cross-pol·li·na·tion (krôsˌpŏlˌə-nāˈshən, krŏsˌ-)
noun
2. Influence or inspiration between or among diverse elements: “Jazz is fundamentally the cross-pollination of individual musicians playing together and against each other in small groups” (Ralph de Toledano).
http://www.yourdictionary.com/cross-pollination


I've often listened to Celtic Connections folk music festivals (Radio 3, Late Junction): it's interesting to hear how the different strains or strands (?) of Celtic music are influenced by the music of the countries in which they develop.
Here's an article about the cross-pollination with USA Celtic music, which explains why they talk about: 'genetically contaminated folk tunes'.

Celtic Connections: The melting pot
On Thursday evening in the Glasgow Royal Concert Hall, the first of two Transatlantic Sessions proves to be the lifeblood of the festival, with the big personality of slide guitar maestro Jerry Douglas pushing things along, fusing the heritage of our home isles with its close cousins abroad – bluegrass, cajun, gospel, blues. If, say, a country-ish tune played by Tim O’Brien or Ashley Cleveland strays too close to Nashville, the whistles and flutes of Michael McGoldrick throw a Celtic leash around its neck. If a set of reels featuring Aly Bain, Phil Cunningham and John McCusker heads off to a Highland ceilidh, the banjo of Dirk Powell steers it towards a bayou hoedown instead.
http://www.heraldscotland.com/arts-ents/music-reviews/celtic...