On the one hand, the bow and arrow is genius and a credit to human ingenuity - on the other hand, it's pretty basic and as a basic tool constructed from easily found materials - it could be present in all cultures that have readily available sticks and have animals that could be more effectively hunted with bows and arrows than with spears. read more
However, fletching, and the use of string and elasticity to launch arrows and darts dates to as early as 16000BC, so all of the people who made use of the bow and arrow in historical times, almost certainly belong to a group of people who either originally had it, as an idea, or obtained it through trade. read more
The reason it's spread was so prolific was that it was the difference between survival of the haves, and the have nots. Whoever possessed Bow technology had significant hunting and defense technology over those who did not. Also technology like Bows can spread faster than migration in that an entire culture doesn't have to show up to pass it along. All that has to show up is a guy from that culture with a bow, and the ability to make another one. read more