Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
Tom Lum Forest
52295 NW Hayward Road
Manning, Oregon 97125
USA
tforest@alum.mit.edu
Abstract
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. System Dynamicists with no prior knowledge of the
Maya are the intended audience.
Introduction
“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.
Problem Statement
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
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
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?
Literature Review
[This paper builds completely on W-PELG and the literature it used. For convenience,
its literature review is repeated here.] “The relevant System Dynamics literature on
civilization-level dynamics is thin. Classic Maya Collapse (Runge et al., 1976) is most
relevant. Based on The Classic Maya Collapse, (1973 University of New Mexico Press
ed. Culbert), it reflects the preeminence of the Peaceful Maya paradigm as championed
by Thompson (1966). Its premise is that the Maya elite were peaceful priest-kings who
responded to stress by building ever-more monumental structures, thus indirectly
lowering the productivity of the populace, who had to build more and farm less. In
response to environmental crisis brought on by over-exploitation, it created a death
spiral of falling yields causing less effort in farming, causing yields to fall faster. Homer's
Civilization as Enterprise (Homer 1978) and Sterman's Self-Organization,
Competition, and Success in the Dynamics of Scientific Revolutions (Sterman 1992) are
also related in topic. Homer’s formulations include resourced-based carrying capacity,
but consider military involvement as a productivity-enhancing factor without
consideration of warfare. Sterman’s formulations can be applied to cultural paradigms
and revolutions as well as scientific ones. But they are focused on “the sociological
dynamics of paradigms as they compete against one another for members... [and
examining] the role of intrinsic versus contextual factors in determining paradigm [sic]
success.” (Sterman 1992, op. cit., p. 1)
“Forest presented three related papers at previous International System Dynamics
Conferences: “Sustainable Civilization: Cohesion, Capacity, and External Contacts,”
Tokyo, 1995; “Byzantine, Bulgarian, and Ottoman: The Dynamics of Empire at the
August 8, 2013 Page 2 of 15
Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
Crossroads of Asia and Europe” Istanbul, 1997; and “The Perilous Frontier: East Asian
Cultural Ecology and Two Millennia of Chinese Dynastic Succession,” Quebec City,
1998. In all three, while internal resource constraints are included, the emphasis is on
dynamics between states. Those papers make use of the concept of social cohesion, and
are more general (and complicated) in their models, as they broadly address multiple
modes.
“[W-PELG introduced] a new mode: steady population growth and catastrophic
collapse, caused by a policy response to resource shortages. In Beyond the Limits
(Meadows et al., 1993) the authors say that Forrester’s World3 model (Forrester 1971)
lacks, among other things, war and so is wildly optimistic. [W-PELG was] intended to
simply and directly temper that optimism.
“The Runge paper, hereinafter referred to as Case Study, embodies several obsolete
concepts. It refers to slash and burn agriculture, which is the prevailing contemporary
practice. The Classic Maya, however, used more intensive methods to achieve higher
yields and population densities, including raised beds and terraced fields. Runge et al do
not include the Late Preclassic sites like Nakbe and Mirador, dating prior to 400 BC,
which are comparable in scale and quality to anything that followed. They also
overemphasize external trade and foreign contacts: while perhaps seminal at the
beginning of the Late Preclassic and Classic phases, the evidence for ongoing political
influence is negligible and trade with other citied cultures was light and only in
nonessential luxury goods.
“The starting point for the [W-PELG] model is Beyond the Limits, with population
growing exponentially until it approaches the carrying capacity—which the population is
simultaneously eroding. Population spikes, then declines exponentially in line with
available production. Maya Apocalypse has just two sectors: people and land.
Population is increased by births and decreased by deaths. Fertility is high enough to
cause exponential growth when production is adequate, and falls below replacement
levels as population exceeds carrying capacity, eventually falling all the way to zero.
Deaths are regulated through a normal lifetime, which in turn is affected by production
adequacy.
“The collapse of organized Mayan society has been extensively considered by
archaeologists but the models are linear, open-loop models. For instance, see Demarest
(2004, p. 258). [W-PELG] is unique in applying closed-loop modeling to post-1976
archaeological research.”
