What evidence shows that modern humans moved from Africa across Asia into Europe and finally into Australia and the Americas between 100000 and 35000 years ago?

National Geographic's Genographic Project has been conducting a huge genetic analysis of as many people as they can get, in order to map out the human population starting about 100,000- 150,000 years ago. They've actually put together a migration map that shows human origins in Africa, and tracked various genetic groups' travels out of Africa into the rest of the world. If you look for their website, it'll explain everything to you.