India, Aug. 14 -- In 1994, the municipal commissioner of Surat, Gujarat, ordered the killing of all the city's dogs. Within two weeks, every single one was dead. Just two weeks later, the first case of bubonic plague - one of history's deadliest diseases - appeared. With their predators gone, rats overran the city. Many people were bitten, and three cases of plague emerged. Across India, people began wearing masks, exports were halted, and tourism came to a standstill.

History is replete with such cautionary tales.

In the 1880s, Paris killed all its dogs and cats, with the same disastrous outcome. In China, a campaign to eradicate sparrows - accused of eating grain - in the late 1950s unleashed a locust invasion that triggered a famine....