This chart is still under construction and additional information will be added as Joe Slavin forwards it to me. Joe wanted to be sure everyone knows that this chart is not complete or comprehensive.
The earliest three generations of the Livingston family in Scotland are shown below.
1. Leving de Livingston (a Saxon immigrant)
.....2. Thurstan de Livingston
..........3. William de Livingston - succeeded his father (Thurstan) to ownership of the family properties, etc. in the year 1200. That succession is the last record of the surname we can find until Andrew and Archibald some 90 years later.
..........3. Alexander de Livingston
..........3. Henry de Livingston - married Marie de Scalebroc
Levin de Livingston may have had two additional sons - Hugh and German (Burgess of St. Andrew's). No descendants are known for either.In the year 1187, two of Thurstan de Livingston's sons (William de Livingston and Alexander de Livingston) witnessed a charter on which Thurston was involved. Thurstan de Livingston's third son, Henry de Livingston did not witness this charter.
The last record of these early Livingstons is a charter around the year 1200. Then there is a gap of about 90 years before the surname surfaces in records again - this time with two kinsmen, possibly brothers, namely: Andrew de Livingston and Archibald de Livingston. Both were members of Parliament in 1296.
Archibald was Sheriff of Linlithgow by 1301 and had his own castle by 1310 or so. His line rose to power earlier on than Andrew's, but died out in the mid 1500's. One of the Salisbury, MD, Livingstons managed to find the earliest yet record of Archibald dating to the year 1291.
Andrew was Sheriff of Lanark in 1296 and probably the Sheriff of Lanark killed in 1297 trying to suppress William Wallace's rebellion. Andrew is the first person on the chart shown below.

First Six Generations:
1. Andrew de Livingston - married Elena de Caranteles
....2. William de Livingston - died about 1339. William married Margaret (Comyn??). They had two sons, William de Livingston (who was given the lands of Callendar by King David II) and John de Livingston
.......3. William de Livingston obtained Callendar (firmed up his claim to these lands by marrying Christian de Callendar, the daughter of Sir Patrick de Callendar. Patrick had been stripped of the lands of Callendar by King Robert the Bruce because he had supported the politically wrong side. William was granted the lands by Robert's son, King David II. William died prior to December 1, 1364.
..........4. Patrick Livingston - died sometime after October 5, 1357 (before his father) Patrick was first in line to inherit Callendar, but his early death prevented that.
..........4. William Livingston
..........4. John Livingston of Callendar - born about 1356 and died September 14, 1402.
He married (1) a daughter of Menteith
.............5. John Livingston Burgess of Stirling - born before 1381
................6. John Livingston Burgess of Stirling
...................7. John Livingston claimant to Terrintirran
.............5. Alexander Livingston of Callendar - Regent of Scotland 1437 - born before 1381 - assumed to have died in the early 1450's - when King James II did his 45 day blitzkrig purge of the Livingston and associated nobles which brought about the death of Robert Livingston (not sure which Robert - there was a Robert, brother of Alexander Livingston of Callendar and there was also one descended several generations down from William de Livingston, or could have been another Robert??) and Alexander Livingston of Phildes via hanging and beheading on Castle Hill in Edinburgh on January 21-22, 1449/50 - at this time Alexander Livingston was in England on a diplomatic mission for King James II. Upon his return to Scotland, Alexander Livingston of Callendar was arrested and imprisoned in Dumbarton Castle - where the others arrested were still being held captive. Alexander Livingston of Callendar seems to have been released within the year of his imprisonment, but apparently he had lost all heart or drive and little more was really heard from him. He was over 70 by then and apparently just faded away and died not long afterward.
