In New England there is a tradition of placing a marker or gravestone for the immigrant ancestor where that gravestone no longer exists. Such markers are found for Edmund Rice in Sudbury, Mass. or Gregory Stone in Cambridge, Mass.
This is an unusual example from the Pine Hill Cemetery in Dover, N.H. It reads "Dea. John Hayes The 1st Born of the Pilgrim Father of the N.E. Hayes Family Died July 3, 1759, aged 72 years."
So this marker is for a second generation man, noting the first generation. I descend from Deacon John's brother Ichabod.