When: Unspecified/unimportant, but pre-industrial era.
I've been using the unsophisticated system of Googling "[whichever island] population" and looking through as many Wikipedia pages on various islands as I can face looking at, but unfortunately they only seem to list current (or at least fairly recent) populations. Googling for more generic things about "island", "population" and "area" (because I'm struggling to think of better search terms!) is bringing up lots of pages about environmental surveys, but nothing useful.
So here's the situation:
I have an island approximately 200km2/72 mile2 (20km long by 10km wide, or about 12 miles by 6 miles)*, with three settlements on it. Apart from occasional military occupations, the people have fairly little contact with the rest of the world. There is no shortage of food, land for farming, or other resources. With this in mind, would it be plausible for this island to have a population of 6000-7000? If not, what kind of population am I likely to be looking at?
Thanks in advance!
* I really hope these conversions are right- please correct me if not!