H. sapiens evolved in place in Europe and Asia with gene flow and considerable convergent evolution. Monogenic H. Erectus evolved in Africa, left Africa 700,000 ya and spread throught Europe and Asia. H. sapeins evovled in Africa a second migration about 100,000 replaced H. erectus with Homo sapiens. Additionally, the only complete record of the transition to modern humans is in Africa B. Molecular 1. All molecular data indicates a origin at about 200,000 to 300,000 ybp, in one site, Africa.
Mutations occur through time.
The longer the time the more the mutations. If Modern humans are founder populations then they would aquire different variations than African populations. The amount would depend on the time they have been separated from the African populations. Given what we know about the rate of mutations in primates, the amount of diversity in modern populations in Europe would require only 200,000 to 300,000 years to accumlate. This time is too short to support the multiregional hypothesis.