Sportfishing groups and environmentalists are calling for a partial moratorium on Virginia’s menhaden reduction fishery, citing troubling declines of certain bird and fish species that feed on them.

A petition, dated Dec. 12 and signed by 18 individuals and organizations, presses the Virginia Marine Resources Commission to ban related menhaden harvests in the state under most conditions until regulators enact a scientifically based catch limit within the Chesapeake Bay.

The effort targets a fishing fleet operated by Omega Protein, a subsidiary of Canada-based Cooke Inc. The company processes the small, oily fish into animal feed and nutritional supplements in a process referred to as “reduction.” Critics have contended for years that Omega’s menhaden harvest leaves too few of the forage fish behind in the bay for ecological purposes, such as supplementing the diets of striped bass, ospreys and other predators.

“We think menhaden are being depleted in the bay,” said Dale Willi...