In my yard and the neighbors here in Torrance, the crows have taken over. The dove and pigeons are gone. Some magpies are still around occasionally and they chase the crows off best they can.
Aren't crows protected in Mexico and revered in folklore there? I understand one of the reasons that we have "limited" crow seasons in the USA is because Mexico wanted to decimate the waterfowl poulation - at least as a bargaining chip - because they felt waterfowl committed crop depredation and generally interfered with the rural farming. I believe, perhaps because having read an old article in a DU magazine, this crow restriction became part of the international treaty with Canada, Mexico, and the USA re migratory birds.
Perhaps that's why you have so many crows in CA? I understand the border is a bit porous...