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I asked a similar question a small while ago. Unfortunately, the way the problem was defined excluded certain viable solutions. So I want to try again.

The society would have to be complex. Perhaps a megacity like singapore.

It would have to use reliable alternative energy like nuclear fission and geothermal.

Top soil would be depleted and mining phosphorous or extracting it from human waste would not be viable on a large scale.

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    $\begingroup$ The post-apocalypse tag and megacity don't really fit in the same place $\endgroup$
    – Separatrix
    Dec 15 '16 at 15:19
  • $\begingroup$ After a global collapse there could still be protected megacities ruled by those who anticipated it. Watched Ergo Proxy? $\endgroup$
    – Ama
    Dec 15 '16 at 17:16
  • $\begingroup$ Megacities are the peak of the infrastructure pyramid, the concept of the apocalypse is very much tied to the collapse of that pyramid. $\endgroup$
    – Separatrix
    Dec 15 '16 at 17:21
  • $\begingroup$ What about a late post-apocalypse, where the initial "shit hits the fan" stage is over and opportunistic security firms have decided to rule over whoever is left behind by taking control of local access to food, water and electricity? $\endgroup$
    – Ama
    Dec 15 '16 at 17:51
  • $\begingroup$ What you're probably looking for is pre-apocalypse dystopia. Everything is either broken or at breaking point but it hasn't yet collapsed. Autocrats, oligarchs etc are taking control either to protect their own position or to hold the last of the system together but you're not yet in a state of Soylent Green. $\endgroup$
    – Separatrix
    Dec 15 '16 at 18:05
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The same way we did from the 17th Century up until artificial fertilisers: The four field system.

http://www.saburchill.com/history/chapters/IR/003f.html

The innovations in this four year rotation system were turnips and clover...

Clover is a plant which is able to add nitrogen compounds to the soil because its roots have special structures, called root nodules, attached to them. Inside these nodules are found symbiotic bacteria which feed by fixing atmospheric nitrogen and producing nitrates (nitrogen-containing salts). The clover, which is more nutritious than grass, was used for grazing the livestock. In turn, the livestock produced manure which could be ploughed back into the soil.

To give you an idea of increased yield:

In 1705, England exported 11,5 million quarters of wheat. By 1765, wheat export had risen to 95 million quarters. The second effect was that livestock, which no longer needed to be slaughtered before the winter months, increased in both quantity and quality.

The bulk of increased yield since then was more due to improved varieties than fertilisers, but use of the fertilisers means that we can keep running the same cash crops in the same fields year after years rather than having to run any sort of land management and rotation.

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  • $\begingroup$ While on the one hand I think that rotation and mixed agriculture need to come back for a healthy Earth, on the other hand, I can't see how we will find the labor at modern prices necessary for such intensive cropping methods. Corn and soy monoculture is great because you barely even need anyone to drive the combine any more. Also, the question asks about space, and feeding calories to animals is a less efficient use of space than, say, rotating through wheat, beans, potatoes, human edible things. $\endgroup$
    – kingledion
    Dec 15 '16 at 15:26
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    $\begingroup$ @kingledion, research into which crops would be ideal is certainly required, they would have to be crops with the right nitrogen fixing ability etc. In terms of labour, the value of food goes up when the people are short of food so the available money to pay people to harvest also goes up. It's just a matter of how much society values having a full stomach and how much they're willing to pay for the privilege. $\endgroup$
    – Separatrix
    Dec 15 '16 at 15:31
  • $\begingroup$ That's interesting but one of my parameters is that top soil and phosphorous are out of the question. I'm thinking of a dust bowl scenario. $\endgroup$
    – Ama
    Dec 15 '16 at 17:20
  • $\begingroup$ @Ama, there are crop combinations that will grow even in dustbowl scenario, it takes a few years after that to rebuild topsoil. The land can be healed if looked after $\endgroup$
    – Separatrix
    Dec 15 '16 at 18:03
  • $\begingroup$ @Ama I don't see how phosphorous can be so depleted. Elements move in a cycle, they can't be created or destroyed. Ultimately, all the phosphorous you eat as food ends up back in the ground, either as poo or your cadaver. Its just a matter of recycling such things. $\endgroup$
    – kingledion
    Dec 15 '16 at 18:10
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Hydroponics

Assuming you have decent recycling systems to keep the appropriate elements in the system - probably mostly extracted from waste systems - you can stack your crops in vertical farms, grown under LED lights tuned to release the perfect wavelengths of light for the plants in question. You can stack your farms as high or as deep as your architecture allows, making this an extremely effective use of limited space.

Aquaculture

If you have access to the sea or at least a pretty decent lake, you can grow large amounts of algae or bacteria to draw in nutrients from a much larger area. Spirulina, in particular, is a 'superfood' cyanobacteria which produces all the amino acids that a human body needs. Other cyanobacteria can fix atmospheric nitrogen, or even produce complex hydrocarbons like oil.

