It seems very clear that a lot of Roman senatorial families survived the barbarian migrations of the 5th and 6th centuries and were incorporated into the governing elites of the post-Roman kingdoms, especially in Merovingian Gaul, Ostrogothic Italy and Visigothic Spain. But I've heard it said that those which did survive didn't survive the upheavals of the 8th century (the Islamic invasions and the rise of the Carolingians) though there are plenty of views to the contrary, such as the attempts to trace continuity between the elites of Merovingian Gaul and Carolingian Francia. How many of these Roman senatorial families might have then survived up to the 11th century and later to form the noble families of the Central Middle Ages (I'm aware of the whole transformation of the family debate and how difficult it is tracing aristocratic lineages before the year 1000)? This is something I'm personally curious about, but its also linked to the novel I'm writing in which the protagonist is from a minor noble family in late 10th century Burgundy that claims to trace its ancestry all the way back to Republican Roman families (I know this might be slightly implausible since I've heard a lot of Classicists say that most Republican senatorial families didn't survive the reigns of Nero and Domitian).