The Pilgrim Migration: Immigrants to Plymouth Colony, 1620-1633. Robert Charles Anderson. The author tells the story of the Pilgrim migration by relating the story of each family or individual known to have resided in Plymouth Colony between 1620 (when the Mayflower arrived) and 1633. Each of the more than two hundred sketches provides information on the early histories of these immigrants as well as their New World experiences. This material is followed by complete genealogical accounts, including all marriages and children of immigrants.