What evidence exists to explain early human migration from one region to another?

Studies show that the pre-modern migration of human populations begins with the movement of Homo erectus out of Africa across Eurasia about 1.75 million years ago. Homo sapiens appears to have occupied all of Africa about 150,000 years ago; some members of this species moved out of Africa 70,000 years ago (or, according to more recent studies, as early as 125,000 years ago into Asia, and even as early as 270,000 years ago), and had spread across Australia, Asia and Europe by 40,000 BC. Migration to the Americas took place 20,000 to 15,000 years ago. By 2000 years ago humans had established settlements in most of the Pacific Islands. Major population-movements notably include those postulated as associated with the Neolithic Revolution and with Indo-European expansion. The Early Medieval Great Migrations including Turkic expansion have left significant traces. In some places, such as Turkey and Azerbaijan, there was a substantial cultural transformation after the migration of relatively small elite populations. Historians see elite-migration parallels in the Roman and Norman conquests of Britain, while "the most hotly debated of all the British cultural transitions is the role of migration in the relatively sudden and drastic change from Romano-Britain to Anglo-Saxon Britain", which may be explained by a possible "substantial migration of Anglo-Saxon Y chromosomes into Central England (contributing 50%–100% to the gene pool at that time)."