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
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
interestingly, food shortages increase warfare which then decreases available land and
intensifies food shortages.
+
———
Ce, pace: Normal Productivity
a o= Population fic Impact Per Person
/
Time Regenerate
a gers oo oraductty
ie : Ss
jane ~~ Deaths co
{ent | OO Productivity ps
Exhaustion Rayoneraing Nt
xe s
~m Productivity
Ea oF Shaina” Effect of Occupal
Predunton ern avatbie—\ gn Produetty mpact
on Fertiliny Desired. Lifetime Production
‘ ats —
Food 0 2 0 Efer a Pere Sw Mie decupaney__ Efect of Occupancy on
Per Persun \ we gf ee Desired Cand “opie Per
es aa a rs { tect of —
z cite on “
xf “vata Frecton of Lan ag
i Eb & Precision
Frod Requited
ed eat a wile a
Kuhul Ahaw
Mutepal Warfare %
Normal Food wage
Required Per Person
ye Available Abandonment
‘Warfare Land 2
GH < 4 ital Lod
Effect of Warfare on ibe for Warfare to
lecaseieMaya Rake
Cause Abandonment
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
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
of that phenomenon.
Petexbatun: Base
0 Dml
0 Dmil ii al malar
-400 -200 0 200 400 600 800 1000 1200 1400 1600
Time (Y ear)
People : Baseline people
Warfare : Baseline Dm
Effect of Climate on Available Production : Baseline Dmnl
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.
Petexbatun: Shift to Multepal at 800 AD
ooo
9
ES
-400 = -200 0 200 400 600 800 1000 1200 1400 1600
People : Baseline people
Warfare : Baseline Dmnl
Effect of Climate on Available Production : Baseline Dmnl
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
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.
Petexbatun: Decreasing Productivity of Add'l Land
r walreny iLtlalal
fee? il
-400 -200 0 200 400 600 800 1000 1200 1400 1600
Time (Y ear)
People : Baseline people
Warfare : Baseline Dmal
Effect of Climate on Available Production : Baseline Dmal
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.
August 8, 2013 Page 6 of 15
Maya Apocalypse: V arying Productivity, Consumption, Impacts, and Results
Petexbatun: Increasing Marginal Productivity Impact on Add'l Land
ooo
9
z
Dmal 1 r
-400 -200 0 200 400 600 800 1000 1200 1400 1600
Time (Year)
People : Baseline people
Warfare : Baseline Dmal
Effect of Climate on Available Production : Baseline Dmal
Combining the two effects reinforces both the peak lowering and cycle shortening.
Petexbatun: Lower Productivity and Higher Population Impact
80,000 people
1 Dml
2 Dm
40,000 people
0.5 Dmal
1 Dml
-400 -200 0 200 400 600 800 1000 1200 1400 1600
People : Baseline people
Warfare : Baseline Dmnl
Effect of Climate on Available Production : Baseline Dm
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.
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
Petexbatun: Step in Productivity at 300 AD
0 people
0 Dml
0 Dml
0.8 food/(Y ear*acre)
-400-200 0 200 ~~-400~«600.~=«800-~S=«i000'-—Ss*«=«S00'Ss”=«iK—SC«éi 00
Time (Y ear)
People : Baseline people
arfare ; Baseline Dml
Effect of Climate on Available Production : Baseline Dml
Productivity Per Acre : Baseline food/(Y ear* acre)
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.
Petexbatun: Step in Food Required at 500 AD
people
Dmal
2 Dml
2. food/(Y ear* Person)
0 people
0 Dml
0 Dml
0.5 food/(Y ear* Person)
-400 — -200 0 200 400 600 800 1000 1200 1400 1600
Time (Y ear)
People : Baseline people
Warfare : Baseline Dmnl
Effect of Climate on Available Production : Baseline Dmal
Food Required Per Person : Baseline food/(Y ear* Person)
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.
