Population migrations have occurred, reoccurred, and are occurring throughout history and today. I am still (unsuccessfully) trying to find out where the earliest ancestor on my Father's side (a Catholic planter in Easter Shore Md, circa 1680's) came from. If I ever do, it will undoubtedly be related to something like the lowland clearances, or the Commonwealth, or?

I believe the largest in modern history was right after WWII when India and Pakistan (both East and West) became independent from Great Brittan.