I must be doing something different, because so far, only one of my villagers has died of starvation. And I actually killed him by accident while making a potion to revive his "weakened" state.

In general, I try to limit my population until I have a big enough food source. It's either that, or spend a lot of time hunting mushrooms and keeping the game paused when I'm not actually at the computer. Farming first, is my motto.