Here is an excellent albeit concise piece taken from another website (Hodgson) and as such it is only proper that credit is given to the authors.
What is really interesting and augments exactly what our society has said for years based on the current evidence, is that this progression clearly shows that Annandale was not greatly influenced by the Gaels from Ireland but rather, as all the research suggests, by the Brythonic Celts and the Anglo-Saxons.
In the Maps, purple shows the influence and immigration of the Gaels from Ireland and red the indiginous Brythonic tribes covering Wales and South West Scotland ie Annandale, ancestral home of Carruthers.
Progression of the Scottish Borders 800-900 AD through the unification of England
The maps below shows the changing political map in Britain from AD 829 to AD 1157. In this period the modern territories of England, Scotland and Wales were created. The boundaries between them have since changed only slightly. Note that the main aim here is to show political territories, rather than the pattern of cultural and ethnic settlement. However, some areas of Norse settlement are indicated where they were largely autonomous and less subject to another political authority.
The Anglo-Saxons arrived on the eastern and southern coasts in large numbers in the sixth and seventh centuries. The Viking invasions started in AD 865, when Danes arrived on the east coast and established settlements. Norse colonised places on the west coast of Britain from AD 902. The Anglo-Saxon Kingdom of Northumbria was defeated by the Viking invaders and forced to pay homage to the Danish Kingdom of York. The Anglo-Saxon kingdoms of Mercia and Wessex remained. To the west were Celtic kingdoms in Wales and Strathclyde.
In AD 918 the Irish-Norse under Ragnall took control of the Danish Kingdom of York.
Subsequently the Strathclyde Britons entered into an alliance with the Irish-Norse in Cumberland. The Norse held York until AD 927 and from AD 939-54.
After his victory over the Anglo-Saxons in the battle of Ashdon in Essex in 1016, the Danish King Canute became the ruler of a united England. He and his sons ruled until 1042, when England returned to Anglo-Saxon control. The Normans invaders arrived on the south coast of England in 1066. They did not take Carlisle and Cumberland until 1092.
The unification of England in this period did not mean that the English subjects all began to speak the same language. The English population was a motley collection of different cultural, ethnic and linguistic groups, as a result of multiple invasions over the preceding centuries.
The Norman aristocracy continued to speak Norman French for some time. Forms of Norse and Danish persisted in the areas of former Viking settlement until the thirteenth century (Bugge 1921). Celtic languages persisted in Wales and Strathclyde. But Celtic speakers were also found in parts of England such as the Fens (Gray 1911). English regional dialects were very different from each other. It was much later that a common English language began to emerge.
Bugge, Alexander (1921) ‘The Norse Settlements in the British Islands’, Transactions of the Royal Historical Society, 4th Series, Vol. 4, pp. 173-210.
Falkus, Malcolm and Gillingham, John (eds) (1981) Historical Atlas of Britain (London: Grisewood and Dempsey).
Gray, Arthur (1911) ‘On the Late Survival of a Celtic Population in East Anglia’, Proceedings of the Cambridge Antiquarian Society, 15, pp. 42-52.
Moore, R. L. (ed.) (1981) The Hamlyn Historical Atlas (London: Hamlyn).
Treharne, R. F. and Fullard, Harold (eds) (1963) Muir’s Historical Atlas: Ancient and Classical, sixth edition (London: George Philip).