1)
In 2011 a Boaz descendent whose distant cousins are in our DNA Project raised the possibility of a completely different and Scottish origin of some of our surname variants. According to his Boaz research:
Another often cited source are the names of the families (septs) associated with Clan Watson...
Belboys, Boas, Boece, Boeis, Boes, Boess, Boice, Boiss, Boiste, Boos, Boost, Bos, Bouse, Boust, Bowayse, Bowes, Bowis, Bows, Bowys, Boyce, Boyes, Boyess, Boyis, Boys, Boyse, Boze, Buist, Buste, ......
It is also interesting to note that in a more complete list of Clans and Septs, the names most similar to Boaz are only associated with Clan Watson [links added to names we have a map page for]. [1]
If any of these names stem from Clan Watson, you would expect their geographic concentrations to overlap with those of Watson. While Clan Watson's chiefs from ? up to at least 1818 lived at Saughton in East Lothian County, [2] Clan Watson's origins based on the 1881 census appear to be in Lanarkshire when using absolute numbers.

When mapped per 100,000 people, the Watson origins change to neighboring Peebleshire:

The last map, showing four high frequency hotspots. indicates there may have been more than one Watson clan in Scotland. Since Watson means "son of Walter" this would not be at all unusual.
It's not clear which of Scotland's Watson population centers may relate to English Watson settlers in Scotland as opposed to a Scottish Clan Watson.
When we compare distribution maps between the Watsons and its associated septs listed above, we find:
[in progress]
2)
Referring to the distribution of similar names in Scotland, Lillian Johnson in Historic Cane Ridge and Its Families writes:
In the eastern counties of Forfar and Fife, on the other hand, the greatest variety of forms are found in actual use and in written documents, and it may be taken that all the present varieties, excepting Boyes and Boss, had their origin in these two counties; the forms Boas, Boes, Boaz, etc. are of Forfarshire, and Bowes, Buist, Boosie, etc. are of Fifeshire. [3]
Here again the 1881 census maps offer clarification using data that was unavailable to Johnson.
Boas is an extremely rare spelling with just one occurence in Angus, Scotland in 1881. It's interesting that by 1973 Johnson finds them in Forfarshire at all.
Boes, another rare spelling, is seen originating in Wigtown, Scotland.
Boaz as a spelling, although rare in Scotland, appears to have origins more clearly associated with western England.
Bowes, while not a rare name in England or Scotland, and many of whom have English roots, only has one occurrence in Fife, Scotland in 1881, with the majority further south and west, again not supporting Johnson's observations.
The maps were created using Archer Software's The British 19th Century Surname Atlas CD.
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1. Boaz, Joel. Boaz Family History Pages. (http://www.boazhistory.com/showmedia.php?mediaID=19&all=1: Accessed 29 Dec 2011).
2. Watson, Shane. "The Chief of Clan Watson," Clan Watson: UK-Based Clan Website" (http://www.clanwatson.co.uk/ClanChief.html: Accessed 30 Dec 2011).
3. Johnson J., Lillian B., Historic Cane Ridge and Its Families. Nashville: Blue and Gray Press, 1973, p. 103.