Original Soundtrack composed by: Jeffery L. Briggs, Ken Lagace and Roland J. Rizzo
Amiga Soundtrack by: Allister Brimble and Anthony Putson
Once again we come across a piece of music in Sid Meier's Colonization that's an adaptation of a real tune. "Shady Grove" is actually based off an Appalachian folk song which is commonly performed today by American bluegrass and old-time musicians. The tune is based off a traditional ballad from Britain called "Matty Groves" which dates as far back as the 17th century. The song travelled to the Appalachians during the American Civil War so it's probably a bit anachronistic having this play in Colonization (as the game is set before the United States even became a country) but hey it's a great track.
I thoroughly recommend you search for live performances of Shady Grove - there are some really good ones on YouTube!
EDIT (15/10/2016): A fellow YouTube user +Plastiware has alerted me to the fact that despite me originally advertising these tracks as the Amiga version of the soundtrack, it's probably not entirely accurate. I originally marked these as the Amiga version due to the source MP3s I used stating Allister Brimble and Anthony Putson as the composers, but when comparing these tracks to Amiga versions of the soundtrack on YouTube and then comparing it to a DOS CD version, it seems these are most likely from the DOS CD version. Apologies for the mistake.
[ VIDEO: Choicest VGM - VGM #233 - Sid Meier's Colonization - Shady Grove ]