Western Alaska villagers have endured the worst chum salmon runs on record, several years of anemic Chinook salmon runs in the Yukon and Kuskokwim rivers, harvest closures from the Bering Sea coast to Canada’s Yukon Territory and such dire conditions that they relied on emergency shipments of salmon from elsewhere in Alaska just to have food to eat.

Many of those suffering see one way to provide some quick relief: Large vessels trawling for pollock and other groundfish in the industrial-scale fisheries of the Bering Sea, they say, must stop intercepting so many salmon.

Advocates for tight...