The beginning point of this family tree of the Murray Earls and Dukes of Atholl is Sir John Murray, 1st Earl of Tullibardine who was created 1st Earl of Tullibardine in 1606. His son William Murray 2nd Earl of Tullibardine inherited the title after his death. The succession following William Murray 2nd Earl of Tullibardine is confusing because William 2nd Earl of Tullibardine resigned the earldome shortly before his death.*
William's 2nd wife was Dorothea Stewart who was the eldest daughter of John Stewart the 5th Earl of Atholl of a previous creation of the earldome of Atholl. Dorothea's father died without a male heir. Dorothea and William petitioned Charles I to recreate the earldome of Atholl so that their son John could become the Earl of Atholl. Part of the petition was to pass the earldome of Tullibardine to William's brother Patrick Murray. William renounced the earldome of Tullibardine but died before the changes were made official.
In 1728, Patrick Murray succeeded to the earldome of Tullibardine and John Murray succeeded to the earldome of Atholl – John Murray became the 1st Earl of Tullibardine and John Murray became the 1st Earl of Atholl. After Patrick Murray's death James Murray inherited the earldome of Tullibardine and became the 2nd Earl of Tullibardine. Finally, after James Murray's death John Murray 2nd Earl of Atholl succeeded to the title of 3rd Earl of Tullibardine.
* p. 133 BURKE'S PEERAGE & BARONETAGE, 106th ed., London : Fitzroy Dearborn, c1999, Vol I:
"WILLIAM MURRAY, 2nd and last EARL OF TULLIBARDINE. which on the understanding that the King would revive the Earldom of Atholl for his (WILLIAM'S) issue by his 2nd w he resigned 1 April 1626 so that it could be regranted to his bro Patrick ..., since he wished the Earldoms of Tullibardine and Atholl to descend in two different branches of the Murrays...."