relax friend. no conflict here. just a discussion.That doesn't mean anything, the "Mediterranean region" is such a large region, you might as well say that Rome was a Afro-Eurasiatic empire, it's just as helpful.
The economic center of chinese empires moved from time to time, it was never permanently on the Yangtze.
This doubly wrong, not only the bulk of the population growth happened from 1000 CE onwards, there is also no reason to say that it was political power that decided things, literally no reason.
Northern France was not subsidized by a large empire contrary to Roman peninsular Italy. Also the mechanism here doesn't work until one explains what "feudal power" means and why it would increase food production.
Except there was no such isolation ever and the demographic growth happened centuries after the collapse of Rome.
1. Unlike Afro Eurasia, Mediterranean spanning trade networks did exist and prospered, with peak roman shipping quantities being unmatched till centuries later. It is helpful as it defines the chief element on which the prosperity of the Roman economy was built- It's control of the entire Mediterranean.
2. Political center of Chinese Empires moved around, mainly due to the foreign origin of the dynasty in question or due to a need to be closer to the perceived threat so as to better manage the active theatres of war. Yangtze was the lifeblood of the Chinese Empires, especially (as I already mentioned) Han Chinese ones.
3. I mentioned that Europe saw intensive deforestation in from 500 to 800 CE. And rate of population increase grew, relative to what we see just before. Sure population may have grown even faster from 1000 CE, but how does it negate my statement? by the same logic, I might as well as say that population grew much faster after 1900 CE, so your statement is false.
And political power shift is a big factor. It promotes immigration, development of urban centers around the great courts, and greater security, all of which promote a growth in population.
4. Correct. It wasn't subsidized, but neither did it have to actively support campaigns and large urban centers. The biggest population estimates I can find for Gaul is 80,000 for Trier and Paris, when they were the capital for the praetorian prefecture. Most of this population was almost certainly tied the prefecture bureaucracy and not actual organic growth. They, and they armed forces they commanded were also definitely supported by North African grain.
It was only in the Carolingian period where the economy was "feudalistic" (meaning decentralized, built around feudal strongholds, instead of trade based, with large urban centers) did local production have reason to increase. Much, much less competition with North African grain chief among them. Also a larger share of population would be supported by subsistence agriculture, which would increase area under cultivation, and overall production (though not productivity I imagine).
5. I meant relatively my man. It just wasn't as well integrated as it once had been under Pax Romana. One can check the drop in overall shipping volumes to corroborate this.