Warren Ramsey, an intense lawyer whose friends call him Ram, is vacationing in the Florida Keys with his wife Leslie when he charters a boat to take them and his old college buddy, Clay Foster, deep sea fishing. Two of the local "Conks," as the natives are called, Captain Lowe and his dockboy, Wicey, take the trio out, and all seems well when Ram hooks a huge fish. He loses the fish, however, and insists on pursuing it, despite Lowe and Wicey's warnings that they will get lost in the maze of tiny islands. When Ram angrily takes the controls, the boat runs into a reef and he is knocked unconscious. The boat's propellor is lost, but the group wades onto a nearby island after Ram awakens. Wicey grows increasingly nervous as the others explore the island, and after they find a small garden and a hut, he appears to wave a man away. The man comes to the hut, however, and tells them that he is Captain Powell, a former mariner seeking solitude. He stitches Ram's head wound, and Ram, suspicious as always, refuses to believe the man's story. The evening passes as Wicey dives in search of the propellor and the others gather food. During the night, Ram awakens and finally recognizes the man as Dr. Sanderson. After assembling everyone, Ram tells them that Sanderson fled the mainland after manslaughter charges were filed against him. When Sanderson was a prison doctor, he administered a sedative to a terrified man about to be executed, but as the man passed out and died from the drug, a reprieve from the governor arrived. Although Sanderson maintained that he had intended only to ease the man's anxiety, a mysterious packet of money sent to him convinced a grand jury that the man's family had bribed Sanderson to commit euthanasia. Wicey and his father helped Sanderson to hide on the island after he had saved Wicey from succumbing to a moray eel bite. Ram becomes obsessed with the idea of returning Sanderson to the mainland and defending him, although Clay maintains that Ram is interested in obtaining glory for himself rather than justice for Sanderson. Tensions grow as the concussion, heat and obsession drive Ram insane, while the others must cope with a growing shortage of food. After Wicey and Lowe find the propellor, they hide it from Ram so that he cannot force Sanderson to return to civilization. Clay, who has loved Leslie since his college days with Ram, tries to convince her to leave with him, but she refuses to desert Ram, even after Sanderson declares that he has become schizophrenic. Ram finds the propellor but is prevented from leaving when Wicey removes the engine's distributor cap and buries it. Lowe then catches a sea bass, and while the others eat, Ram continues his bitter efforts to repair the boat. Later that evening, Wicey hangs the fish head over the distributor cap's hiding place in an attempt to draw the protection of a huge alligator living on the island. The boy's plan turns tragic, however, when the crazed Ram begins to dig up the cap and is killed by the alligator. The next day, Sanderson waves goodbye from the island as Lowe, Wicey, Clay and Leslie return to the mainland.