Final answer:
The situation depicted by the dates on the map implies a Migration Period involving various Germanic tribes, such as the Goths and Vandals, who were seeking territories to settle and establish kingdoms, influenced by the westward movement of the Huns. This process indicates a gradual migration and settlement rather than a swift military conquest of Rome.
Step-by-step explanation:
The data given about the invaders in the texts suggests that what took place was not merely a rapid conquest but a Migration Period of people into Roman territories. This period, occurring from the fourth through the sixth century, involved various Germanic tribes including the Goths and Vandals, who were influenced by the westward push of the Huns from Central Asia. These migrations were characterized by group movements rather than rapid military invasions aimed at immediate conquest. While there were certainly instances of looting and the occasional seizure of territory as seen with the Goths and Vandals, many of these groups, such as the Vandals moving through Spain or the Goths establishing in southern Gaul, eventually settled down and created kingdoms of their own within the former Roman territories.
Furthermore, the pressure from Attila's Huns and the sheer number of barbarians crossing into Roman lands indicated a more complex dynamic than just conquest. It was a mix of forced migration, search for land, and power, leading to the reorganization of what was formerly the Western Roman Empire. The invaders established new cultural and linguistic groups in Roman territories with events such as the Anglo-Saxon establishment of England. Hence, the dates on the map would likely indicate a slower movement involving a combination of invasion, settlement, and cultural integration.