You'd have to work out the maximum theoretical food production without phosphorus fertilizers or petrochemical insecticides, and without using aquifers or artificial irrigation. Basically roll back the green revolution. The world was bumping up against food production limits when the green revolution happened in the 60s. But the green revolution is totally unsustainable. The sustainable population is probably somewhere around a pre-1960 number.
Organic (CNHO) chemicals aren't in the slightest dependent on petroleum, it is only a passing quirk of the early 21st-century economy that oil and natural gas byproducts are the most common chemical feedstocks. CNHO atoms are everywhere on earth, and they're not going anywhere (mass doesn't leave the earth, for the most part). Basic organic chemistry building-blocks, e.g. ethylene, are not much more difficult to obtain from biological matter (e.g. ethanol) than from oil/gas. Organic chemistry -- insecticides, plastics, pharma, what have you -- isn't going anywhere, and this is all a silly misunderstanding from confused Malthusians.
...aquifers...
...artificial irrigation...
There's no theoretical limit to artificial irrigation (well there is, but it's ludicrous). In refutation: nuclear or solar powered ocean desalination plants, with aqueducts, large pipes, or underground canals piping freshwater inland -- thousands of miles if need be. Elementary, existing technology, and I think not too far from economic feasibility even today. Desalination is already economic (if not directly competitive with natural freshwater sources, when they are available) -- lots of it in the Middle East, Southeast Asia. Aqueducts are ancient technology.
...phosphorus fertilizers...
Nothing stopping us from recycling phosphorus -- it's not like we're flinging it off the earth into space. The whole earth is a closed cycle for chemicals -- water, CNOH, trace minerals, all of them sustainable. Since the issue is framed as "maximum theoretical", well, in the limit we can ion-exchange phosphorus out of the seas -- the ultimate repository for "used" phosphorus. (Although in the nearer term there's more simple resolutions, like preventing runoff waste, recovery from sewers/rivers, mining new types of phosphorus minerals, etc.)
But the green revolution is totally unsustainable.
Ignorance is totally unsustainable. Please conserve.
Irrigation always builds up salt in the soil. Areas of California are falling out of production for this reason, after a good 100 year run. Irrigation is what turned much of the middle east into desert.
The rest of your points I guess boil down to needing infinite cheap energy. Anything's possible with massive amounts of free power, I suppose. I wouldn't bet on it.
Large areas of China, Egypt, ect have been under continuous irrigation for thousands of years and they can still grow just fine. If California is having issues with irrigation over what 100 years then it's a separate issue.
They probably do have issues due to the amount of rainfall vs. irrigation and their crop rotation etc. But, it's not really an issue with irrigation just their approach to irrigation. Desalination also gives you the option to have much lower salinity than river water which should allow areas like California to cope with this issue.
The tipping point was around 1915 when the world had slightly less than 2 billion people, with the introduction of the Haber-Bosch process. After that the population growth is virtually dependent upon artificial nitrogen fixing fertilizers.
Naturally-produced fertilizers can provide approximately 200 kg. of nitrogen per hectare annually; this allows for the production of between 200 and 250 kg. of plant proteins. This places a theoretical limit on the number of people that each hectare of land could sustain. Under ideal conditions this would amount to around 15 people per hectare; in practice, the historical limit has been about 5 people per hectare.
In this paper he shows - dramatically - that there is a hard limit to the number of people that can be supported by natural nitrogen fixation. The population could have continued to grow through more drastic conversion of land to agriculture and better use of natural mechanisms, but at the end of the day, as he puts it:
"... at least two billion people are alive because the proteins in their bodies are built with nitrogen that came from a factory using [the Haber-Bosch] process."
Why does the answer have to forgo everything that facilitates optimal modern high-tech food production?
Gladwell's "Outliers" spent a lot of time on farming technologies thru the ages (and subsequent impact on cultural success). Japanese rice farming amounts to a sustainable long-term high-tech process making heavy use of artificial irrigation and any other suitable tech, maximizing production with limited space and growing seasons.
For starters, one could compute an outer limit of calories per square meter and match that to basic caloric needs per person: given an average solar energy concentration there is no way (unless you want to turn geothermal & fossil fuel) to produce more food (whatever manifestation) in caloric terms than sunlight provides. From there the answer requires providing assorted limiters, reducing the potential caloric output to more realistic levels based on viable technologies.
Computing from a different angle:
149M sq km total land, 15M sq km farmland, 7000M people
Dividing current farmland by population and rounding the result up a bit, each person gets a plot 47x47m for 603 sq ft for living and the rest for farmland. Assuming half the land is rank (unusable) wilderness, that roughs out to an optimistic carrying capacity of 33000M people.
If history is any indicator, there have been events that wiped out most or all of a species. Even in our times, nature has swayed at her discretion; look at the earthquakes and tsunamis and the destruction to human life and property.
