The American Compendium of Genealogy Vol. II, p. 53 claims that Thomas BARNES *who died 1688 came from England to Plymouth 1630 and married first Mary ANDREWS who was convicted of witchcraft and executed, married second Mary ANDRUS who died 1689, daughter of John of Farmington.
If you haven't done so, check out the family tree of Frederic Barnes on ancestry.com. Also, he has written
two books about the Barnes family, the most recent one is THE GENEALOGY OF THOMAS BARNES of HARTFORD, CONNECTICUT
8,591 Descendants, 14 Generations, 1615-2001. $79.95 for each two volume set. California Residents, add $5.89 tax for each set. Price includes Shipping & Handling.
Frederic W. Barnes
794 Chestnut Drive
Fairfield, CA 94533-1465
Phone: (707) 422-1794
Hope this helps.