You must use food tokens from your personal supply next to your player mat, not cached food on bird cards, when paying the food cost to play a bird—including when using two food tokens as a wild food.

This is supported by the following rules:

• "Pay the bird’s food cost. Discard food tokens to the supply (these tokens must be from next to your player mat, not food tokens cached on bird cards, a concept that will be explained later)."
  (Page 6)

• "When playing birds, you may spend any 2 food tokens as if they are any 1 food token. This exchange cannot be used during other parts of the game. For example, if you need 1 fish, you could use any other 2 food tokens instead."
  (Page 6)

The rulebook makes it clear that only food tokens from your personal supply can be used to pay for birds, whether paying the exact cost or using the two-for-one wild exchange. Cached food on bird cards cannot be used for this purpose.

Source: page 6

Source: Core Rulebook (pp. 1, 2, 6, 7)