Another example might be the Anglo-Saxons "invasion" of Britain near the end of the Western Roman Empire. The reason why the Anglo-Saxons migrated to Britain isn't entirely clear but it appears throughout history there are periods of mass population movements due to various reasons such as climate change, population explosions or invasion by "steppe people" as Dan Carlin refers to them.
The entire history of Europe for the past 4,000 years is of migrations from the East to the West. First the Lusitaninans, Basques, Etruscans, and Belgae, then the Celts (let's include the Gauls in that group), then the Mycenaeans, then the Greeks, then the Romans (who were Latins,), then the Franks, Angles, Saxons, and other Germanic tribes, then the Huns and Slavs. Roughly.
In the Iberian Peninsula we also had a migration from the South to the North with the Muslim conquest that started in 711, but apparently they didn't leave that big of a genetic legacy.
Yeap there does seem to be a general drift from bottom-right towards top-left on the map of europe. Except, perhaps, the vikings who went from north to south?
> The reason why the Anglo-Saxons migrated to Britain isn't entirely clear
Ye, it's really complicated. I was taught as a kid that the initial Anglo Saxon 'invasion' was a rebellion by Anglo-Saxon warriors against the British King whop had hired them as mercenaries. But in fact it was a really complex movement of populations that played out over > two hundred years [0].