Composed by Natalie MacMaster.
"Official" Website Version
She has the tune (hand written) up on her website without the alternate A3-4 bars. Just for completeness’ sake, the tune as seen there is:
D:Natalie MacMaster - "Live" 2002
|:G2 D GAB|AFD G2 B|AFF dFF|cBA Acf|
|G2 D GAB|AFD G2 g|gfd cdf|cdf [1 cAF:|[2cdf||
|:e2 d gab|gfd e2 a|fcc acc|gcc fga|
|[1 g2 d gab|afd g2 a|fgf cdf|cAF G3:|
|[2 gag gfc|dff fcA|Bdd dBG|Acc cAF|
David’s Jig, here, to be distinguished from David’s Hornpipe.
This tune is to be distinguished from David’s Hornpipe, recorded by the Northumbrian piper and fiddler Kathryn Tickell on her album "Borderlands".
In the first setting, Errik has written the "A" section twice, to include a slight variation on the melody in measures 3 & 4 of the "A" section, which is measures 11 & 12 of the score as written. If my (admittedly feeble) memory is correct, I believe that the variation that Errik has penned is how Natalie actually plays the tune.
The second setting correctly transcribes the tune as written on Natalie McMaster’s web site, EXCEPT that the two "g" notes in the first two measures of the "B" section (the 1st note of the first triplet in the first measure, and the 1st note in the second triplet of the second measure) are incorrectly notated as "e" notes.
The "g" notes in the first two measures of the "B" section are correctly notated in the first setting here.
As noted on her website, Natalie McMaster plays a set with David’s Jig, followed by "Valerie Pringles" reel. She then plays an improvisation, and finished the set with David’s Jig.