This is an almost impossible question because population density hardly correlates with anything.Originally Posted by Azelor
Example :
Let's take some surface S defined for example by a kingdom. This S is rather arbitrary.
This kingdom has a population P so a density P/S. As this is an average it will fluctuate wildly in sedentary civilisations where this P/S is an average of a very high density in cities and very low density in the rest.
Then for this same surface you need a total food growth per year F so a density F/S. Only this factor which will also wildly fluctuate, will depend on biomes and climate (always keeping the same S)
Last let's have µ which is the minimum food per year and per person so that this person doesn't starve.
Now let's compare µ and F/P (notice that surface disappeared - it stays only implicitely in F because F = Sum of Fi/Si x Si where i is the climatic zone and there is a constraint Sum Si = S)
If µ<F/P all is well and your population will increase. You may suppose that it stays put when it reaches P=F/µ. We know that it won't.
If µ > F/P then theoretically some people will starve untill we get back to the magical P=F/µ.
But in reality we know that this won't happen either. In reality the lacking food will be imported from places where µ<F/P. This was already true thousands of years ago - Carthago imported grain from Sicily and Rome imported grain from Egypt. Both Carthago and Rome had a high population density so a large power and wealth but both had to import the food.
Today's Egypt with its 60 M people has a µ far above F/P so they can' export anything and about a third might theoretically starve. But they import the difference (f.ex from US or Europe where the µ is far below F/P) and continue to happily increase P farther.
So when you arrived at this point you realize that there is no correlation between P and S as soon as people invented trade. If you wanted still to have an estimate of P on a given S then you'd have to estimate the food trade happening on this particular surface.
This is an impossible task because you'd have to practically reconstruct the whole food market and import/export flows on a world scale (for very technological civilisations) or at least a regional scale (for less technological civilisations).
And it can't be reconstructed independently - to reconstruct that, you need to reconstruct the whole economy because to buy food, you need money (or a very strong army which costs money too).
So you must reconstruct who is rich and who isn't.
Incidentally there is an amusing question what is the best strategy. Coming back to my historical example, Carthago lead by merchants thought that it was cheaper to pay for food rather than for a standing army while Rome lead by aristocracy thought the opposite. The latter strategy was the winning one
Etc.
The only feasible and simple model would be the one where µ = F/P but this is the only one which is not realistic as soon as agriculture and trade are invented.
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