I'm not sure why the desert gene would considered dead since the males can pass on the genes to offspring?
Sure, there's "no use" for desert FEMALES, because they can't reproduce(as far as has been proven so far), but that doesn't mean that the gene is of no use at all. It's just a risky gene, since if it produces female deserts, they aren't as valuable.
I thought that someone posted a picture of a desert on eggs, but I don't remember the particulars, and the eggs had not hatched when I'd seen the picture.