The statement that did NOT affect the rise of empires in West Africa is:
Competition with Europe eventually diminished the need for Trans-Saharan trade route.
This is because the rise of empires in West Africa was primarily influenced by the richness of resources such as gold and salt, the spread of Islam, and the establishment of educational centers. The competition with Europe, while significant in later historical contexts, did not initially diminish the importance of the Trans-Saharan trade routes in the rise of these empires.