Sadly the common European dove is being more and more scarce, following the same path than the migratory pigeon. The Eurasian collared dove or Turkish dove is invasive, but spreading naturally. They don't overlap.
As they suffer predation by magpies, the more spikes that humans put in the nest, the more attractive became to nest on it, it seems.
Haha, had the same problem. Don't even mind the doves, would gladly build them a place to live myself. But the early morning wake up alarm they create is too much.
My household had to change our sleeping schedule because of these stupid rats. In Europe they are both protected and invasive at the same time.