................6. James Livingston First Lord Livingston, of Callendar
................6. Alexander Livingston of Phildes (d January 21, 1449/50 - The year by current calendar systems was 1450, recorded by the old calendar system was 1449)
.............5. Robert Livingston - born before 1381
John Livingston of Callendar married (2) Agnes Douglas
.............5. William Livingston (the first of the Kilsyth Livingston line - one of the lines that leads to Robert Livingston of New York)
Kilsyth Line:
............5. William Livingston of Kilsyth
...............6. Edward Livingston of Kilsyth
..................7. William Livingston of Kilsyth
.....................8. William Livingston of Kilsyth
........................9. Alexander Livingston of Kilsyth
...........................10. Barbara Livingston of Kilsyth - married Alexander Livingston of Monyabroach who was son of James Livingston, who was another son of (9) William Livingston, the Fourth Lord Livingston of Callendar. Barbara Livingston of Kilsyth and Alexander Livingston of Monyabroach were the parents of William Livingston of Monyabroach who married Agnes Livingston of the Halls of Airth (see # 11. Agnes Livingston of the Halls of Airth)
.....3. John de Livingston (son of William, grandson of Andrew) died about 1366. John married a daughter of Wemyss and the line of his descendants lived in East Wemyss and Drumry, Scotland.
.........4. Robert Livingston - died about 1402
............5. Robert Livingston - died about 1466
...............6. James Livingston - died in Newbigging
...............6. William Livingston - died about 1494
..................7. Robert Livingston - died about 1503. Married Christian Presteun
.....................8. Robert Livingston - died in Flodden, Scotland, about 1513. Married Janet Beatoun
........................9. Margaret Livingston - died in Finnart, Scotland. Married James Hamilton

Descendents of James Livingston, First Lord Livingston of Callendar:
................6. James Livingston First Lord Livingston of Callendar
...................7. James Livingston Second Lord Livingston of Callendar
...................7. Alexander Livingston
......................8. James Livingston 3'rd Lord Livingston of Callendar
.........................9. Alexander Livingston of Terrintirran
............................(one of the guardians of Mary Queen of Scots)
............................10. Alexander Livingston of Terrintirran
................................11. Gabriel Livingston of Terrintirran
....................................12. ALexander Livingston of Terrintirran
........................................13. Alexander Livingston of Terrintirran
............................................14. John Livingston of Terrintirran
.........................9. William Livingston 4'th Lord Liv. of Callendar
............................10. Alexander Livingston 5'th. Lord Liv Callendar
................................guardian of Mary Queen of Scots...
................................11. William Livingston 6'th Lord Liv of Callendar
11. William Livingston, sixth Lord Livingston of Callendar
....(See above)
....12. Alexander Livingston, Seventh Lord Livingston of Callendar and First Livingston Earl of Linlithgow)
........13. James Livingston, First Earl of Callendar
........13. Alexander Livingston, Second Earl of Linlithgow
............14. George Livingston, Third Earl of Linlithgow
................15. George Livingston, Fourth Earl of Linlithgow
................15. Alexander Livingston, Third Earl of Callendar
....................16. James Livingston, Fourth Earl of Callendar and Fifth Earl of Linlithgow
........................17. Anne Livingston, Last Livingston of Callendar and Last Livingston of Linlithgow (married William Boyd, Earl of Kinmarnock
............14. Alexander Livingston, Second Earl of Callendar
................15. Alexander Livingston (a natural son)(could not inherit Callendar, made a Baronet)

Descendents of Alexander Livingston of Phildes:
6. Alexander Livingston of Phildes
....(See above)
.....7. Alexander Livingston of Dunipace
........(purchased the lands of Dunipace)
........8. David Livingston of Bantaskine
...........9. Alexander Livingston of Bantaskine - Alexander earned his Master's of Arts degree at St. Andrew's College. For a number of years, Master Alexander Livingston of Bantaskine (the natural son of David Livingston of Bantaskine) was placed higher in the hierarchy of potential inheritors of some properties (by Master Alexander Livingston of Dunipace) than his legitimate half-brother, Alexander Livingston of Bantaskine.