These algae can also be grown in tanks similar to the hydroponics option; open water is not strictly essential.

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The limiting nutrients (assuming plant physiology like ours) are N, P and K: nitrogen, phosphorous and potassium.

Recycling of (sterilized) nitrogen from biowaste gets one only so far; available nitrogen is probably the main constraint, after water, light and correct temperature. However, the nitrogen must be 'fixed,' rather than triple-bonded to another nitrogen atom, N2. With sufficient energy (and technical base), one can artificially fix N2 from the atmosphere into ammonia (NH3), via the Haber-Bosch process, which can in turn be converted into urea or nitrates -- or even used directly as a fertilizer (though there are some volatility losses with the latter approach.) For a coastal city/state, aquaculture is another option for fixing nitrogen, as there are marine Archea species that fix nitrogen, just as legumes and their symbiotic root bacteria do on land. Most naturally occurring sources of fixed nitrogen (like guano) have been exhausted.

Phosphorous and potassium will probably be more economical to trade for, so long as naturally occurring sources are available. Recycling from bio-waste or seawater is also possible, though expensive due to their relatively dilution.

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You have two problems to solve in your question, both related to modern high-intensity agriculture:

  • How to power your fleet of farming equipment with Diesel, and
  • How to fertilize the land

Another answer has discussed fertilization by using crop rotation and land management which works, but it doesn't allow the high density that modern agriculture depends on.

This can be solved for your mega city, by spreading out the farms over more land to replace density with quantity. Livestock is a great way to convert inedible plants into edible meats; again, we can't do intensive farming of animals, but we could go back to the Cowboy days of open fields of clover being eaten by livestock.

So the problem really is one of energy post-oil, which we seem to be pretty close to having in abundance. You mention nuclear power; giant hill-scrawling combines can have onboard nuclear generators (or at least radioisotope heat engines). The bug combines could be owned and operated by the city-state, to keep "weapons out of the hands of terrorists" or whatever you want, but we have portable nuclear electricity and steam available today. If anything, feeding a large city without oil would require even BIGGER farms with BIGGER mechanization, so that we can have BIG machines run off nuclear power. The trucks that rotate off the combines could be battery powered; they get topped off at the combine while they're loading and topped off at the silo while unloading.

Oil isn't magical, it's just the easiest form of portable energy we have today. But there's plenty of ways to generate energy without oil; it's just that none are as safe, reliable, or available to the public as oil is today. In a situation where no more oil was available, we would find a way to power the infrastructure to keep us fed; especially if we're only worried about one city-state.

Science and nodules. One other thing. Clover is so useful because it's got symbiotic bacteria that fix nitrogen and the like in the soil. Cows eat the clover to produce manure which then fertilizes the fields. I know you said that recovering waste from the city was a no-starter... but why? If we recovered the human waste from the city and used nuclear power to process it, it could easily fertilize fields. And biotech firms in this future would probably crack the fixing problem in giant tanks of bacteria; we're not worried about it today because fertilizer is still relatively cheap.

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You really have two incompatible questions, 1) post-hydrocarbon and 2) using as little space as possible. The solution to #1 is to relax the constraint on #2.

Multiple cropping (3/4 field methods &c) and other techniques needed to grow crops without hydrocarbon-based artifical fertilizers are already well known. You may not get as high a yield, so you may have to use more land.

For mechanized harvesting, there seems to be no good reason why the widely used central pivot irrigation systems couldn't be adapted to power electrically-driven equipment. Field to market transport could of course be electrified, and waste could be turned into biofuels.

For meats, someone has already suggested a return to open-range cattle grazing. Extend that to more species, and restore lands to prairie conditions (thus dealing with dustbowls & lands that are marginal without artificial fertilizers).

Finally, get rid of the idea that megacities are a good, or even inevitable, thing. With the growth of the internet, many jobs can be done by telecommuting, making it unnecessary to physically be where your job is. (A few years ago I worked two jobs, one in Silicon Valley, the other in Switzerland, while living somewhere else.) So people can live closer to their food sources, instead of being forced by economics to live in large cities.

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  • $\begingroup$ Eh no. I'm talking about a post collapse scenario. The situation isn't ideal. Land is not usable, and megacities are already there. $\endgroup$
    – Ama
    Dec 15 '16 at 19:22
  • $\begingroup$ @Ama: Well, if it's a sudden collapse rather than a gradual evolution, there's only one simple answer: Most of the people in your megacities die. The remainder - rural folk and escapees from urban chaos - adopt a lifestyle similar to what I've described. And land is always usable: it just depends on how much effort you want to devote to making it usable. $\endgroup$
    – jamesqf
    Dec 15 '16 at 20:33

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