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Malthus was one of the first one who raised the concern about overpopulation and it is today seen as a potential threat to humanity.

Are there any historical examples where overpopulation led to resource exhaustion and a major city or civilization collapse?

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    There's tons of examples; the Garamantes for instance. Basically every famine is an example of overpopulation to some degree, even if they don't lead to total collapse. – Semaphore May 26 '18 at 11:41
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    This is more resources that suddenly became scarce than overpopulation? Isn't it? – AsTeR May 26 '18 at 12:56
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    That's part of the point. If the population were lower, a bad harvest wouldn't result in famine. One of the reasons theorised for the frequency of late Medieval famines was that Europe was already overpopulated, and thus constantly teetering on the brink of starvation. – Semaphore May 26 '18 at 13:10
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    You may be interested in Collapse by Jared Diamond. – Schwern May 26 '18 at 17:37
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    @Semaphore Equally, you can define famine as an politico-economic problem underproduction, poor planning or distribution. Overpopulation is an issue only when it is not possible to provide the resources to sustain it rather than episodes poor governance. – James Jun 1 '18 at 11:01
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Because people are quibbling in comments over the meaning of "overpopulation", it might suggest that this question is broad or unclear. So let's look at it from a different angle.

In the 1960's, Dr. John Calhoun, working at NIH, conducted his famous (some would say infamous) "mouse utopia experiment".

Mice were placed in an enclosure (named "Universe 25") where they were provided with an unlimited supply of food and water. The only constraint was the size of enclosure.

For a while, the mouse population exploded, as one might expect. After a while the population leveled off, and in the crowded conditions, several peculiar patterns of behavior emerged. For example, there were gangs of unattached male mice who would get into violent fights with , and individuals that Calhoun dubbed "the beautiful ones" who would do nothing but eat, groom, and sleep.

Eventually, all of the mice just went about their business, ignoring each other as if they were on their phones all the time, and the population plummeted. In fact, none of the mice survived despite having unlimited resources. The devolution of the mice's social behavior (called a "behavioral sink" by Calhoun), and only that, led to their extinction.

Other researchers produced similar results using rats. It isn't clear how well this experiment applies to human behavior, and Calhoun's methodology has been criticized, but it is a good example of the effects of overcrowding that we should think about.

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Easter Island is one example. From the Wikipedia article:

It is believed that Easter Island's Polynesian inhabitants arrived on Easter Island sometime between 700 and 1100 CE. They created a thriving and industrious culture as evidenced by the island's numerous enormous stone moai and other artifacts. However, human activity, the introduction of the Polynesian rat and overpopulation led to gradual deforestation and extinction of many important natural resources, which severely weakened the Rapa Nui civilization. By the time of European arrival in 1722, the island's population had dropped to 2,000–3,000 from an estimated high of approximately 15,000 just a century earlier.

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    I think there is a good debate whether Easter island ever had a population in the 15,000s. I have read that number was arrived at by early explorers guestimating how many people they thought it would take to create and move the moai statues, whereas in reality there were ever only around 3k people on the island. – ed.hank May 27 '18 at 12:55
  • Unabashed self-aggrandizement follows: Were the Rapa Nui starving? – CGCampbell Jun 1 '18 at 14:11
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As noted in the discussion on the question, there are two kinds of overpopulation which I'll call "chronic" and "acute". Chronic overpopulation, where the full production capacity of agriculture in normal times is insufficient to feed the population, is sometimes the only case people consider. But acute overpopulation, where the population "only" starves in times of famine, is also over population, because famines caused by things like droughts or blights (or war or plagues of locusts) are an inescapable part of the landscape.

It seems to me that the fact of acute overpopulation makes chronic overpopulation rare -- before you get so many people that you strain food production in good times, you get a famine when times turn bad.

Given that, pretty much any major famine (one big enough to kill a significant number of people) is evidence of overpopulation. (The exception is man-made famines, e.g., the ones caused by Stalin in the 30s and Mao in the 50s.)

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Maybe not

Joseph Tainter argues, in Archeology of Overshoot and Collapse, that so far there is no evidence of a Malthusian catastrophy. wetheryou follow Tainter in this assertion will in part depend on how wide or narrow your definition of overpopulation is.

Problem with definition

According to Malthus, population grows exponentially while food production grows linearily, until the first outstrips the latter. This definition of overpoulation is IMO overly narrow, as any case where food production drops would be excluded. As we see, in numerous cases food production would rise for a while and then collapse through environmental degradation or other causes. This overshoot theory is applied in the case studies below.

