The argument that modern homo sapiens evolved first in africa, migrated outward, and eventually replaced archaic homo sapiens is known as the

It is known as the 'replacement theory' or 'Out of Africa' theory.

This model proposes a single origin of modern humans, although the model does not preclude limited mixing between modern humans and earlier forms.

There appears to have been several waves of movement of modern humans out of Africa to other continents. The earliest was approximately 270,000 years ago, and then again around 130,000 years ago. These earlier migrations appeared to have mostly died out.

The most significant wave occurred 70,000 years ago, which spread along the coast of Asia, reaching Australia around 65,000-50,000 years ago.