But are believed to be reliable. Constantinople and Baghdad had populations over 1/2 mill prior to 1204 for Constantinople (The date of the Sacking of Constantinople by the Fourth Crusade) and 1258 for Baghdad (When the Mongols took the city which they called the greatest city they had ever taken, by 1258 the Mongols had almost all of China which gives you an idea of how large the Cities of China were at that time period).
Cities with large Population need an extensive way to get food into the city. Rome did this by being in the Richest Agriculture region in Europe AND importation of Grain from Egypt and North Africa. After the wars of the 6th Century Rome cease to be a city it had been, Constantinople became the largest city in the world, drawing Grain from Egypt till about 650 AD and the Arab Conquest and then from the Ukraine till 1204. Baghdad drew from the "Fertile Crescent" of Mesopotamia.
The basic thought is that the Arabs believe Baghdad was smaller then Constantinople at the height of both cities and the Mongols comment on Baghdad being the largest city they ever conquered (With Comment from Constantinople it was only 1/2 the size of Rome at Rome's height).
The only alternatives that MAY compete with Rome, Constantinople and Baghdad were Ancient Ctesphon (Capital of Persia and eastern Mesopotamia during the time of the Roman Empire), Ancient Babylon (prior to and including the time of Alexandria the Great), and Nijing (Under various Names). All of these cities (Except Nijing) were compared to Rome in Ancient text, with Rome coming out on top a a general rule.
Now, while food was an important factor, other trade was important for as these capital cities expanded wealth returned to these cities. With that wealth traders came to trade for that wealth. After a while Trade became more important then conquest. Thus trade built on trade. These cities is were you went when you wanted something you could not get locally. These Capital Cities is where you went when you had something different to sell. This trade is what really made these cities take off in population and even survive (For Example Constantinople is NOT to believe to have suffered a population drop after the loses of the Arab Conquest, in fact it might have GAINED population given the new trading opportunities from territories opened up to trade by the Arab Conquest).
The third factor is the ability to keep Foreign invaders from taking the city. If a city is taken, its ability to attract trade decline rapidly. Baghdad never recovered from the Mongol Invasion till about 1800. Constantinople never truly survived the Fourth Crusade, the City of Rome's decline started when it was first sacked in 410 AD (Through how and what was to be sacked was agreed to in terms by the Citizens of the City of Rome and the Goths so not much of a Sack). The Vandals came in the 460s and looted for months (But again agreed to leave a lot of private property alone). It is the Vandal Sacking that seems to start the economic decline of the City of Rome (as opposed to the Roman Empire which had been in decline for Centuries at this point). The fall of the Empire in the West was peaceful as far as the city of Rome was concerned and seems to have NO affect on Rome trade or Size. The real problem started in the 530s as Justinian launched his attempt to retake the Western Empire. In a ten year period Rome fell five times, Three times to the Romans fighting for Justinian and Twice for the Goths defending what had been their since the late 400s. This was the death blow, after 530 Rome never exceeded 100,000 till the 1600s and only recently became again the largest City in Italy (Milan was the largest City for most of the 20th Century).
Thus these three factor are the determining factors in the size of any city, how much food can get to the city, how much trade did it support, and can it stay safe from any attacker. This is often difficult to determine and historians often disagree but here is a website that tries to estimate the largest City of the World for the last 5000 years:
http://geography.about.com/library/weekly/aa011201a.htmI have some problem with this list, for example it list Constantinople have a population of 500,000 by 340 AD (Or it might be saying that Constantinople passed Rome as the largest City in 340 AD but only reached 500,000 in 500 AD). This is a problem, for while Constantine moved the Capital to Constantinople, it was a tiny administrative headquarters compared to Rome till about 400 when finally it was accepted as a co-Capital with Rome (at which point the population of Constantinople shoot up, but Rome was still the larger city till the Wars to retake Italy Justinian started about 530 AD which lead to the population of Rome dropping to Zero at one point when the Gothic King vacated Rome and took all of its citizens with him).
