Why were there no agricultural, city-state forming civilizations in the Ice Age?

As far as I understand it from David Christian's 'Maps of Time', civilization is a direct function of population density.

When groupings of people in any given geographic area can no longer support themselves via hunting/gathering, they need to intensify their ability to extract resources from the region, which results in agriculture, which results in a more sedentary lifestyle, which results in food surpluses, which results in civilization.

So the answer to your question is likely something like: there were no populations dense enough yet to necessitate the need for robust agriculture, which would form a complex social structure, which we deem as civilization

Tying it in with the ice age is something that I'm not as clear about. I wonder, though, if the diminishing of the ice age produced conditions where people could more easily thrive and see population growth, which led to the various agricultural revolutions you mention.

The root of towns (and later cities) is specialization. The town houses the people whose "job" requires there be only 1 of them per few hundred other people. Think of a tool-maker, or clothes-maker, or indeed a priest.

Maslow's pyramid of needs teaches us that before a person can grow professionally, they must be able to supply their basic needs, first physically, then emotionally.

Specialization could not have happened without an abundance of food. Until the hunter/gatherer/farmer produces enough food for their family with enough left to give/sell to others, everyone has to be a hunter/gatherer/farmer, otherwise they will go hungry.

Once food is abundant enough, there starts to be enough "leisure" time for people to innovate and specialize. Only then will towns spring up. It seems simple enough to correlate the end of an ice-age to the availability of food, and to the ease of acquiring it.

Note: I asked a similar question about cradles of civilization. Let's go backwards in time from then.

By around 5.5ka (3500BCE), we have several independent examples of fairly sophisticated cultures with cities, agriculture, food storage, writing, and politics. How did this come about? These technologies developed gradually, over thousands of years, from earlier, less sophisticated antecedents. Technological progress is driven by need (pressure from food shortages, climate change, competition, etc), is convergent (different populations solve similar problems in different ways), and is haphazard (like evolution, it is not steady or goal-oriented). But, once certain pre-conditions were in place, technological progress was somewhat "inevitable" given sufficient time and chance.

The pre-conditions for the urban revolution were presumably in place before 11-10ka, when Beringia disappeared, and the Americas became isolated from the rest of the world. These included basic construction, early plant breeding and animal domestication, social organization, and commerce. Armed with these traditions, human populations were primed to take the next steps towards civilization at a gradual pace, even after being physically separated from one another. Many of the pressures faced by independent populations were the same (climate change was global, eventual food shortages are inevitable, competition is endemic, etc) - sooner or later, all populations face them, and either develop a solution or abandon civilization.

This pre-condition period, known as the Neolithic revolution started around 12.5ka:

The relationship of the above-mentioned Neolithic characteristics to the onset of agriculture, their sequence of emergence, and empirical relation to each other at various Neolithic sites remains the subject of academic debate, and varies from place to place, rather than being the outcome of universal laws of social evolution.

There are quite a few theories for the advent of the Neolithic revolution. However, one thing that is fairly well accepted, is that this period of technological progress was preceded by sedentism:

... most researchers now believe that sedentism was a prerequisite for the first agriculture to occur.

That is, as @PhillS correctly noted, humans began settling down permanently before agriculture, around 14.5 ka, and it is this change that led to farming - presumably because sedentism afforded the opportunity for farming, and because sedentism eventually led to the necessity to farm - whether because of climate change, or over-population, or some other reason.

So the next question is, what led to sedentism, and how come it didn't happen sooner? Permanent settlements were preceded by semi-sedentary sites (inhabited seasonally):

The first sedentary sites were pre-agricultural, and they appeared during the Upper Paleolithic in Moravia and on the East European Plain between c. 25000-17000 BC.

The transition from semi-sedentary to fully-sedentary lifestyles without agriculture presumably depends on local naturally occurring resources. Climate change therefore, is a likely suspect, and indeed, this period is marked by a gradual warming, prior to which it is less likely that sedentary life would have been very practical. Yes, other regions may have experienced high temperatures previously, but there is a reason for the name "Fertile Crescent", as it had far more cultivatable plants - especially grains - and domesticatable animals than anywhere else in the world. This was a unique place and time in the world with sufficient resources to support a significant permanent human population. Tropical regions do not have such a high carrying capacity, and do not readily enable the development of farming.

