i've noticed that the initial settler location tends to have fresh water nearby. one AI in my current game has no rivers or lakes in his close territory, but he does have a one-tile-long strip of river right next to his capital, which i assume he settled directly on the spot that he started at.
but, you starting location also tends to have multiple food bonuses. so yes, it tends to get bigger than a lot of other cities. and many of us like to run some specialists there, and not whip folks away as often as in other cities. most people chop at the capital for early wonders or early troops to go rush somebody. i hyper-micro-manage the forests i forests i chop there so that the ones i leave give the highest chance for forests to grow back. but i'm insane.
sometimes i obsess about health, sometimes i don't. if they're losing food because they have too many people, it's because they had too much food in the first place after all. but that green cloud sure is ugly.
definitely check out cabert's article.