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Laly and Rothaer, re: the survival of Latin in Britain, as said Latin didn't take root outside cities/towns in Roman Britain, and the urban population at the end of the fourth century AD was only about 6%, so after the withdrawal of Roman troops in 410, abandonment of towns and probable emigration of many Romano-Britons it would be drowned amongst Brittonic speakers. Then starting less than 50 years later the Anglo-Saxons ~75% replaced the Britons (Celtic or Roman) in Southeastern Britain (where Roman settlement had been mostly concentrated) and culturally assimilated the rest, so a double-whammy.
The idea that the French speak Romance because Romance speakers outnumbered Celtic speakers at the end of the Empire sounds plausible, but I'm more curious how the hell Latin came to be spoken by most Gauls in a few centuries without large-scale immigration.
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