I find the coincidence of the cradles of civilization much more interesting. The rise of semi-permanent and permanent settlements is less interesting because the human population was still largely connected then, and there would have been enough trade and cultural exchange over such a long period of time that even a rare technological innovation could spread across the world. Following the emergence of behavioural modernity, the paleolithic is marked by an increasing rate of technological innovation, that included pottery (16ka), dwellings (15ka), and domestication (15ka), all technologies that gained widespread use. This layed the foundation for a kind of "perfect storm" just waiting for the climate to change to make permanent settlements practical, eventually leading to everything that happened next.

Much of this is summarized in a very nice video series here: https://www.youtube.com/watch?v=nTgIPVi1yPs

Blame the weather.

Larger version

The reason it took so long for agriculture to develop can be summed up in this chart which shows variation in global temperature against time. The analysis in the academic paper from which this chart is taken, isn't terribly insightful. But, the chart really says it all.

In a nutshell, temperatures fluctuated wildly (as much as four degrees) pretty much all of the time from the beginning of the Upper Paleolithic era (40,000 years ago on the chart) to the beginning of the Holocene era (10,000 year ago).

This was particularly difficult (even in places where the entire human populations wasn't wiped out by glaciers or frigid temperatures that hunter-gatherers didn't have the technology to survive in) around the time of the Last Glacial Maximum (ca. 20000 years ago) when DNA studies of modern populations have been able to reveal that every community on Earth experienced population bottlenecks, which were particularly deep outside of Africa.

Europe's population was confined to three small refugia that were barely liveable; Northern Asia was completely depopulated outside of Berginia and perhaps a small enclave in the Altai Mountains. Places further South weren't completely uninhabitable, but everyone living there had to make profound lifestyle changes in order to adapt enough to survive.

Needless to say, it was also impossible to form any civilization, agricultural or otherwise, city-state forming or otherwise, in places where glaciers that were miles thick covered the better part of a continent, which was true for most of northern North America, most of Europe, and most of Northern Asia.

Four degrees may not seem like all that much, but even 1.25 degrees is a wild enough fluctuation to cause agricultural civilizations to collapse over areas thousands of miles across. This happened ca. 2200 BCE (which ended the Akkadian Empire, the reigning dynasty in Egypt, and Harappan Civilization, while fueling Indo-European expansion in multiple directions) and 1200 BCE (a.k.a. Bronze Age Collapse) for example. Smaller climate shocks, for example in the 400s CE and in the Little Ice Age, were still enough to push whole kingdoms towards falling (the Western Roman Empire in the 400s, and the Mississippian culture of the Americas in the Little Ice Age) and to make major long term changes in how society was organized.

From a climate perspective, there were 30,000 continuous years of apocalyptic fluctuations in global temperature.

With temperatures going up and down so rapidly, plants that would have thrived somewhere as a child and you had one average temperature could change so rapidly that by the time you were middle aged or a grandparent, you might not be able to grow that very same plant in the same place.

It takes hundreds of years a fine tuning a plant to a particular set of target conditions through selective breeding to domesticate a plant, and to the extent that this is a moving target it just cannot be done.

It also means that the geographic range of animals that you might conceivably hope to domesticate also moves many hundreds of miles up or down in latitude every generation, again, confounding the domestication process for pretty much anything other than dogs.

Once global temperatures stabilized in the Holocene era, agriculture immediately emerged independently in half a dozen places across the global over the course of the next 2000 years or so.

You also need domesticated plants and animals to have cities. For example, when agriculture reached Egypt, the population density increased by a factor of 100. So, you basically can't have a city-state forming civilization in a society based upon hunting and gathering.

The only real exception to this is that small villages did spring up in areas were there were stable sedentary communities that relied on rich fishing resources in a few places like Japan and the Southern Chinese coast where pottery first arose ca. 16000 years ago.

