A simple differential equation model of population and environmental decay got a lot of early play, perhaps because its normative conditions made the usual suspects comfortable with their prejudices.

The dissenting commentary is now coming to light, starting with College Insurrection.
Contrary to early reports, the research is neither funded nor endorsed by the National Aeronautics and Space Administration.It is an independent study by the university researchers utilizing research tools developed for a separate NASA activity. As is the case with all independent research, the views and conclusions in the paper are those of the authors alone. NASA does not endorse the paper or its conclusions.
A Cornell statistician notes a fundamental flaw with the simple model.
It’s based on standard predator-prey models which work like this: a population of wolves eat the locally available deer, whose population necessarily declines, perhaps to the point where some wolves starve, decreasing their population; the concomitant reduced predation allows the deer to rebound, which gives the opportunity for more hot dinners for the wolves, which begins the cycle anew.

[The model] swaps the wolves for human beings and the deer for “Nature.” Just how people prey on Nature is not too clear, especially since people are part of Nature. This difficulty is ignored. [The model] introduces a twist which allows mankind to accumulate Nature for future use, a surplus which the model calls “wealth”. This would be like the wolves discovering how to make and store venison jerky.

About that wealth: “Empirically, however, this accumulated surplus is not evenly distributed throughout society, but rather has been controlled by an elite. The mass of the population, while producing the wealth, is only allocated a small portion of it by elites, usually at or just above subsistence levels.” Some wolves are more equal than other wolves.
First, you have to get the simple model working. Then you can go on to introducing a perhaps more realistic model of wealth accumulation, in which ideas to augment the productivity of Nature occur to individuals who share the gains from trade with others.  But something as simple as the dynamics by which an entrepreneur contracts with workers to perform one of eighteen tasks involved in making a common pin cannot easily be reduced to mathematics.  We know that finer divisions of labour emerge, and we know that living standards can rise above the subsistence level for more than the elite.  A proper simulation is not going to be easy.
Particularly absent is the idea that only in a society which admits Elites can there be technological progress (what else is a writer of scientific papers but an Elite?). Consider how much food production has swelled over the last century as the discoveries made by Elites are implemented to the benefit of Commoners. Nature, in this sense, is not static as the model assumes.
There are a couple of stochastic processes rattling around in my head that I may be able to commit to paper in the near future. (Now that there is NO pressure to publish any more, I can go back to thinking, once the end of semester administrative scut-work is done.)
Commoners become Elites and vice versa. There is no real-life strict dichotomy between an Elite and Commoner. And new forms of wealth and ways of increasing Nature’s bounty are often unanticipated.
The challenge for the researcher is to incorporate these forces in a way that can't automatically be hijacked to support one world-view or another.

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