Children walking in the forest don’t censor their expectations when it comes to animals. They hope to see not just foxes and owls, but lions, polar bears, and goblins too. As we grow older, our encounters with animals become more rote—we know what’s around, and what isn’t.

Which is why it’s such a delight to occasionally see animals out of place. Looking up from a drink in Telegraph Hill, for example, to hear San Francisco’s parrots squawking through the fog. Or coming upon wild pigs crowding a beach in the Bahamas. These oddities revive old hopes that anything can happen.

London, a city that has hosted exiles for centuries, is home to thousands of rose-ringed parakeets. How these nonmigratory African birds arrived in Britain is a matter of debate. Some say the original mati...