What is considered the most accurate estimate of the population of City of Rome at its height until 5th century. How the sackings of 410 and 476 changed the demographics of the city and the number of inhabitants?

I have been studying the most populated cities of Holy Roman Empire and was astonished to read that in the 11th century Rome came third with the population of 40-50 thousand inhabitants. I remember that at school we were told that Rome was the most populated city with nearly a million people living there during the first two centuries AD.

Trying to find out the reason behind such decline in the numbers and historical demographics of Rome, I searched the web, however I found accurate data only since 1861 (195000 people). In the wikipedia article it was said that the estimates about demographics of the city varied from 200 thousand to 2 million according to different studies.

My first guess was the sackings of 5th century caused the decline. If I am correct, were most of the people slaughtered by the barbarians or did they become refugees and where could they possibly move?

Source: reddit post

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