For ants, an icon will appear on top of an ant to signal that it needs to eat. Ant development items such as larva also need to eat, and will have an icon signaling workers to feed them. If not fed, the ant will eventually die. If the queen isn't fed, it will stop laying eggs and eventually die.
The two current prey in the game, the Beetle and the Anate don't need to eat.
The two predators, Spiders and Centipedes, will not attack an ant unless hungry or provoked. However, the predators will not die of hunger either. After eating, it will take predators 5 minutes to get hungry again.