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I believe brown is dominate over white, and the degree of the brown is dependent on modifiers. Also, the blue egg gene is dominate over the brown egg gene. Many times you will see gene dominance notated as such:
Bl>Br>w
(Don't take this example as gospel, since I have no idea how the egg color gene is actually notated. Each gene normally has a letter(s) to represent it.)
Anyone who has Easter Eggers will tell you that many times they will have layers with green eggs, and the eggs will be in various shades. This is because the brown coloring is laid over the blue coloring before the egg is laid. To know what shade of blue the hen is actually laying, you have to look at the inside of the shell where the brown isn't present.
Also, I do not know if this is a separate gene from brown eggs, since the shell of brown eggs is completely colored, but I would suspect so given the mechanics of it. I do know I have cleaned brown eggs before, and scrubbing will sometimes take a layer of the color off, as it sometimes does on the green eggs.