Isaac Burlingame married Sophronia Wolcott (or Walcott) who is a direct descendant of William Walcott of Salem, MA. The following is an excerpt from the Walcott family history:
William Walcott of Salem MA was the head of the third Wolcott/Walcott family in America. He was formerly thought to have come from Stokeinteignhead in Devonshire where a William Walcott/Woolcott, a mariner involved in the Newfoundland trade, was born. New DNA studies indicate this is not so. William's descendants have DNA quite distinct from both the Somerset Wolcotts and the Shropshire Walcots, of a classification called "Nordic", derived from Danes or Normans who settled on the East coast of England .
(1) William Walcott, b. c.1610, was granted 30 acres of land at Jeffrey's Creek near Salem MA in 1636. He must have returned to England, however, as he is listed as leaving England for America in 1638: "William Walcot for Capt. Butler, passenger for Providence Island by the Swallow". William held land at Salem for a family of 4 people in 1640. He married Alice Ingersoll, daughter of Richard Ingersoll of Salem. Richard Ingersoll's daughter, Alice Walcott, was mentioned in his will to receive "my house at town with 10 acres upland & meadow after my wifes decease." William Walcott was one of several residents of Salem, including the founder of Rhode Island, Roger Williams, who were censured in a letter from the Salem church to the Dorchester Church, dated 1639: "William Walcott for refusing to bring his child to the ordinance, neglecting willingly family duties, etc." This probably means that he did not have his child baptized, and may indicate he was a follower of Roger Williams who advocated adult baptism. The Quarterly Court at Salem ordered in 1642 that William Walcott be whipped for idleness. Essex Co. Quarterly Court records state: "Willia. Walcotts wife children & estate committed to Richard Inkersell hs father in law 27:10:1643 to be disposed of according to God and the said Wm. Walcott to bee & Remaine as his servant." William is thought to have left Salem about 1644, leaving his family behind. In that year a law was passed saying that all who opposed infant baptism were subject to banishment from the colony. In 1651 he or another William Walcott was a shoals witness in Maine. In 1652 the Salem records show that "means were taken by the court to preserve his estate." This probably included selling his land, because in 1652, Robert Goodell of Salem owned land at Salem which included 30 acres that had formerly been granted to William Walcott.
Source: http://www.wolcottfamily.com/salem.html