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Depopulation is often correlated with decline

Roman population declined greatly between 2nd and 7th centuries, which led to inability to defend against various Euro-barbarians, Arabs, etc. There's apparently tons of archaeological evidence for this: declining sizes of cities as witnessed by receding city walls. Main reasons for the population decline may have been diseases:

According to the Early Middle Ages lecture, the cause of decline was depopulation, but this seems wrong to me. Probably some other factor caused depopulation, and this is just an easily traced symptom.

Other examples:

Clearly population decline is not a good thing, regardless of how the arrow of causality fits.

Looking to the future, Cowen suggested that instead of worrying so much about GDP per capita, let's talk about the capitas. He noted that many wealthy countries are on the verge of depopulating. Consequently, he argued that very important innovations would be those that lessen the burdens of rearing children. Vollrath observed that in general the more people the more ideas that are generated and that a shrinking population might slow down the pace of innovation.