Recent sightings of a gray whale and her infant calf swimming near Alcatraz and Sausalito in San Francisco Bay illuminated a likely repercussion of melting polar ice, scientists said.

Gray whales normally mate in the tropical lagoons of Baja California in the winter, migrate north to chilly polar waters to feed on shrimp-like prey that blanket ocean floors in the spring and summer, and return to Mexico the following winter to give birth in the lagoons, where the young are protected from sharks and orcas that hunt in the open ocean.

But the relatively small size of the calf that followed its wayward mother into the Bay — about that of a newborn, which is 15 feet — indicated that its mother calved as she migrated south along the coastline — just as others of her kind are heading north for the summer feeding grounds.

“We’re seeing more and more calves born before they get all the way down to Mexico,” said Wayne Perryman, leader of the National Oceanic and Atmospheric Administration’s cetacean health and life history program at the agency’s office in La Jolla.