Final answer:
The 'Out of Africa' model, asserting that Homo sapiens originated in Africa and then spread worldwide, is supported by genetic evidence. This model shows the closest ties between human genomes inside and outside Africa. While the multiregional evolution model has less support, recent DNA evidence suggests some interbreeding with Neanderthals occurred during the global spread of humans.
Step-by-step explanation:
The explanatory model for the spread of Homo sapiens out of Africa that is best supported by the evidence is the "Out of Africa" model. This theory posits that modern humans first appeared in Africa about 200,000 years ago, and around 100,000 years ago, they began spreading out of the continent, ultimately replacing other human species. This model is substantiated mainly by genetic evidence showing that non-African human genomes have close ties to African genomes.
Research supports the assertion that there is greater genetic diversity within Africa than in populations outside of Africa, suggesting a single origin for modern humans in Africa. Additionally, the genetic variance observed in Africa is not found elsewhere in the world. However, DNA evidence indicates that there was also some interbreeding with Neanderthals as humans migrated out of Africa, which points to a nuanced understanding where initial migration and subsequent interbreeding are complementary events in human evolution.
While the multiregional evolution model suggests simultaneous evolution of Homo sapiens from Homo erectus in different regions, the lack of genetic backing has made this model less favored compared to the Out of Africa model complemented by genetic intermixing with Neanderthals.