Did Alexander I use Presby/Scottish Naming Practices for his children?

I have wondered if Alexander I used the Presbyterian/Scottish naming practices, when he named his children?
If he did, would the tree below be accurate?
If others have a different order for his children, pleas post it here.

http://johnbrobb.com/Content/TheScottishOnomasticPattern.pdf

The ANCESTRAL Scottish Onomastic Child-naming Pattern:

The 1st son was named for his father’s father. William
The 2nd son was named for his mother’s father. John
The 3rd son was named for his father’s father’s father. Alexander
The 4th son was named for his mother’s mother’s father. Michael
The 5th son was named for his father’s mother’s father. James
The 6th son was named for his mother’s father’s father.
The 7th through 10th sons were named for their father’s 4 great-grandfathers.
The 11th through 14th sons were named for their mother’s 4 great-grandfathers.

The 1st daughter was named for her mother’s mother. Mary
The 2nd daughter was named for her father’s mother. Anna, or, Mary
The 3rd daughter was named for her mother’s father’s mother. Elizabeth
The 4th daughter was named for her father’s father’s mother. Jane
The 5th daughter was named for her mother’s mother’s mother.
The 6th daughter was named for her father’s mother’s mother.
The 7th through 10th daughters were named for their mother’s 4 great-grandmothers.
The 11th through 14th daughters were named for their father’s 4 great-grandmothers.

Alexander's Line:.............................His 1st Wife's Line:

Alexander Montgomery...................Unknown ???.
..m. Jane ???......................................m. Elizabeth ???.
| |
William Montgomery........................John ???
..m. Ana ??? (her father: James)........m. Mary
|
Alexander Montgomery I..m.......Mary, 1st & only wife ???
..Mary (Catherine?)..........m.......Robert Barnett
..Ana.................................m.......Hugh Dobbins
..William...........................m.......Jane Patterson
..John...............................m.......Martha Miller
..Elizabeth........................m.......William Maxwell
..Alexander II...................m.......Martha (Walker?) (her father: Alexander)

or

..Mary, 2nd Wife???.............................................................
..Michael..........................m.......Unknown
..James............................m.......Rebecca Davis
..Jane...............................m.......??? Casey?