We know little of small peoples who died out in antiquity or even Medieval times, but the case histories that have come down to us are compelling, precisely because they include the most successful civilizations of the West, namely classical Greece, Rome and Byzantium. Countless small tribes disappeared into the hands of the Roman slavers, doubtless quite against their inclinations. As Robert Marcellus wrote in The Human Life Review:
The Greek geographer and historian Strabo (63 BCE-21 CE) described Greece as "a land entirely deserted; the depopulation begun since long continues. Roman soldiers camp in abandoned houses; Athens is populated by statues". Plutarch observed that "one would no longer find in Greece 3,000 hoplites [infantrymen]." The historian Polybius (204-122 BCE) wrote: "One remarks nowadays all over Greece such a diminution in natality and in general manner such a depopulation that the towns are deserted and the fields lie fallow. Although this country has not been ravaged by wars or epidemics, the cause of the harm is evident: by avarice or cowardice the people, if they marry, will not bring up the children they ought to have. At most they bring up one or two. It is in this way that the scourge before it is noticed is rapidly developed. The remedy is in ourselves; we have but to change our morals." 
Sparta, the model of slave-based military oligarchy, had 5,000 land-owning families at the time of the Peloponnesian War, but only 700 by the third century AD after Epiminondas broke the Spartan hold over its helot population. Rome's population fell to perhaps 100,000 during the seventh century from 1 million in the second century. Between 150 AD and 450 AD, the population of Rome's Western empire fell by about four-fifths. Constantinople held 250,000 people in the ninth century and between 600,000 and one million during the 12th century, yet it had fallen to only 100,000 when the Turks took it, at least in 1453. After Constantinople, the world's largest city west of the Indus, well may have been the Aztec capital Tenochtitlan. Estimates of the annual number of humans sacrificed by the Aztecs range from 20,000 to a quarter million per year. Although Aztec civilization was overthrown by the conquering Spaniards, it could not have lasted indefinitely given such practices.
There is endless debate about such data. Roman population data are somewhat conjectural, and Strabo's estimates have been disputed by some scholars. Explanations have been forwarded that range from the collapse of the slave-based agricultural system to mass infanticide and venereal disease.
Nonetheless, it seems clear that the Romans did not so much conquer Greece as to occupy its shell; that the Germanic tribes did not so much conquer Rome so much as to move into what remained of it; and that the Arabs did not so much conquer the Byzantine hinterland as migrate into it. On this last point, a new book by Yehuda Nevo and Judith Koren argues convincingly that the Byzantines ceded frontier territories to Arab foederati in the mid-seventh century and that the famous battles of the Islamic conquest in fact never took place.  In one form or another the antecedents of Western civilization died of existential causes, rather than external ones.