The Venerable Bede tells us in his history of the English People and Church that different tribes from continental Europe came to England to make their homes and that certain parts of the country were settled by certain tribes, the Angles, jutes, and Saxons, hence names like West Saxons, East Anglians, and so on. This is the view that has come down through history and is widely repeated in less academic writings on the subject. Only this isn't how it happened, and modern scholarship has harshly critiqued the old views on the subject of the Anglo-Saxon migration.

Robin Fleming talks about how the "Anglo-Saxon migration" was really a broader movement of North Sea adjacent peoples into Roman Britain. This included people from Denmark (Jutland), and Northern Germany (Saxony), but also people from Norway, Ireland, and Sweden. The idea of the Anglo-Saxons as a purely Germanic culture is misguided and not supported by the evidence that we have available through archaeology. She points to the blend of clothing and jewelry styles that emerged following "Anglo-Saxon" migration to Britain as evidence that these two cultures were assimilating into something difference from either that came before. She views this process as more or less a peaceful one. While they was some endemic violence inherent to the time period, she does not see evidence for the mass violence that is often assumed to have accompanied the Germanic migration into Britain.

The idea that the newcomers, be they Angle, Saxon, Pict, or Irish, waded through Roman blood to carve out new kingdoms on the island of Britain that were derived of singular ethnic groups is entirely false.

One thing that is paramount to remember is that these various tribal groups and "peoples" did not form coherent national identities that were set in stone and unchanging. This view of the angles, saxons, and jutes, forming one coherent polity and the British another, oversimplifies the situation to an extreme degree and is an unfortunate holdover of the 19th Century.

Peter Heather argues that the identities of these groups were quite malleable in the social upheaval accompanying the end of the Western Roman Empire. Instead of kinship among these disparate groups of people, we should instead see loyalty between the armed retainers of a warlord/chieftain/insert your preferred noun here/ as the most paramount social identity. Status and position as an armed retained, a precursor to the later Huskarls and Housecarls, were much more important that subscribing to an identity of being "Saxon" "Anglish" or "Jutish".

England was not entirely repopulated by tribes from Denmark and the Low Countries, and the Vandals didn't even repopulate the city of Carthage, much less all of Iberia and Roman Africa. Indeed the newcomers to the Roman world, loosely defined as "Germanic" migrants, never constituted a majority of the population in any portion of the empire. Certainly in some areas, Gaul, Britain, Northern Italy maybe, the newcomers eventually became a culturally dominant force, and in these areas perhaps they formed a large portion of the population, but they did not ever come close to "repopulating" the area.

Indeed the idea of "repopulating" implies that the areas were depopulated and were settled by an equal, or at te very least sizable, number of newcomers. This idea is wrong and based in long antiquated notions of what migration was like in the Late Antique world. So to really to answer this question there are two smaller questions that we need to look at first. Did the population of native Romanized people decline so drastically as to necessitate a "re-population" and were the numbers of migrants sufficient to achieve this?

The first point is unclear. During the collapse of Roman authority in the west, there were many parts of the empire that entered into a long term economic decline. As different parts of the empire fractured and were removed from the broader world of Mediterranean trade the local economies had to de-specialize. At the height of Roman power and prosperity, goods from Africa could flow into the Balkans and Britain easily. Once Africa and Britain were removed from Roman control this ease of movement ended, and luxury goods from Africa such as the red slip pottery that is used to identify long range trade in Late Antiquity start becoming extremely rare.

In some parts of the Roman world this economic down turn was rapid. Britain and northern Gaul both experienced economic catastrophe that all but ended Roman urban life, ie living in cities with a specialized economy. The idea of Roman continuity and identity did not fade entirely, but the hallmarks of robust Roman life city dwelling, villas, pubic works, the army, and so on, all do start to fade from view. In other parts of the Empire, Africa, Italy, and Iberia for example, the economic downturn was much slower and it took several centuries to manifest itself. It was once thought that the Roman economy actually survived until the Islamic invasions of Africa, Egypt, and the Levant in the early 700's, but newer scholarship points the nadir of the Mediterranean economy somewhat earlier.

In both cases, rapid vs gradual, the economic decline of late Antiquity turned the Roman economy upside down. The large cities in the west, never as big as they were in the East (except Rome), collapsed in population due to a bout of plagues, the inability of large cities to sustain themselves, and the movement of people back into the countryside due to the economic collapse of cities. However these cities were not the location of most of the population. Despite being hailed as an urbanizing phenomenon, Roman authority typically oversaw the vast majority of people in the empire living as farmers in small villages and towns, not city dwellers, so a decline in city populations need not have been a problem for the primarily rural majority. At this same time however, the countryside was also in crisis. The number of inhabited sites in central Italy continuously decreased during this time, indicating that agricultural yields were also falling. Combined with falling populations in major urban areas, pre-modern cities were always falling in population without migration from the country side, and the first part of our answer is then:

Yes the population of Romans in western Europe did decline, through the economic downturns of Late Antiquity combined with the double whammy of a series of plagues, and according to some sources at least, the crushing taxes imposed on Italy and other parts of the Empire after the Eastern Romans reconquered them.

Were the numbers of ostensibly Germanic migrants into the empire enough to make up for the population decline in the Roman world? Quite simply no. We do not know the numbers that they came in or whether the groups of Germanic warriors contained large civilian components, and these are two vital pieces of information that we need to know to determine how much of a "re-population" these people were in these areas.

One area that we can speak comfortably on though is their relationship to the people they conquered and now ruled over. The idea that the newcomers, be they Angle, Saxon, Vandal, or Goth, waded through Roman blood to carve out new kingdoms is entirely false. These people were as often as not fighting alongside the Romans and entering into Imperial service. They had no interest in the wholesale destruction of Roman life, they wanted a piece of the pie for themselves. In many areas of the Empire, the newcomers functioned as new elite. Peter Heather indeed refers to the migration period often as a process of elite replacement, whereby the newcomers established themselves as the new ruling class (often in an uneasy relationship with local notables) but did not seek to replace the population at large. The newcomers became the new elite and at first attempted to maintain a certain division between the two societies, evidenced by legal codes in Francia for example, but over time they assimilated into the broader post-Roman population through both cultural exchanges as well as intermarrying.

Peter Heather proposed that the ethnic groups that came into the Roman world and settled into the new post-Roman kingdoms were not really ethnic groups as we traditionally think. Rather than imagining the entire Gothic population pulling up to the Roman border in the tens of thousands, we should instead think of these formations as primarily military organizations in relatively small numbers (the tens of thousands), that crafted an ethnic identity only after.

In Britain the situation was different and the populace at large did in fact adopt "Germanic" customs, though this has more to do with the fragility of Roman life in Britain and the piecemeal conquest of Britain than it has to do with the numbers of migrants coming in.

The last issue that I will mention in this context are modern DNA tests to examine the amount of Germanic DNA in Britain. There has been at least one study on the genetic make up of eastern England that looked for evidence of Germanic migration, and the conclusions were that approximately 1/3 of the population bears genetic markers consistent with North Sea populations in Germany, Low Countries, and Scandinavia. However this needs to be tempered. The study was not capable of detailing when the population bearing these markers came over. It could be reflective of changes from the Migration period, but subsequent migrations over the course of the Middle Ages, Early Modern, and Modern period also would have turned up. Current consensus is that the newcomers to Britain for example constituted a large portion of the population, and perhaps numbered into the hundreds of thousands at the higher range of estimates, but they never constituted a majority of the population.