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
Petexbatun: Ramp in Productivity from 200 AD
200,000 people
2 Dm
2 Dm
food/(Y ear*acre)
-
people
Dmil
Dmal
food/(¥ ear*acre) i litte laua tc les]
-400 -200 0 200 400 600 800 1000 1200 1400 1600
Time (Y ear)
People : Baseline people
Warfare : Baseline Dm
Effect of Climate on Available Production : Baseline Dmal
Productivity Per Acre : Baseline food/(Y ear* acre)
ococoo
Validation and Verification
At this point it is necessary to delve into the archaeology and history of the Maya,
exploring the different types of data, and what can (and cannot) be gleaned from them.
Per Webster (2007, p. 294), several types of data inform this model: architectural;
epigraphic (monumental inscriptions); settlement (regional survey/demographics); and
paleo-environmental (e.g., pollen content in sediment cores).
The Maya typically dedicated their buildings, and in doing so, dated them. This is the
single most obvious data source throughout Mayan lands. Buildings can also
occasionally be carbon-dated. The clear variation in construction of monumental
buildings over time was the first piece of evidence to the outside world that the Classical
Maya civilization existed, and that it had come to an unequivocal and apparently abrupt
end. Most of the buildings visible now were built on top of earlier buildings of the same
site that were decommissioned. There was a Preclassic increase in construction from
about 600 BC in the Mirador Basin, in places like Nakbe and El Mirador. Those sites
were abandoned c. 150 AD. There was also Preclassic construction in places like Tikal,
some of which was abandoned and some of which was buried by later and larger
structures. There may be more pre-collapse buildings yet to be found, as comprehensive
excavations have not been done uniformly through the area, but the overall pattern is
clear. Construction crescendoed until the late eighth century, and then collapsed
precipitously.
The earliest Mayan monumental inscriptions yet found date to 36 BC; the last are from
910 AD. Before the Spanish arrived there were numerous written records on bark, but
most were destroyed: only four books have survived. They and the monuments
(primarily stelae) describe warfare, coronations, births, and period endings (analogous
to New Year’s, End of Decade, and End of Century observances, but in the Mayan base-
20 calendar). No population data is in them, but like construction the surviving
monuments themselves rise steadily in numbers from the third century to the seventh
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
century, and then drop off precipitously in the next century (Webster 2007, p. 209).
This curve represents an aggregate from all areas of the Mayan world, with the caveats
that preservation is not as good in northern areas, and exploration has been uneven.
Since the inscriptions are so large and difficult to move, they are the most uniformly
studied inscriptions throughout the Mayan lands, wherever found.
Mayan archaeology is done on a site-by site basis. While all sites with large
concentrations of buildings and inscriptions have had their inscriptions studied, the
other types of data have been more unevenly sought or available. Some sites, like Tikal,
have nearby lake whose sediments can be retrieved and analyzed for tree ring-like
layers, within which the concentrations of various pollen and chemicals are indicative of
environmental changes in its drainage basin (Webster 2007, p. 256). Phosphorus
loading, vegetation, soil erosion, and several other proxies for environmental changes
and stress can be divined from sediments. The pattern in Tikal seems to be of monotonic
exponential growth, starting in the Preclassic, to a peak in the Late Classic then a more
precipitous logarithmic decline.
Finally, at some sites comprehensive cross-sectional surveys have been done of
residential structures. Again at Tikal, “the 16 sq. km zone immediately around Tikal’s
monumental precincts has been extensively mapped, as have sites in survey arms
extending radially out in the cardinal directions.” (Webster 2007, p. 263). From these
surveys population densities can be calculated and applied to the entire area, revealing
substantial populations that fluctuated considerably over time.
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
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
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.
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
Conclusion
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 living 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.
It is heartening that a major civilization made a major paradigm shift, downsized, and
got out of the epic boom/bust cycle. It can be done, though they went through a lot of
pain before doing so. I was reminded of a Star Trek episode, “A Taste of Armageddon,”
where they did much like the Maya — they had war casualties even though the
nations/planets involved were not at war as we understand it. There are of course other
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Maya Apocalypse: Varying Productivity, Consumption, Impacts, and Results
ways to get to the same result — zero consumption growth from a sustainable level with
reserves, most saliently — which seem far less likely to me than chronic war or a nuclear
apocalypse. But the future is not yet written. There is always hope. Our challenge is to
heed Ben Franklin: "We must indeed all hang together, or most assuredly we shall all
hang separately."
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