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Question

From around 400 BCE to 1000 CE, what could what would a reasonable greatest achievable population be – under the best of all circumstances – in a rural area of about $\mathrm{900 km^2}$ (In which people may live in villages, but disregarding areas containing towns or cities with a population greater than 1000 people)

Edit: by best of all circumstances, I mean best of all circumstances achievable on an Earth-like planet, which includes the best climate for agriculture which could realistically exist.

Background

I am currently working on a strategy game set in a fictional -- but in all ways very Earth-like -- world in a period technologically -- including domesticated plants and animals -- comparable to the old world (Eurasia and Africa) from around the year 400 BCE to 1000 CE.

Data regarding the world is stored in a mesh, where each cell in this mesh stores information for an area with an area of close to $900\,\mathrm{km}^2$ (same as a $30\,\mathrm{km}$ by $30\,\mathrm{km}$ square but not necessarily a square).

One of these things which need storing is the rural population of the cells (towns and cities with a population greater than 1000 [a somewhat arbitrary limit] are by the game engine stored separately).
For performance and file size reasons, only 8 bit may be used to save the population of each cell; this 8-bit number will represent the population of the cell on a scale from 0 to 255 (the greatest 8-bit number) where 0 is a population of 0 and 255 is a population equal to the greatest population which might live in this area, and this is why I need to know this maximum population.

Further criteria

Note that I am not simply asking about the greatest population density of an entire iron age or medieval state or empire: consider for instance that the population density of a small rural area -- for instance near rivers like the Nile, the Tigris or Euphrates rivers -- may be much much greater than that of the states surrounding them.

For this reason, I do not consider my question to be answered by (and thus a duplicate of) this question: What is the difference of population density between the population of a nomadic and a sendentary territory?

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Theoretically, in a reasonable temperate climate with good soil you can assume that one hectare can feed about 4 people. Because the technology level is medieval, you cannot use more than about one quarter of the land for agriculture -- some land needs to be left fallow, and you also need pasture and forest. This comes to about 100 people per square kilometer, so on 900 square kilometers you could have 90,000 people.

In practice, medieval European countries never ever came close to such population densities. In ancient times, the Nile delta reached about 40 to 50 people per square kilometer, so 900 square kilometers had about 36,000 to 45,000 people; this was the maximum population density of any area I can think of within the classical world.

Overall, I would say that having 0..255 map to 0..127500 (a scale of 1:500) would be absolutely sufficient for any time period; before the introduction of modern agriculture the land would not support more people, and after the introduction of modern agriculture rural areas would not need more people.

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The highest population density was about 200 per square kilometer in ancient Egypt, and could be as high as 500 in Maya civilization. This gives us a range between 180,000 to 450,000 as the upper bound of your total population.

But this answers the question about the highest sustainable density - the one that you are not asking. If you need to ask about population of a small area, then it depends on the basis of which you disregard cities and towns, because they will have the maximum population density.

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Value 1

According to this source the highest population desity per square mile where 100 people in medieval france. So for a square km this is 39 people. so for 900 $km^2$ it would be 35 156 people. But this is only achivable when the distance between villages is 0.

Value 2

When we assume between every village is a distance of 1 km in all directions and our village is 1 $km^2$. We end up with this formula: $Area = \pi \cdot r^2$ while r is 2 km (one for the village and one for the distance to the next). So the area per village would be 12.57 $km^2$ and when using this value we end up with 2 792 people within 900 $km^2$.

Conclusion

If you want a more realistic value stick to the secound value if you can explain a 900 $km^2$ big village you should use the first.

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