My people keep running out of food. Can anyone help me? I am playing via iTouch.

Most of the food supplies require a combination of technology and solved puzzles to obtain. It's best to keep the population fairly low until you have unlimited food sources. You don't say which food sources you've discovered so far, but the fish available prior to the appearance of the algae and coconut trees will not support the tribe for very long.

You can look here to see detailed spoilers for each of the puzzles.