Mary Pierce was born between 12-18 Sep 1740 in Lebanon, New London Connecticut. The records from both Find A Grave and the second volume of The Mayflower Births and Deaths indicate she was born on the 12th of Sept 1740, but the Barbour Collection and Mayflower Families Fifth Generation Descendants report she was born on 18 Sep 1740.  It is possible this discrepancy is related to a confusion between birth and baptismal records, or to an initial typing error when the first transcriptions were made, but until additional sources are found, one may not definitively state the date of her birth or baptism.
She and William Murdock were married by the Reverend Mr. Williams in Lebanon, New London, Connecticut on 11 Dec 1760.
The couple had at least five children who survived past infancy [Need citation]
Mary is buried in Old Cemetery, Lebanon, Connecticut, British Colony.
Get additional information about the other children. One source is: Murdock, J. B. (1925). Murdock genealogy: Robert Murdock of Roxbury, Massachusetts and some of his descendants. Boston: C. E. Goodspeed, but other sources should be used as well.
↑ Mayflower Births and Deaths: Volume 2
Source Information Ancestry.com. Mayflower Births and Deaths, Vol. 1 and 2 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2013. This collection was indexed by Ancestry World Archives Project contributors. P 357 of online database
↑ Mayflower Families Fifth Generation Descendants, 1700-1880. (Online database: AmericanAncestors.org, New England Historic Genealogical Society, 2017). From Mayflower Families Through Five Generations: Descendants of the Pilgrims who landed at Plymouth, Mass., December 1620. Plymouth, MA: General Society of Mayflower Descendants, 1975-2015. http://www.americanancestors.org/DB2728/rd/48785/125/1417089116
↑ Chapter Name: Lebanon Vital Records Volumes 1 and 2, 1700-1854. Ancestry.com. Connecticut Town Birth Records, pre-1870 (Barbour Collection) [database on-line]. P167 of online database. Provo, UT, USA: Ancestry.com Operations Inc, 2006. Original data: White, Lorraine Cook, ed. The Barbour Collection of Connecticut Town Vital Records. Vol. 1-55. Baltimore, MD, USA: Genealogical Publishing Co., 1994-2002.
Mayflower Families Through Five Generations, Silver Books, Volume Eighteen, Part 2, The Descendants of Richard Warren Through His Children Mary, Anna, and Elizabeth, Published 2011, Page 125
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It may be possible to confirm family relationships with Mary by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Mary: