Blue shaded area is estimated as descendants of. Of special interest would be the area of Cumbria.
I-BY101763 1037 CE Scotland
https://heraldry.celticradio.net/search.php?id=35
As stated by the eminent historian, William F. Skene in 1837, "the Robertsons of Struan are unquestionably the oldest family in Scotland, being the sole remaining branch of that Royal House of Atholl which occupied the throne of Scotland during the 11th and 12th centuries." The male line of this royal house ended in 1286 with the untimely death of Alexander III when he fell from his horse.

Who are the Donnachaidhs, the "Children of Duncan"? Their ancestors were known to the Romans as the Kaledonioi, one of the eleven tribes of the northern Pictish nation. The Kaledonioi inhabited that part of Scotland now known as Atholl in Perthshire. One of the first recorded entries on this people occurred in the year 84 A.D., when they fought in the great battle known as Mons Graupius against the Romans.

The Clan Donnachaidh descends from King Malcolm II who reigned from 1005 to 1034 and was the last king in the direct male line to descend from Kenneth MacAlpine, who united the Scots and Picts in 843 A.D. and is considered the founder of Scotland. One of Malcolm's three daughters, Bethoc, married Crinan, the secular hereditary Abbot of Dunkeld. Through her, the Abbot's son, Duncan, was installed by Malcolm as the King of Cumbria in 1018.

Ancient YDNA Matches, Denmark: https://discover.familytreedna.com/y-dna/I-BY78405/ancient

Roberson BigY GlobeTrekker Map
Dec 9 2023 Hap I-FT223253
https://discover.familytreedna.com/groups/clan-donnachaidh/tree?subgroups=24716
M253>DF29>Z58>Z59>Z2041>Z2040>Z382>FGC24333>S26361>S16414>S22349>FGC24357>
FGC24347>FGC24356>S10350>BY19383>Y125947>S14393>BY149414>BY101763>BY78405>FT223253

https://discover.familytreedna.com/y-dna/I-S10350/tree
Enters Britainia I-FGC24347 450 BCE
Kingdom of East Anglia, East Coast of the North Sea
https://en.wikipedia.org/wiki/Kingdom_of_East_Anglia
https://www.historyfiles.co.uk/KingListsBritain/EnglandEastAnglia.htm
I-S10350 3 CE
I-BY19383 210 CE

I-BY101763 1037 CE Scotland
I-BY78405 1423 CE Scotland
I-FT223253 1697 CE Preston on the River Ribble > Virginia Colony and TN