Eurasion connection

They are a non-native species. Invasive maybe?

Check your states hunting regulations and see if they are listed.

ADDED:

Your state's hunting guide says you may shoot unprotected birds with a license. Check to make sure. 

Here's a section of law that says which ones are unprotected:

41-11-10. Birds not protected or conditionally protected by chapter. The English or European house sparrow, unbanded undomesticated pigeon (rock dove), Eurasian collared dove, and European starling are not included among the birds protected by this chapter. Purple grackle, crow, magpie, brown headed cow bird, red-winged blackbird, Brewers blackbird, rusty blackbird, and the bronzed grackle may be taken when committing or about to commit depredation upon ornamental or shade trees, agricultural crops, livestock or wildlife, or when concentrated in such numbers and manner as to constitute a health hazard or other nuisance.

Source: SDC 1939, § 25.0407; SL 1959, ch 114; SL 1961, ch 119; SL 1967, ch 85, § 2; SL 1981, ch 301, § 2; SL 1998, ch 252, § 22; SL 2007, ch 244, § 1.