UPDATE (September 22, 2020):

One more thing I missed back then: Some evidence of earlier attempts at cultivation of "proto-weeds" during the ice age has been found. see Snir et al. (2015) on the 23000 year old Ohalo II site near the Sea of Gallilee. This would suggest that before climate stabilized after the end of the Ice Age, some hunter-gatherer communities were in a much better position to embark on an agricultural revolution and form city-states etc. than other groups ever before.

Another fine point made in the economics literature on the Neolithic Revolution (which is the name that Western anthropologists used for the adoption of food production technologies involving domestic plants and animals, and former Soviet and Eastern anthropologists use for the adoption of pottery) relevant to the update to the question, is that the Neolithic Revolution was a heterogeneous process.

Communities and individuals in optimal conditions for a terrestrial hunting and gathering society, like the African Savanah were modern humans probably evolved, tended to experience a Neolithic Revolution later.

Communities and individuals in optimal conditions (e.g. good soils, good weather, and wild type plants and animals well suited to domestication present) tended to experience the Neolithic Revolution sooner. For example, the Neolithic Revolution spread swiftly to the basins of the Nile River, the Indus River (in South Asia), and the Danube River (in Europe), but came much more slowly to Siberia and the Baltic region.

Early adopters of sedentary food production consumed fewer calories per capita than average, successful nomadic terrestrial hunter-gatherers, but more than their families, who for various reasons may have been below average at nomadic terrestrial hunting and gathering could have obtained in that fashion. Eventually, as the package of technologies associated with a particular instance of the Neolithic Revolution was improved upon and refined, however, the proportion of people and the range of geographic locations in which farming and herding led to greater selective fitness than hunting and gathering increased until only a few relict populations in places utterly unsuited for farming and herding remained.

Sites like Ohalo II reflect the heterogenous nature of this process (and, of course, Ohalo II didn't manage to persist continuously into the Holocene era because ultimately, the fickle climate and the lack of critical mass to make real advances in the domestication of plants and animals wasn't sufficient to do so). The two little bumps in the bar chart portion of the chart above (as opposed to the line charge portion showing temperature variability) reflect a couple instances of false starts, with one of them located approximately where Ohalo II belongs in the timeline.

(Most of what I'm writing is a summary of "After the Ice: A global human history 20,000-5,000 BC" by Steven Mithen - published 2003 so it's pretty up to date as an overview of what is known).

It is indeed tied to the end of the last ice age. All the sites known from the ice age and immediately afterwards are temporary hunter gatherer camps.

In the middle east, when the ice age ends (15-13,000 years ago), temperatures rise and the availability of food increases greatly. Temporary hunter gatherer camps give way to permanent settlements pretty quickly. Although it is important to note that these are not actually doing agriculture - they are still hunter gatherers, but able to be sedentary now because the abundance of food is sufficient to feed a community without it having to range over a large area following prey. Communities in the fertile crescent area at this time are largely located on the boundaries of forests and plains to give access to the greatest diversity of food. Note that there are no domesticated crops at this point.

The along comes the younger dryas period, 13,000 years ago and lasting for around 1000 years. This is a return to ice-age conditions in europe and the near east, and those permanent settlements disappear as people revert to nomadic hunter gatherer lifestyles.

When the younger Dryas ends and warm temperatures return, food availability shoots up again, and permanent settlements re-appear. But now they have agriculture, because now there are domesticated cereal crops in the near east, and are situated on agricultural land rather than the edges of forests. "After the Ice" has some discussion of the role of the younger Dryas in the domestication of cereal crops - that the knowledge of plant tending was gained during the previous warm period and was maintained to keep seed stocks while traveling during the younger Dryas to sow wild gardens - and the selection pressures there created domesticated varieties that could be exploited fully once the warm climate returned (the argument in the books is more involved than this, and it is all rather speculative as far as I know)

And bang, you have the rise of the first villages and towns supported by agriculture, very broadly speaking.

Other parts of the world had fewer domesticatable plant and animal species, and also the younger Dryas was (I believe) not a global event, so if it did indeed accelerate the domestication of eurasian cereal crops, then it gave the area an additional head start over the rest of the world. But the end of the ice age did indeed leed to permanent settlements and varieties of agriculture in unconnected communities across the world: there is no doubt that the availability of food went up enormously in the 15-10,000 years ago period.