Hi @mstn and all, guess what: someone ended up using a Lotka-Volterra-type model to write a paper about sustainability (thanks @matthias and @nadia for pointing it out). It’s a very different paper from what we had in mind, and closer to the origins of the math in ecology: it looks at the influence of inequality on the cycles of prosperity and collapse in a world where production is based on labor and “nature” (a stylized renewable natural resource) and “wealth”, the possibility to accumulate resources.
“Wealth” is the most fascinating part of the paper. It is seen as a sort of buffer, where the economy can store resources for later consumption. Inequality (“economic stratification”) is modeled by the existence of two classes – élites and commoners – with unequal access to “wealth”. This part is reminescent of the classical economic tradition!
Having a buffer means that, even as production declines, population size and extraction (in the model the latter is linear to the former) can still increase. People look around and think “hey, things are going great! Restaurants are full! Everyone is renovating their homes! Things cannot be that bad!”. In fact, they might be living on borrowed time, in the imminence of a collapse. Kind of a “don’t look up scenario”, which hits close to home.
The mathematical approach of the paper is even simpler than what Marco and I were trying to do: just choose some parameters so that they will result in a certain outcome, and then reflect on how the choice of parameters drive the model. And it made the Journal of Ecological Economics! Way to go.
Full text accessible if you want to dive in: http://dx.doi.org/10.1016/j.ecolecon.2014.02.014