There are two ways that birds produce color. The first is by pigments, which include melanin, lipichromes (reds, yellows, oranges), carotenoids (reds, greens, browns), and porhyrins. The second is through ultrastructures (= blues) (black, dull yellow, brown). If you place a Blue Jay in a blender, all you get are fragments of brownish feathers.
We have no predictive theory for adaptive coloration: knowing habits, we can't predict color. Of course, color plays roles in species and sexual recognition.