As she prepares for Thanksgiving each year, Betsy Slagle thinks about an ancestor: Francis Cooke, who arrived in Massachusetts with fellow Pilgrims on the Mayflower in 1620. Thirteen generations later, Slagle, of Pompano Beach, feels a connection with this pioneering forebear. She describes him as “not one of the better known” Pilgrims, but her research shows he was a Protestant separatist, a father of five and one of the signers of The Mayflower Compact, the historic agreement to create a political entity in Plymouth Colony.