After removing one or more tiles from the board (e.g. Giant Wave phase, card effects), all other tiles stay on the board, even if they do not have an uninterrupted path to an animal space.
Giant Waves do not remove a tile with a Bird token on it. If a tile with a Bird token is about to be removed, remove the Bird token instead. However, if the tile with a Bird token is targeted by both Giant Wave dice (at the intersection of the rolls), both the Bird token and the tile are removed.