In 1959, off the southern coast of France, a tuna boat hauled up a largetooth sawfish. The catch wasn't particularly large. The razor-snouted fish only stretched about four feet long; still a baby by the standards of its species. But it was one of the last to be seen in those waters. Within a decade, the largetooth sawfish entirely disappeared from the Mediterranean Sea.

Such accidental catches and sightings in the Mediterranean have often been regarded as signs of largetooth and smalltooth sawfish migrating into the sea from the coast of Africa. When sawfish experts gathered in London in May 2012 ...