( CNN ) -- A Los Angeles-area man has been charged with murder in the death of his wife while on a cruise along the Mexican coast , an FBI spokesman told CNN sister network HLN . Shirley McGill , 55 , was found dead on Tuesday in her cabin on the Carnival Elation . Shirley McGill , 55 , was found dead in her cabin on the Carnival Elation on Tuesday as the ship , after a five-day cruise to Cabo San Lucas , was heading back to its origination point of San Diego , California , authorities said . Robert McGill , who is in his mid-50s , is charged with murder on the high seas , FBI Special Agent in Charge Keith Slotter told HLN . The FBI and the Carnival cruise line said that a domestic dispute Tuesday night resulted in the woman 's death , but did not elaborate on how she was killed . The FBI said the cause of death would be determined through autopsy . Another passenger became suspicious that foul play had taken place `` for a variety of possible reasons , '' Slotter said , and notified ship security . When security checked the couple 's room , Shirley McGill was found dead inside , he said . Authorities believe she had been dead for no more than a couple of hours . Watch Slotter describe how the body was found » . Robert McGill was arrested on board the ship and was kept in its brig for the remainder of the cruise , the FBI said . After the ship docked , he was taken into federal custody , as crimes on the high seas fall under federal jurisdiction . FBI agents boarded the ship to start the investigation as the vessel neared San Diego , with the Coast Guard transporting the agents about 10 miles offshore . Agents were completing their work on the ship Thursday , having interviewed about 50 passengers and processed the crime scene , Slotter said . He would not elaborate on the domestic dispute , saying authorities are still trying to piece together what happened . The 2,052-passenger Carnival Elation had departed on the cruise July 11 . CNN 's Scott Thompson contributed to this report .
Robert McGill , Tuesday , was found dead in her cabin on the Carnival Elation on mid-50s . Husband Robert McGill , in mid-50s , charged with murder on the high seas , Carnival says . FBI and Carnival cruise line said domestic dispute Tuesday night led to death .