Well, in my neck of the woods it's different, very very different.
Hive / colony density depends on many factors and I doubt any formula could be used... Very often 2 "wild" colonies in the same building or within meters of each other. This is a common occurrence in high value forage areas.
My opinion, bees are foragers, so they should be compared to foraging livestock.
(Some times to be considered as cannibalistic livestock when robbing starts) - another topic...
How many cows or sheep can you run on 1000 sqm ? - depends on what is available to eat...
Spring = 10,,,,,,, summer = 8,,,,, winter =4 etc etc etc
If you over stock you will need to supplement feed during times of need... if this is not an option simply move your stock to another camp/apiary during the tougher/leaner times.
Wild colonies.
If the going is good, bees will make a plan to move in somewhere.... some long term huge colony builders and some limited for space that just cast swarm after swarm almost as if destined to do so...... Nature left alone has a way of thriving....
Disease
Firstly, Im very fortunate here, so this is based on my little protected piece of the world I call home.
Another point was so many colonies close together may/could be a risk with regards to disease.... Another way of looking at it is natures way of keeping them healthy and apart from other diseased colonies...
See below pics, (Pls excuse other lines drawn through pics, they are for measuring distance when moving caught swarms)
6 colonies within 100m of each other and another 2 very large colonies perhaps 70 meters away. (All within 1sqkm)
4 colonies also within 100 sqm of each other.