In the past, I tried to generate an AT with negative food, but was unable to do it. The best I got was zero food, unless... and here is the thing... the source of food was in undiscovered terrain. The AT can indeed be negative food at best.... if you have undiscovered terrain in the AT's city radius. You'd best discover that food source, or lose population if faced with a food deficit.
@ La Fayette: Yes, a city on a mountain definitely provides one food.
Since I have never had an AT on a Montain or Glacier in a random game, it might be because of starting on a premade world, or because of the unnatural mixture of terrain. I've never seen a scenario or map with a lone mountain, under a hut, surrounded by plains. But those are the conditions (in early game) that gave an AT on mountains, swamps, glaciers, etc. I was not testing for that situation in partiular, so I did not continue to try different combinations of surrounding terrain, like all grassland, all ocean, all swamp, etc. I am assuming that all desert, all glacier, all mountain will yeild no AT, since even size 1 cities cannot survive on such unimproved terrain.
My guess is that the algorithm used to allow an AT is similar, but not identical to, that used to place the AI settler location.