I'm not sure where I read it, but Taubes wrote somewhere that 800 calories would probably be sufficient to receive all needed nutrients if it were made up of meat and fat only. The reason the Ancel Keys experiment with 1,570 calories was starvation was because of the content of those calories, not the number of calories alone.

When I first did Atkins, I wasn't actively counting calories or even grams of fat or protein. I counted only carbs to ensure I was eating no more than 20 grams. Plugging my meals into Fitday, I found that I routinely ate around 1,250 calories. I lost weight easily and kept it off ... until I started not following the plan as closely. I did not feel starved in the least at 1,250 calories because I was getting the nutrition I needed from the protein and fat.