On Aug. 7, 1954, an almost 14-foot-long great white shark swam into a small harbor on Cuttyhunk Island, just west of Martha’s Vineyard off the coast of Massachusetts. Within hours, two fishing guides from the island had harpooned and killed the potential menace.

Almost exactly 50 years later, in September 2004, another great white shark appeared in the same area, near the neighboring island of Naushon. The reaction this time was very different: At considerable expense, the shark was ushered back to sea (an effort in which...