Final answer:
The best support for the 'out of Africa' model is the high genetic diversity found in African populations, indicating Africa as the origin of modern humans.
Step-by-step explanation:
The piece of evidence that BEST supports the 'out of Africa' model of the evolution of modern humans is that African populations show the greatest diversity in numbers at a short tandem repeat (STR) locus on chromosome 12. This genetic evidence indicates that human populations in Africa have the longest established genetic lineage, matching the 'out of Africa' model, which suggests modern humans first emerged in Africa about 200,000 years ago and later expanded out of Africa, spreading across the globe.
Genetic variance found in Africa that is not present in other parts of the world further supports this model, indicating a single originating population with subsequent mutations and adaptations occurring after the dispersion. Hence, genetic diversity in Africa aligns best with the suggestion that all modern humans can trace their lineage back to this continent.