The list states that Baghdad was larger then Constantinople by 1000 AD, which is NOT reflected in opinions I have read of the time period. Constantinople was still the place to go in 1000 AD (Through Baghdad was also a place to go, Viking reached BOTH places to trade). Another problem giving Rome a population of 450,000 in 100 AD, Alexander a population of 250,000, Antioch 150,000 and Carthage 100,000. The problem in my mind is Antioch (Alexandria having 1/2 the population of Rome is another problem but again one of degree more than anything else). Carthage was considered the second largest City in the Western Empire as late as the Arab Conquest (It could draw on North African Grain AND trade from central Africa). Alexandria was Considered the Second largest City in the Roman Empire (It could draw on Egyptian grain). My problem is Antioch with a population of 250,000? Where did it gets its food? Mesopotamian was under Parthian rule not Roman Rule, Egypt grain was aimed at Rome and Alexandria (Some could be to other areas but the main thrust was these two cities). Where did Antioch gets its food? I can NOT see Antioch beating out Carthage in population in 100 AD, the trade with Persia was NOT that great.
I think the problem is the author is trying to off-set Europe centric bias but by doing so he is downplaying the Population of Rome and Constantinople. One way to see this is the list for 1500 which gives Constantinople's population at 200,000. This I believe is high, you had population drop do to the final conquest of Constantinople in 1453 by the Turks, but the real drop in population occurred between 1204 and 1453 as people left the City a it declined further under the Latin Empire and then the restored Greeks. 200,000 would make Constantinople in 1500 larger than Paris or London which by 1500 I have doubts (In 1204 on the other had several Paris or Londons of the time period could fit nicely inside Constantinople, but that is 1204 NOT 1500).
One good thing about this list it does show the problem of comparing populations of ancient cities. Some time it is just plan impossible to do so. One of the reason is Capital Cities tended to draw in a lot of traders from the rest of the Country. These traders would trade and then go back home. Thus you often had one large City (For example Rome at over a million people) supported by hundreds of small cites with population of less than 20,000 (if that high). Constantinople and Baghdad were the same till both were sacked (and the same regarded ancient Babylon which is one of the first cities to exceed 1/2 million population).
If you use this list look at it with care. Remember any city over 20,000 people has to draw in food from large distances and prior to the Railroad that meant ships and only ships. Prior to the Dark ages (Roughly 500-1000 AD) wagons did not even have ball-bearing so what weight you could carry on a wagon was limited. As to the cities themselves, Baghdad has its two rivers, Alexandria and later Cairo has the Nile, Rome had the Mediterranean, Constantinople has the Mediterranean and the Black Sea. Thus all could be feed. Beijing has the sea but is way north of the major rivers of China so its population probably never exceeded 100,000 till after 1800. Nicking on the other hand could draw from both "Wheat" and "Rice" China so its population could be much higher but since about 950 AD the Capital of China tended to the north do to the major threats to China were from the North. Thus while Nicking probably was a Trading center, it could NOT be the center of the Country like Rome was to the Roman Empire (Or Constantinople was from 400-1204 AD).
As to India, no one ever ruled India as one united Country (Even the British ruled India based on its "independent" states till independence in 1947). The Mongols did try for 200 years but failed. Thus while India has the rivers to ship the food to the Capital, it never had the unity to produce a high population Capital city. Some of of the Indian City became quite large but none over 100,000 till British Rule.
Thus once you look at the restrictions cities must live under in pre-railroad days, you had very few cities that could go over 100,000 people without violating one of the three requirements, of bring a large city. Those requirements are being a Capital City so trade can occur, an ability to feed its large population and the ability to protect the city from falling to an enemy.
Here is another Cite that Claims Rome was 1 million Population for about 300 years and then the text city was Chargan in China during the Tang Dynasty (800 AD). Than goes with Baghdad as the next 1 million population city in 1000 AD.
http://faculty.washington.edu/modelski/WcitiesH.htmA cite on Population of the Roman Empire:
http://www.tulane.edu/~august/H303/handouts/Population.htm For more on Rome:
http://en.wikipedia.org/wiki/Rome