According to my understanding of the M222 y-dna genetic tree M222 S588 descends from Donald II the 9th Lord of the Isles (r. 1387-1423). I also propose that S603 y-dna descends though his son Duncan. However there is a branch of S588 that descends through Alexander IV the 11th Lord of the Isles (r.1440-1449) another son of Donald II. This Alexander I propose was also Alexander the 1st Lord of Keppoch as well as the Earl of Mar. He has been confused by some with his uncle Alexander III the 10th Lord of the Isles (r.1423-1440) from whom the A259 and A260 clades of M222 descend.
In doing some research into the McAtee, I found that they descend from S588 along with an O'Donnell and some other surnames. There is a legend that the MacAteer and MacAtee families of Scotland took this name when a O'Donnell or MacDonald ancestor plugged a boat that was sinking with his chopped off thumb. This legend is also part of the origin legend of the MacIntyre family. The Gaelic version of MacAteer, MacAtee and MacIntyre is Mhac an t'Saoir.(see McIan, R.R. and Logan, James. The Clans of the Scottish Highlands. New York: Crescent Books, 1985.)
In fact Alexander IV MacDonald was also known as Alexander McDonell (McDonnell) as the 1st Lord of Keppoch (died 1478). The legend states that the ancestor who did this heroic deed was a son of the Lord of the Isles. These are the MacDonald Lord of the Isles which are divided into two male lineages of R1a and R1b M222.
Thus this branch of S588 may descend from Angus McDonell the 2nd Lord of Keppoch. From him also descends S7814 y-dna clade of S588 y-dna. By the 18th century one branch of this family was using O'Donnell rather than McDonell as their surname. This probably means the family moved to Ireland. It would seem that some who took the name O'Donnell had their origin in FGC4077 y-dna branch of M222 descended from Donald III King of Scots (r.1034-1040). Are these the Donegal O'Donnell lineage? Another Irish branch of the O'Donnell family are DF85 y-dna who are a brother clade to S588 and descend from another brother of Donald II who is the son of John Alexander the 8th Lord of the Isles (r.1345-1387) the ancestor of all DF105 y-dna. It is possible that Donald II the 9th Lord of the Isles is himself both the ancestor of S588 and DF85.
It is also interesting that MacIntyre is associated with the clan of the Earls of Mar. This latest research would seem to once again confirm my dating of the M222 haplogroups as proposed in my numerous blog posts on this topic. It is important to keep in mind the more rapid periods of dna mutation during the heights of the Medieval Warm period as well as the Little Ice Age. We see a diversity of surnames due to men taking maternal surnames of their mothers or wives as well as love affairs with married women. Many of the Scots who came to Ireland in the Middle Ages adopted Irish versions of their surname or took the name of their wives of the clan in which they joined in Ireland.