Case studies

Tainter adresses several cases commonly cited as overshoot, I'll cite only conclusions regarding the examples from Jared Diamonds Collapse:

Henderson and Pitcairn Islands:

Pitcairn and Henderson is- lands, for example, are small, remote, and lacking critical resources. They could not be occupied for long without obtaining resources from elsewhere. The failure of attempts to oc- cupy them (which I do not consider collapses) is attributed by Diamond as much to prob- lems plaguing trade partners on Mangareva as to anything done by the occupants of Pitcairn and Henderson islands (pp. 120–35). For comparison, if the resupply of the Inter- national Space Station were to fail, future his- torians would not wonder at the fate of the astronauts, nor draw broader inferences.

Norse Greenland:

Norse Greenland is not an enduring les- son for the same reason: Local resources could not indefinitely support a medieval European society. [...] the dilemma is not that the Green- land Norse went extinct or left, but that they need not have done either. The continued oc- cupation of the area by the Inuit shows that alternative subsistence strategies and ways of life would have allowed the Norse to sur- vive in Greenland.

This also points to a problem with definig overpopulation: The "carrying capacity" will always depend on agricultural and other technologies used, consumption patters etc.

Chaco Canyon, Anasazi & southwestern Native Americans, Maya:

Diamond would have liked to have shown that Chaco Canyon, the Anasazi and other Southwesterners, and the Maya overshot the capacity of their environments, degraded them, and collapsed. In each case, though, he was confronted with the potential roles of climate and other factors. These were not Malthusian overshoots. In Diamond’s formu- lation, these cases may illustrate overshoot in reference to extreme climatic conditions. If the extreme conditions had not occurred, the societies in question might not have collapsed

Easter Island:
The case of easter island, deforestation is often seen as the primary cause of collapse:

Several authors see the deforestation as the start of a cascading process that led to a decline in fishing and farming; changes in farming technology; increases in warfare and insecu- rity; changes in settlement patterns; popula- tion decline; and sociopolitical collapse. For- est depletion, in this view, led to a shortage of wood for canoe construction, and thus to a decline in the consumption of fish (espe- cially deep, pelagic fish) and marine mam- mals.

However, Tainter doubts the deforestation neccesarily has these consequences:

Even if lack of wood meant a decline in the availability of sea mammals and large fish, the entire population would not have been equally affected. As is common in Polynesia, the high-ranking Miru clan controlled fishing in deeper, offshore waters. [...] If de- forestation did lead to a decline in the catch of larger fish and marine mammals, a large part of the population was only minimally affected.

A decline in agriculture would have been more serious than the loss of marine delica- cies. Easter Island undoubtedly experienced erosion. It is a common mistake, though, to assume that erosion is always detrimental. Ancient Egypt and Mesopotamia were sus- tained by upstream erosion, as other places have been. No research has shown that ero- sion adversely affected Easter Island agricul- ture. Removing forest cover would have ex- posed soils to drying and challenged young plantings. The islanders responded by dig- ging pits, erecting small windbreaks, and em- ploying lithic mulch. Problems of soil fertility could have been addressed by shifting cultiva- tion and/or by use of night soil.

Nearly the entire surface of Easter Island is arable, yet in recent centuries only the coast and the interior of Rano Kau crater were intensively cultivated. The factor limiting agri- culture may have been water, rather than erosion, wind, or soil fertility. If agricultural productivity declined with deforestation, this could have been com- pensated for by increasing the area under intensive cultivation. [...] When people face agricultural prob- lems, a common response is to intensify pro- duction. This is what the Easter Islanders did

Tainter draws the conclusion that we cannot show that the Polynesians overextended the "carrying capacity" of their islands, and thus cannot prove that the Easter Islands are a case of ecological overshoot.

Conclusion
You can always argue that every case where another immediate cause (draught, war ...) can be identified as the culprit for the collapse of a society, this immediate cuplrit was the way Malthus harsh law manifests itself. This is not entirely wrong - there are hard thermodynamic limits on how much life (as activity, not biomass) earth can support - but in my eyes not really useful. The more useful question would be - and this is where I find Tainter more convincing than in his many quibbles with Diamond and Chew - how a society handles ressources & consumption. Diamond (in Collapse) gives a, in my eyes, instructive example from the ultimately doomed Henderson & Pitcairn islands: Archeological evidence seems to show that the islanders imported pigs, until apparently all pigs where culled - it appears they saw that raising pigs yields less food than eating the pig fodder themselves, and adpoted accordingly. So the question is would be, what adaptions are possible today?

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