Ruth....There was a William Davidson who was on the 1830 Lincoln Co., TN census (age 30-40).Then in 1840, a William "J." Davidson was again on the Lincoln Co., TN census (then shown as age 40-50; I assume that this was the same man, but no real proof).I believe that this was the William Davidson who married Elizabeth Dyer and who was then shown as age 53 on the 1850 Lincoln Co., TN census (so it certainly could have been the same man who appeared on those three censuses in a row in Lincoln Co., TN).
It seems almost certain (albeit no "concrete proof") that the above William J.(?) Davidson who married Elizabeth Dyer was a member of the same family as the John Davidson and Bryant Davidson (probably father and son) who had been on the 1820 Lincoln Co., VA census, and it appears that they were all members of my DNA "Family 10" out of Buckingham Co., VA, then Pittsylvania/Henry/Patrick Co. VA, and then later Grainger Co. TN (by the early-1800s).Some members of this family were then in Lincoln, Lawrence and Lewis Co., TN later.
The later/younger William John Davidson....who married Rhoda Keeling in Lewis Co., TN in 1851 and who then moved to Barry Co., MO by 1860....could have been out of this family, I assume, or perhaps he could have been a member of your DNA "Family 4."As I recall, this younger William J. Davidson was shown as age 30 in 1860, so he was born about 1830 (so he would have been around the age of 20 in 1850).
While possible, I rather doubt that any of the above people were out of Josiah and Mary (Finch) Davidson's "branch" of DNA "Family 10."Josiah "Junior's" father....Josiah Davidson, Senior....was a son of a William Davidson who left VA and who moved to Orange Co., NC around 1780.The Davidsons in Lincoln Co., KY in 1820 were instead out of one of the BROTHERS of that William Davidson in Orange Co., NC, and that brother was either John, David or Richard (who had appeared in VA and also in Stokes Co., NC)....with the brother named John Davidson being the most likely ancestor of the men in Lincoln Co., NC in 1820.I don't see any "direct connection" between the descendants of William Davidson in Orange Co., NC and Lewis, Lawrence and/or Lincoln Co., TN (though Josiah, Senior and Junior were eventually over in Rutherford Co., TN and Hickman Co., TN).
I note that in 1840, both Bryant Davidson in Lawrence, and Joel Davidson (probably Bryant's brother) in Lincoln, had sons in their homes who were in the correct age range to have been the younger William J. Davidson (born about 1830)....and those two men were almost certainly members of DNA "Family 10."There was also a later/younger Joel Davidson who was on the 1850 Lawrence Co., TN census, and I believe that he was a son of Bryant Davidson.Living in that home with that younger Joel Davidson was the widow of Bryant Davidson named Mrs. Sarah (James) Davidson (who Bryant had married back in Grainger Co., TN).One of the other people living in that home with Joel and his apparent mother Sarah in 1850 is shown on my census transcription as William "D." Davidson, age 20.I wonder if he was actually the William "J." Davidson who married Rhoda Keeling a year later in Lewis Co., TN in 1851?One of Joel's obvious relatives named Jesse Davidson lived over in Lewis Co., TN in 1850, and Joel Davidson's future wife Mary Cody lived in the home of that Jesse Davidson in 1850 (the younger Joel Davidson and Mary Cody married a year later in 1851....just like William J. Davidson and Rhoda Keeling did)!If you have access to the original 1850 census, perhaps you could look to see if William's middle initial looks like a "J" versus a "D" on the 1850 Lawrence Co., TN census.
By the way, when some of the above Davidsons were in Grainger Co., TN in the early-1800s, there were also members of at least two other (and almost certainly unrelated) Davidson families who there.One of those other families was part of DNA "Family 8," but the other family in Grainger Co., TN was out of the James Davidson/Mary Bean family from PA, and several members of that family moved to Orange Co., NC (they were there well before "my" William Davidson in DNA "Family 10" went there in 1780).Some people have "suggested" that this group COULD have been part of your overall DNA "Family 4"....but I have no idea if that is correct.If it is correct, however, then perhaps your family and some of the above members my family became friends and neighbors in Grainger Co., TN in the early-1800s, and maybe that led to them both appearing in close proximity in Missouri later on (but that is just me "thinking way outside of the box")!Comments? Bill