Sir Gilbert Fraser, Kt., Sheriff of Tweeddale - A brother, not a son, of Bernard?

https://archive.org/details/scotspeeragefoun07paul/page/419/mode/1u...
SCOTS PEERAGE states Gilbert is a brother of Bernard and son of Udard.

pg 418 - Udard Fraser married a sister of Oliver . . . He was the father of Adam Fraser, named below.
pg 418 - During the early part of the thirteenth century the three chief Frasers in Scotland were Bernard, Gilbert, and Adam, who were all probably the sons of Udard. (cites Fraser of Philorth, I. 15, 16
pg 420- Sir Gilbert Fraser, probably a brother of Sir Bernard and Adam Fraser, is the direct ancestor of the Frasers of Philorth.

What is the source that Bernard is his father?