Brit/Irish tunes and North American variants

An English pub session friend wrote: “There must have been studies done on similarity of tunes that ‘crossed the water’…..you know the kind of thing, Irish A part, Appalachian B part because they’d forgotten the Irish B part etc. etc. are you aware of anything published on the subject?”
I suppose Samuel Bayard and Bertrand Bronson must have dealt with this somewhat (under the “tune family” concept), but I haven’t read their stuff for 30 years (and even then mostly to support my research on Japanese folk song). Can anyone suggest good readings for my friend?

A good website that provides background and sources for the tunes is The Fiddler’s Companion, http://www.ibiblio.org/fiddlers/.

My home state of West Virginia can boast of the famous Hammons family (there are numerous spelling variants).

Edden Hammons was regarded a top fiddler in the late 19th century. He was recorded, though as a very old man, out of practice, and on a borrowed fiddle. His great store of music was handed down to him within his family, who were among the first white settlers in Appalachia.

You may recognize this lovely tune

https://www.youtube.com/watch?v=baYoQMkXXRY

play video

This Edden Hammons tune reminds me more of Shetland fiddling than Irish

https://www.youtube.com/watch?v=irYc6bG78lw

play video