Final answer:
The 'out of Africa' model is the best supported by genetic evidence for the spread of Homo sapiens, suggesting a single origin in Africa with subsequent global migration and potential interbreeding with other human species.
Step-by-step explanation:
The explanatory model for the spread of Homo sapiens out of Africa that is best supported by current evidence is the "out of Africa" model.
This model posits that modern humans first appeared in Africa about 200,000 years ago and then moved out of the continent roughly 100,000 years ago, subsequently replacing all other hominin species.
This theory is backed up by genetic research showing that human genomes tested outside of Africa have close ties to the genomes of people in Africa, but with a genetic variance that is not found in the rest of the world, indicating a common origin.
On the other hand, the "multiregional evolution model", which suggests concurrent evolution of Homo sapiens from Homo erectus in various regions, relies more on fossil and archaeological data rather than genetic evidence.
The growing complexity of genetic evidence hints that interbreeding with other human species, such as Neanderthals, may have occurred as modern humans expanded globally, suggesting a potential blend of both models in our evolutionary history.