In the still-dark mornings, at the Texaco gas station in Menemsha, local fishermen load up on lures and bait, cheap cups of coffee and the daily newspaper before setting out to sea. Behind the rustic station is a long wooden bench where the men gather.

“Early in the morning, it’s always the same crowd,” recalls Albert Fischer 3rd, an 11th-generation Islander. Mr. Fischer, a commercial fisherman in his younger years, can still rattle off names of the old guard.