Arran mac Somairle - Sources?

What primary sources validate this profile?

Disconnecting as a child of Somerled, “King of the Isles”, pending primary sources

cf Brother [and sister], parents not known:
*1. [Somerled, “King of the Isles” SOMERLED] (-killed in battle 1164). Balfour Paul says that the first reference to Somerled records him as living in the district of Morven with his father Gillebride, but he does not cite the precise source[1019]. Lord of Argyll. He acquired control of the Western Isles and assumed the title "King of the Isles". The Chronicle of Melrose records that Somerled Lord of Argyll landed at Renfrew in 1164, after 12 years of rebellion against Malcolm IV King of Scotland, with a large army from Ireland but was defeated and killed with his son[1020]. The Extracta ex Cronicis Scocie records that "Sumerlendus regulus Ergadie" rebelled against King Malcolm for 12 years, landed at Renfrew from Ireland, and was killed "et filium suum Gillecolanem", among passages dealing with events in 1164[1021]. The Annals of Ulster record that "Somharlidh Mac Gilla-Adhamhnain and his son were killed" in 1164[1022]. The Book of Clanranald records that that no battle was fought and that Somerled was killed in his tent, after which his followers dispersed[1023]. m [Ragnhildr Óláfsdóttir, of Man --- of Man], illegitimate daughter of OLAV King of Man & his mistress ---. The Chronicon Manniæ et Insularum records that “Olavus filius Godredi Crovan” had many concubines by whom he fathered “filios tres…Reignaldum, Lagmannum et Haraldum et filias multas”, adding that one daughter married “Sumerledo regulo Herergaildel”[1024]. Balfour Paul names her "Ragnhildis" but he does not cite the corresponding primary source[1025]. Somerled & his wife had five children:
>*a) [Dougal MacRory, 1st of Dunollie and of Lorn DUGALD] (-after 1175). The Chronicon Manniæ et Insularum names “Dulgallum, Reginaldum, Engus et Olavum” as the four sons of “Sumerledo regulo Herergaildel” and his wife the daughter of Olav King of Man[1026].
>*b) [Ragnall mac Somhairle, Lord of the Isles REGINALD] . The Chronicon Manniæ et Insularum names “Dulgallum, Reginaldum, Engus et Olavum” as the four sons of “Sumerledo regulo Herergaildel” and his wife the daughter of Olav King of Man[1027]. The Chronicon Manniæ et Insularum records that Engus, son of Somerled, defeated his brother Reginald in 1192[1028].
>*c) [Angus of Bute & Arran ANGUS] (-killed 1210). The Chronicon Manniæ et Insularum names “Dulgallum, Reginaldum, Engus et Olavum” as the four sons of “Sumerledo regulo Herergaildel” and his wife the daughter of Olav King of Man[1029]. The Chronicon Manniæ et Insularum records that Engus, son of Somerled, defeated his brother Reginald in 1192, adding in a later passage that Engus was killed in 1210[1030]. Balfour Paul states that Angus inherited "Bute, with a part of Arran, and the Rough Bounds (Garmoran) extending from Ardnamurchan to Gleneig"[1031]. m ---. The name of Angus’s wife is not known. Angus & his wife had one child:
>*d) [Olav OLAV] . The Chronicon Manniæ et Insularum names “Dulgallum, Reginaldum, Engus et Olavum” as the four sons of “Sumerledo regulo Herergaildel” and his wife the daughter of Olav King of Man[1035].
>*e) [Gilliecolum mac Somairle GILLECOLAN] (-killed in battle 1164). The Chronicle of Melrose records that he was killed in battle with his father[1036]. The Extracta ex Cronicis Scocie records that "Sumerlendus regulus Ergadie" rebelled against King Malcolm for 12 years, landed at Renfrew from Ireland, and was killed "et filium suum Gillecolanem", among passages dealing with events in 1164[1037].
>*f) [Gall "the Foreigner" mac Somairle GALL Macsgillin] . Balfour Paul names "Olave and Gall Macsgillin" as two other possible sons of Somerled, but does not cite the corresponding primary source[1038]. Olav is named in the Chronicon Manniæ (see above) but not Gall.]
>*g) [Bethoc, Prioress of Iona BEATRICE] . Balfour Paul names "Beatrice prioress of Iona" as the daughter of Somerled, but does not cite the corresponding primary source[1039]. Olav is named in the Chronicon Manniæ (see above) but not Gall.]

*2. [Unknown sister of Somerled, of the Isles --] . Her parentage and marriage are confirmed by John of Fordun’s Scotichronicon (Continuator) records that "Summerledus regulus Ergadiæ et sui nepotes, filii…Malcolmi Macheth" rebelled against King Malcolm IV in the first year of his reign[1040]. This assumes that the term "nepos" should be interpreted as "nephews" in that source. Her marriage date is estimated assuming that it is correct that her husband was imprisoned from 1134, before which his two children must have been born. There would be no such restriction on the date if Malcolm son of King Alexander I and Malcolm MacHeth were two different persons as suggested by Duncan[1041]. m ([1130]) [Malcolm MacEth, Earl of Ross MALCOLM MacEth] … ([1105/15]-23 Oct 1168). He was created Earl of Ross in 1162 or before.]
*http://fmg.ac/Projects/MedLands/SCOTTISH%20NOBILITY.htm#_ftnref1019