The Maya are a cautionary example for all of us, a prophecy not by words but by deeds. A formal follow-up to a paper I wrote in 2007 and a non-technical version of which I published here, I'll be delivering this paper at the International System Dynamics Conference in Boston this July.
This paper explores the dynamics of population levels in Maya lowlands from the Late Preclassic to Post Classic, roughly 400 BC–1600 AD. Building on the 2007 ISDC paper “Maya Apocalypse: Warfare-Punctuated Equilibrium at the Limit of Growth,” this paper considers the effect of changing productivity, per capita consumption, and per capita environmental impact from constants to variables. It also considers the effect of political paradigm shifts.
“Maya Apocalypse: Warfare-Punctuated Equilibrium at the Limit of Growth” (W-PELG) described a logarithmic growth/slow exponential decay “Limits to Growth” mode as well as a novel logarithmic growth/fast exponential collapse “Punctuated Equilibrium” mode. The fast exponential collapse mode was triggered by climatic variation and powered by warfare. It assumed that normal food/acre/year productivity was a constant, and that the only relevant modifiers were constant per-person degradation; a constant fractional regeneration rate; and random climate variability. Adding an analysis of variable productivity/acre, whether through technology or preferential land usage, would provide additional insight, as would a variable per-person degradation impact.
W-PELG also assumes a constant per-capita desired level of production. If the socio-political structure of society changes, such that actionable levels of consumption change, that too could provide additional dynamics.
The political organization of the Maya changed fundamentally at the end of the Classic period c. 900 AD, which had effects on the population dynamics that are not reflected in W-PELG. All of these missing factors are considered in the current paper.
It has been clear since the 19th Century that the Classic Maya civilization, with its monumental architecture, Long Count calendar, hieroglyphics, and divine kings, had flourished and declined long before Europeans arrived. What was not clear was how, when, or why. W-PELG explored the literature and formulated a model to fit the broad patterns of sustained growth to a plateau; growth followed by a slow exponential decay; and growth followed by an abrupt cataclysmic collapse. It concluded that growth to a limit combined with stress-response warfare and fluctuating climate were sufficient to cause the observed patterns. But W-PELG made some simplifications that, while perhaps acceptable for Preclassic and Classic Maya, were not tested. They may fail for post-Classic Maya, and thereby make transferability to non-Maya contexts problematic.
Preclassic Maya seem to have relied on slash and burn agriculture, which was not sustainable for long periods of time. The Classic Maya adopted more sustainable forms of agriculture, particularly using flooded bottomlands or bajos for their agriculture. W-PELG assumes a constant technology for agriculture, as well as a constant degradation/person, without change in the baseline productivity of land or labor. What effect would steady or discontinuous changes in productivity and impact have had?
Demarest (2007) discusses the growth of the minor nobility in the Late Classic and notes their higher consumption levels. Did consumption/person standards go up, increasing the pressures on carrying capacity? W-PELG assumes a constant desired consumption/person. What would an increase have meant in either or both, especially as growth slowed in the Late Preclassic?
The most serious limitation of W-PELG is that it does not well describe the Postclassic population dynamics of lower population levels and lack of catastrophic collapses. The political system became less centralized, and warfare more common yet less intense, so that there was a smaller prosperity ‘peace dividend’ but the extreme episodic lows were also mitigated. What effect would changing the levels of military response mean, across the full range of population levels, in either continuous or stepwise manners?
Model Description and Simulation Results
A brief synopsis of the W-PELG model is that it has four levels: population; productivity; and farmed and abandoned land. The last two are dependent on each other, as they add to equal constant total land. Two positive and two negative feedback loops dominate the behavior. Population tends to increase itself, provided more food is available. Land availability provides a negative loop to limit population growth through food sufficiency. Population has a negative impact on itself through productivity degradation. Most interestingly, food shortages increase warfare which then decreases available land and intensifies food shortages.
This is the basic punctuated equilibrium mode generated by W-PELG. It matches the Preclassic and Classic boom/bust episodes, but fails to describe the Postclassic absence of that phenomenon.
The first modification: shift away from divine kings to councils at the end of the Classic period, c. 800 in Petexbatun. More specifically, warfare became endemic at low stress levels, thus having an inoculative effect on the boom/bust cycle. To accomplish this in the model, the table lookup relating resource stress to warfare was changed from a straight proportional response by adding a small positive bias at low levels of stress, and nonzero war in the complete absence of resource stress.
Accounting for a decreasing return to farming additional land – by an average of 20% when all available land is used – lowers the peak population and shortens the boom/bust cycle in the Preclassic and Classic periods. This is done via an Effect of Occupancy on Productivity Per Acre which depends on how big the desired fraction of potential land usage is.
Similarly, to account for increasingly negative productivity impacts as more fragile land is used, an Effect of Occupancy on Productivity Impact is added. It also depends on how big the desired fraction of potential land usage is, and lowers the peak population and shortens the boom/bust cycle in the Preclassic and Classic periods.
Combining the two effects reinforces both the peak lowering and cycle shortening.
If a 10% step increase in productivity is added at 300 AD, in the early Classic -- representing a uniform technical advance, or the introduction of a new, more productive crop -- the Classic peak is higher but the collapse is hastened.