..............10. John Livingston of Bantaskine
..................11. Alexander Livingston of Bantaskine
..................11. Elizabeth (Elspeth) Livingston of Bantaskine
......................(married David Livingston of Banton)
......................12. David Livingston of Polmont and Bantaskine
..........................13. Alexander Livingston b 1621 Falkirk Parish
..............................(inherited Bantaskine, died bef. 1646)
..........................13. John Livingston b 1623/24 Falkirk Parish
..............................(Did John die young ?? no further records of him exist in Scotland)
..........................13. David Livingston b 1629 Falkirk Parish
..............................(inherited Bantaskine 1653)
..............................14. Michael Livingston b Falkirk Parish
..................................(a poet, Michael lived long, m twice)
..................................15. Isobel Livingston d 1757, never married
......................................(Bantaskine line ends here)
............9. Master Alexander Livingston (of Bantaskine)
...............(a 'Natural' son of David Liv. of Bantaskine)
.........8. Master Alexander Livingston of Dunipace and Phildes
............(recovered the lands of Phildes)
............9. Thomas Livingston of Kirkland
...............10. John Livinston of Kirkland
...................11. Alexander Livingston of Kirkland
.......................12. David Livingston of Delajoy
...........................13. William Livingston 1'st Merchant Aberdeen (Note: It was under the children of William Livingston and Bessie Goodall that Edwin Brockholst Livingston found sons, John born 1684 and William born 1682 that he mistook for John III and his brother, William, both of Poropotank Creek, Virginia)
...............................married Bessie Goodall...
...............................(Aberdeen line descends here..)
...............10. Alexander Livingston of the Halls of Airth
...................11. Agnes Livingston of the Halls of Airth
.......................(married William Livingston of Monyabroach
.......................12. Master John Livingston of Kilsyth (or Monyabroach??)
...........................13. Robert Livingston (head of the NY line)
.......................12. Rev. William Livingston (moved to County Dowe, Ireland)
...........................13. George Livingston (moved to South Carolina)
...........................13. Henry Livingston (moved to Barbados)
...........................13. William Livingston (moved to Barbados)
.......................12. Samuel Livingston
...........................(this is the man Lucille Barco Coone hoped had a son named John, but NO such son shows in NY records)
..........9. John Livingston the Elder of Dunipace
..............10. John Livingston the Younger of Dunipace (Named a Knight, besides being third Lord Dunipace)
..................11. David Livingston, First Knight Baronet of 'Livingston - Dunipace' (Note: Jean Livingston, who married John Kincaid, the Laird of Warrestoun in the Scottish ballad of 1600 about this Laird's murder and Jean's execution - was a sister of this David Livingston. She was born in 1579, married by 1594, dead in 1600.)
......................12. John Livingston of 'Livingston - Dunipace'
..........................(the John that Julian Livingston thinks was John Livingston I of Poropotank Creek)
Information provided by Joe Slavin
Note:
This chart is very incomplete - just skeletal and only of the lines Joe has explored to date and does not give dates, include wives (multiple in many cases) and skips all siblings not involved in the actual descendancy shown here.
There are many more siblings and many more lines that descend from both those in this chart and from siblings of those that are not shown here. The purpose of this chart is to simplify the structure to show how some of the main lines of interest to us in the U.S. descended and were linked together - nothing more than that. There is plenty of room in this chart for flushing it out and enhancing it.
The sources are several - some of them being Edwin Brockholst Livingston's first (1887) and second (1920) editions of his 'The Livingstons of Callendar and Their Principal Cadre'; John C. Gibson's 1903 Stirling, Scotland published 'The Lands and Lairds of Dunipace'; and annotated ancestral heraldry writings done by Master John Livingston, D.D.
Additional Note: Double dating is a practice introduced to show both the recorded date (by the old system) and the actual date (by today's system) for an event. It only affects the dates between January 1 and March 23rd or 24th. If a recorded date fell between those two dates in a given year and the country was under the old system (the U.S. was for all the Colonial period up till the 1740's) then the date for genealogical purposes should be recorded with double dating (i.e. January 21, 1449/50).