With a little reading (thank you, Wikipedia), I found out that the collared dove is native to Eurasia (imagine that!) and was introduced into the Americas in 1974, when 50 escaped captivity in the Bahamas. Since then, it has done a bang-up job of spreading throughout North America and Mexico.
So, I expect they're here to stay - especially since I saw two of them under the feeder today!
Have you seen any around, yet?