And there is if a 10% increase in food demand at 400 AD – in response to an increase in the proportion of minor nobility in the population as growth slows – the Classic peak is lowered and the collapse hastened.
Finally, if productivity somehow ramped up by 0.1%/year at 200AD immediately after the Preclassic collapse, growth can be sustained indefinitely, regardless of divine kingship or council rulership.
Analysis, Inferences and Implications
This paper has expanded on the M-PELG model to explore variability in land productivity and environmental impacts; political paradigm shifts; step improvements in productivity and food requirements; and ramped improvements in productivity. Most of these changes only affected the system’s behavior quantitatively – changing the gain of the feedback loops or the frequency of oscillation. Heterogeneous treatment of the land and its productivity change the timing and height of demographic peaks and valleys, but leave the punctuated equilibria of boom and bust behavior unchanged. Similarly, unique improvements in productivity exacerbate the cyclical responses by quickening and magnifying them.
Only two changes produce dynamically interesting behavioral modifications. One is the shift from divine kings to councillorships – from an individual god-king executive to a group of nobles. That change is embodied here by a variation in the nonlinear relationship between scarcity and warfare. Under the divine kings, war seems to have been a largely ceremonial undertaking, to establish dominance hierarchies and provide a few token human sacrifices. But at the Terminal Classic, warfare escalated and never really seems to have stopped. Substantial no-man’s-lands were created where it was unsafe to farm. Paradoxically, it created reserves of unused land -- often the most damaged and least productive, giving them time to recover their productivity. It also created a persistent buffer that could be used if there was a climatic fluctuation that reduced productivity. Whereas in Classic times drought meant that all usable land was taken and the starving had to rob each other, in Postclassic times there was always some land available.
The Preclassic and Classic Maya did not change their material way of life much. For over a thousand years, they ate the same crops, hunted the same animals, and used the same tools for all their daily activities. They had no beasts of burden, no transportation but by foot or canoe. The one innovation they seem to have made was between the Preclassic and Classic periods, when they began using flooded fields to grow crops more productively and maintainably. Yet had their productivity per acre somehow continuously increased, they could have gotten out of their food-based boom and bust cycles. But that was not to be.
It would be possible, perhaps even desirable, to have war casualties represented in the model. But pre-modern wars, wars before firearms, were much less deadly than what we experience, and throughout the world’s history far more people have died in famines than in wars. Adding warfare to this model would almost certainly have no effect on the qualitative model behavior, just amplify the peaks and accelerate the advent of collapses.
Mentioned in W-PELG also but done neither there nor in this paper, a spatial disaggregation would be interesting – permitting immigration, emigration, invasion and expansion to other areas. Overall population in the Highlands and Southern Lowlands seems to have permanently dropped after the Classic, while population along the coast was steadier and in the Yucatan actually increased. But even in those places, the days of the divine kings were over. The Long Count calendar was abandoned, as was the hieroglyphic writing. Warfare became endemic. So the paradigmatic shift in governance spread north, whether through conduction or convection – through migration or trade. It spared the Postclassic Maya any further major collapses, but limited the peaks of their growth.
The most interesting finding in M-PELG was that environmental degradation is not needed at all to simulate the reference mode: climatic variation can trigger apocalyptic warfare all by itself. This paper builds on that finding by examining some previously omitted factors. The Maya themselves continue to exist to this day, speaking their languages and much of the lifestyle that their ancestors lived a millennium ago and longer. But their politics were transformed at the end of the Classic period, by their own choice, and they have never gone back. That an advanced society should adapt to its present through a substantial, persistent simplification of their political and social culture is fascinating, and is a primary motivator for this paper. It may also be a harbinger of what is in store for all of humanity.
To adapt this model to fit 21st Century Earth wouldn’t take much: indeed, it well describes where we are. One could disaggregate the landed economy into consumption and investment; disaggregate productivity into capital and labor sectors; and disaggregate the population into several classes, cohorts, and locations. The model could be articulated spatially, allowing trade, innovation, and people to flow from one place to another. But that would be unnecessary complexity to understand our global punctuated equilibrium: Earth is the only planet we have.
As dire a problem as global warming is, as epochal as the changes it has brought and will continue to bring for millennia to come even if we cease our carbon dioxide emissions right now, it will only decrease the height of the next peak and the increase the proximity of the next collapse. A mere 100 nuclear weapons detonated by anyone who has them now – China, Russia, America, Israel, India, Pakistan – would plunge us into a nuclear winter. “The combination of nuclear proliferation, political instability and urban demographics may constitute one of the greatest dangers to the stability of society since the dawn of humans. Only abolition of nuclear weapons will prevent a potential nightmare.” (Robock & Toon, 2009). Regardless of how coarsely or finely measured, our collective ability to care for all seven billion plus people on Earth would be fatally compromised in a Nuclear Winter.
The Postclassic Maya inadvertently created reserves for themselves through continuous low-level warfare. That will not work for us. We do not create reserves. We have created social, economic, and political institutions that sacrifice the future for the present at too many turns. We are also a violent species, and when our time comes we will not be as fortunate as the Classic Maya. Our next nuclear war will be our Terminal period. Humanity will surely survive – killing every last human would be hard, even for us – but Classic and Postclassic Maya will seem identical when we are compared to our Postmodern selves.
Simulations done with Vensim