Today I stumbled on a discussion of a cute little modeling paper, that opened my eyes to a whole world of modeling I didn’t know was happening. The discussion was at the blog Resource Crisis, and it concerned a paper which uses a relatively simple predator-prey model (a Lotka-Volterra model, in other words) to model civilization collapse. The paper can be read here. Apparently it caused a bit of a stir, attracting a write-up in the Guardian and subsequent controversy for having been called a NASA-funded study. The model in the paper has been derided by some as just another piece of Malthusian silliness, but the really interesting aspects of the model arise from the model processes where it does not predict Malthusian outcomes: instead, under some conditions, this model predicts civilization collapse without exhaustion of natural resources, i.e. the social structures in this model bring about collapse without necessarily exhausting resources. This arises from social inequality in the model, in which a small class of elites live parasitically off of a large population of labourers. Some commentators have related the model to global warming (see e.g. the picture in the Guardian article) but I don’t think the model is intended to talk about this. It appears from discussion within and outside the paper that the main interest is in modelling civilization collapses of the past which came about despite abundant wealth and resources: especially, Rome and the Mayan empire.
The model is a fairly simple one and the paper relatively easy to read, along with a very large number of references to similar work in the field. The basic idea is to set out two resource stocks, one natural and the other accrued as time passes. Nature regenerates at a fixed rate, and the human population is assumed to have a carrying capacity above which it is no longer sustainable, but unlike in classic predator prey models with a carrying capacity, humans can live off their accrued wealth when they pass the carrying capacity. Wealth is built by one class of humans (called “commoners” in the model paper) but the wealth is controlled by another, smaller class, called “elites.” These elites give the commoners a subsistence level of wealth, and retain the remainder. Mortality among humans is set by a base rate that modifies according to whether the population is above the carrying capacity threshold, and by access to wealth. Mortality reaches its maximum once wealth is exhausted, but the thresholds for mortality to begin increasing are different for commoners and elites, and they have different consumption rates. Basically the model assumes a fairly nasty imperial society, in which elites control wealth and ensure that once past the carrying capacity it is the poor who suffer first.
The authors then divide societies into three types: Egalitarian, in which there are no elites; Equitable, in which there are elites but equal consumption rates; and Inequitable, in which the elites have different consumption rates. The first two societies suffer collapse, but generally only through resource depletion. The interesting situation is what the authors call “Type-L collapse,” wherein the population of commoners dies out, wealth stops being produced, and then the elite population collapses, even though natural resources have not been depleted. This is visible in Figure 6a of the paper, and leads to an interesting scenario in which natural resources recover but neither population does. This, the authors argue, is a replication of the Mayan collapse. The authors also point out that this collapse happens when the society is at the peak of its wealth and power, and the elites are still growing in size. There is a period of plateauing total wealth, in which the amount of wealth created and consumed are equal. The charts in the paper show net wealth, but of course from the perspective of the people within the society wealth would appear to be growing, since an increasing population of elites consuming wealth at 100x the rate of the commoners must mean that gross wealth (before consumption effects) is growing rapidly. So from within society it looks like a period of unparalleled success and wealth, but it is actually the beginning of the end.
I was struck by the thought that this may already be happening in some countries not through death but through emigration. Thinking of the state of emigration from Nepal and Mexico, for example, it seems that these are countries with high inequality and large population outflows – perhaps they are on the cusp of such a disaster. The obvious example is North Korea, where the elites are sucking the common population dry without any regard for restoring natural resources. Of course in a connected world it is difficult for a single nation to collapse, since they can trade their way out of disaster (though perhaps, over time, this trade forces them into poverty and acts as a natural brake on further exploitation of the natural world). The bigger example is the earth as a whole, but I don’t think that this is a realistic model for the earth as a whole. The only global environmental problem so serious that it could lead to a major extinction event is, in my opinion, global warming, and this is not a resource depletion problem, nor is it necessarily related to inequality. It’s perfectly possible to wipe ourselves out through global warming without much affecting the overall stock of natural resources at all. In fact, the conditions given in the paper for achieving equilibrium are being partially achieved, with the likelihood of population stabilizing at around 9 billion. The second condition – of reducing inequality below some threshold level – may also be achieved once the low-income nations are lifted out of poverty, which Bill Gates seems to think will happen in a generation. So I think this model is more apt for societies of bygone eras, when people were less connected and more vulnerable to resource depletion, due to having access to a smaller range of resources, and less knowledge with which to change technologies as their component resources exhausted, and when in additional to relative inequality, the absolute poverty of the commoners was so great as to make them fatally vulnerable to any sudden reduction in wealth. Although these models are obviously analogous to what could happen to the whole of earth, I think it’s difficult to claim that they apply given the huge range of possibilities for resource consumption and adaptation on the planet as a whole. Still, as cautionary tales they’re interesting, and I think it’s safe to say that we’re at a point in our ecological history where careful custodianship of natural resources will always be a good idea.
As an interesting aside, one of the blog posts connected with this discussion led me to a blog post criticizing the story of Easter Island as portrayed in Jared Diamond’s Collapse. In Diamond’s version of the Easter Island story – which was apparently the mainstream scientific view until just about 10 years ago – the Islanders brought on their own destruction through poor ecological management, but it seems that the opposite is true: they were good custodians of their land, despite deforestation brought on by rats they accidentally brought with them, and their population collapse was actually the fault of western visitors bringing disease. The soil erosion the island is famous for was the fault of 100 years of sheep-farming by Chilean colonists who also brutalized the local population. Jared Diamond responds to the criticisms on the same blog, but his response is frankly a little mean-spirited and unreasonable. This response is in turn met with a blistering critique by his two most trenchant critics, and although I know nothing about archaeology and anthropology, I was certainly impressed by the thoroughness of their response. The truth of this story is heartening on many levels: it indicates that humans can live sustainably with much less knowledge than we currently possess, in very fragile environments, without major conflict. This debate also shows how pernicious and far-reaching the early racist colonial interpretations of history and anthropology could be, with sensationalist and incorrect fables about the Easter Islanders still being carried through academia 100 years later. Anyone who has read Jared Diamond’s books knows that this particular debate – about the relationship between ecology and human social collapse – is not merely academic, with some recent events such as the massacres in Rwanda being slated home to ecological problems, and the obvious bigger environmental issue of how to live together on this earth without destroying it. It’s sad to see someone of Diamond’s calibre and reputation being misled by racist and colonialist stories from 100 years ago, and drawing wrong conclusions about our environmental vulnerabilities as a result.
Anyway, I was fascinated to see simple predator-prey models being used to model civilization collapse, and collapse due to inequality rather than resource depletion, at that. It’s also interesting to note that a lot of the major collapses in history seem to have been driven by inequality rather than simple resource depletion. And interesting that these models should spark debate just at a time when an influential new book is putting forward the idea that modern capitalism is structurally designed to increase inequality (here I am referring to Piketty of course). It doesn’t bode well for the future, does it? These models are fundamentally too simple and limited to describe the risks facing the planet as a whole (which I do not believe are first and foremost resource depletion issues), but the finding that collapse can happen without resource depletion in the presence of inequality is fascinating, and food for thought for those people who think that inequality is only a social justice issue. It’s for the species, Rico!