for a single species to cover enough ground to really exhaust the environment (until now, that is...)
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