What were the demographics of the ancient Greek colonies of Cyprus (any population estimates from 500BCE to 1BCE will do)?

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For a second opinion, here's what McEvedy and Jones had to say on the matter1 back in 1979:

The population then enters the 100-200,000 band within which it remains for the whole of the period from the Iron Age to the mid 19th century. It touches the upper limit during the halcyon days of the Roman Empire, again during the Crusader era (13th century) and during the final phase of Venetian rule (16th century). It falls back sharply with the Black Death and, more lastingly, after the Turkish conquest.

They do credit Beloch with a much higher figure of 500,000 in AD 14, but go on to discuss why that figure, in light of later data, seems far too high. Colin McEvedy's own map for AD 3622 shows its population at roughly 125,000.

1 - Atlas of World Population History, p115 (Part 1, "15a Cyprus")

2 - The New Penguin Atlas of Ancient History, page 109

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A book, Salamis of Cyprus: History and Archaeology from the Earliest Times to Late ... offers an estimation of the population of the city-kingdom of Salamis during your desired time frame. The estimate is derived by applying percentages of the population against the number of troops recorded as being fielded.

This model used applies a figure of 21% of the population which could be enlisted in a war, so comes up with the following (emphasis mine) :

Considering that the number of almost all men (80-85%) of the kingdom aged 20-49 at the beginning of the war was 18,000, then the entire male population of that age group would have amounted to 21,000 to 22,500 men. Mogens Hansen, whose model ('Model West 4' of A.J. Coale and P. Demeney) I used in this research, ascribes this age group to around 42% of the entire male population, or 21% of the whole population. Applying this percentage to the total, the whole population of the kingdom at the beginning of the 4th century BC can be suggested to range between 101,000 and 107,000, including men women and children.

So Salamis, arguably the largest of the city-kingdoms at 400BCE, had an estimated population of around 104,000.

--- Extrapolations:

From this you can extrapolate an (unlikely-think upper limit) maximum population of around 1 million, or you can do some more math and apply some Rank–size distribution or Zipfs power laws to try to tighten up the estimate.

An article which explains Zipfs law as applied to groups of city populations can be found here.

Running the numbers through Zipf based on Salamis as the largest of the city-kingdoms at 104,000 I come up with a lower-end estimate of around 304,000 for the entire island population.

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