Based partly on funding from NASA but incorporating independently conducted research, a paper has been published in the journal Ecological Economics by applied mathematician Safa Motesharrei of the National Socio-Environmental Synthesis Center, modeling the role of unsustainable resource exploitation and increasingly unequal wealth distribution in civilizational collapse scenarios.
Utilizing their HANDY (Human and Nature DYnamics) model, built on the classical predator-prey model, Motesharrei and his co-authors outline several possibilities for societies with varying levels of cooperation and sharing between Elite (wealthy) and Commoner (poor) populations. These include Egalitarian societies (without Elites), Equitable societies, and Unequal societies, with the third group of societies most closely resembling our own current civilization.
Their conclusion is that:
Under such conditions, we find that collapse is difficult to avoid, which helps to explain why economic stratification is one of the elements recurrently found in past collapsed societies. Importantly, in the first of these unequal society scenarios, the solution appears to be on a sustainable path for quite a long time, but even using an optimal depletion rate and starting with a very small number of Elites, the Elites eventually consume too much, resulting in a famine among Commoners that eventually causes the collapse of society.
...in the context of economic stratification, inequality must be greatly reduced and population growth must be maintained below critical levels in order to avoid a societal collapse...
...Given economic stratification, collapse is very difficult to avoid and requires major policy changes, including major reductions in inequality and population growth rates. Even in the absence of economic stratification, collapse can still occur if depletion per capita is too high. However, collapse can be avoided and population can reach equilibrium if the per capita rate of depletion of nature is reduced to a sustainable level, and if resources are distributed in a reasonably equitable fashion.