The best explanation for how humans populated the Earth is

they migrated from Asia to other continents over the last two million years.
they migrated mostly over land from Africa over the last eighty thousand years.
they developed varied human species in different places over millions of years.
they traveled by boat from Africa to other continents over the last forty thousand years.

The most accurate and widely accepted explanation for how humans populated the Earth is that they migrated from Africa over the last eighty thousand years. This theory, known as the Out of Africa theory or the recent African origin of modern humans, suggests that Homo sapiens evolved in Africa and then gradually spread to other continents.

Archaeological and genetic evidence supports the theory that humans originated in Africa and began to migrate in multiple waves. These migrations were likely facilitated by various factors such as climate change, the availability of resources, and technological advancements. As humans gradually migrated out of Africa, they encountered different environments and adapted to them over time, leading to the development of varied human species in different places.

While humans did travel by boat and potentially reached certain islands or coastal areas, such as the movement across the Wallace Line in Southeast Asia, most of the initial migration is believed to have occurred over land. These land migrations would have allowed early humans to follow resources, explore new territories, and encounter other hominin species, such as Neanderthals and Denisovans.

It is important to note that the exact timeline and details of human migration are still subjects of ongoing research and continue to be refined as new discoveries are made. However, the prevailing consensus among scientists is that the majority of human population expansion occurred through land-based migration from Africa, rather than primarily by boat travel or long-term development of isolated human species.

The best explanation for how humans populated the Earth is that they migrated mostly over land from Africa over the last eighty thousand years. This theory, known as the "Out of Africa" theory or the "replacement model," suggests that anatomically modern humans originated in Africa and then gradually migrated and replaced other hominin populations, such as Neanderthals, across different continents. It is supported by genetic and fossil evidence and is widely accepted by the scientific community.