In the 10th century, Rhodri the Great had inherited Gwynedd from his father and Powys from his mother, and he added Seisyllwg (Ceredigion and Carmarthenshire) by a dynastic marriage to Angharad of Seisyllwg. Rhodri's influence in the rest of Wales was significant, and he left a lasting legacy.
The family were able to assert their influence within Gwynedd, their traditional sphere of influence, but by the 11th century they were ousted from Powys (Mid Wales) and Deheubarth (West Wales) by a series of strong rulers from the House of Dinefwr in Deheubarth, their dynastically junior cousins. The Dinefwr family were descended from the second son of Rhodri the Great. However, Gruffudd ap Cynan Aberffraw was able to recover his heritage and position as Prince of Gwynedd from Norman invaders by 1100. Owain Gwynedd, Gruffudd's son, defeated King Henry II of England and the vast Angevin host in 1157 and 1166, which led to Owain being proclaimed as Princeps Wallensium, the Prince of the Welsh, by other Welsh rulers. This proclamation reasserted and updated the Aberffraw claims to be the principal royal family of Wales, as senior line descendants of Rhodri the Great. This position was further reaffirmed in the biography The History of Gruffydd ap Cynan. Written in Latin, the biography was intended for an audience outside Wales. The significance of this claim was that the Aberffraw family owed nothing to the English king for their position in Wales, and that they held authority in Wales "by absolute right through descent", wrote historian John Davies.
By 1216 Llywelyn the Great had received the fealty and homage of the Dinefwr rulers of Deheubarth at the Council of Aberdyfi. With homage and fealty paid by other Welsh lords to Llywelyn at the Council of Aberdyfi, Llywelyn the Great became the de facto first "Prince of Wales" in the modern sense, though it was his son Dafydd ap Llywelyn who was the first to adopt that title. However, the 1282 Conquest of Wales by Edward I greatly reduced the influence of the family. King Edward I of England forced the remaining members of the family to surrender their claim to the title of Prince of Wales under the Statute of Rhuddlan in 1284, which also abolished the independent Welsh peerage. The Aberffraw family members closest to Llywelyn II were imprisoned for life by Edward, while the more distant Aberffraw members went into deep hiding and fell into obscurity. Other members of the family did lay claim to their heritage; they included Owain Lawgoch in the 14th century.
Royal succession within the House of Aberffraw (as with succession in Wales in general) was a complex matter due to the unique character of Welsh law. According to Hurbert Lewis, though not explicitly codified as such, the edling, or heir apparent, was by convention, custom, and practice the eldest son of the lord or Prince and was entitled to inherit the position and title as "head of the family" from the father. This was effectively primogeniture with local variations. However, all sons were provided for out of the lands of the father, and in certain circumstances so too were daughters (with children born both in and out of wedlock considered legitimate). Men could also claim royal title through the maternal patrimony of their mother's line in certain circumstances (which occurred several times during the period of Welsh independence). The female line of the dynasty was also considered to remain royal, as marriage was an important means of strengthening individual claims to the various kingdoms of Wales and uniting various royal families to that of Aberffraw, or reuniting factions after dynastic civil wars (for example with the marriage of Hywel Dda, a member of the Dinefwr branch of the Aberffraw dynasty, and Elen of Dyfed, daughter of Llywarch ap Hyfaidd, King of Dyfed). This meant that the female line was considered as a legitimate path of royal descent within the House of Aberffraw, with the claims of royal women to titles usually transferring to their sons.
Members of the House of Aberffraw would include Idwal Foel, Iago ab Idwal, Cynan ab Iago, Gruffudd ap Cynan, Owain Gwynedd, Gwenllian ferch Gruffydd, Llywelyn the Great, Llywelyn ap Gruffudd, and Owain Lawgoch. Several later Welsh families, including the Wynn family of Gwydir and the Anwyl family of Tywyn, would claim to be heirs of the dynasty.
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