What makes you think Italy was not a farming center? The volcano soil made Italy very fertile.
Because it was importing vast amount of farm products, especially grain, from Egypt and Scicily. I have very rich potting soil mix in my backyard; that doesn't make my house a farming center. The flow of trade is what decides and qualifies specializations. As far as food trade flow is concerned, my household specializes in food consumption not production :-)
Yes, Rome relied very much on importing grain from Egypt. It was the reason of the war between Octavian and Antonio. It still didn't change that the more grain export to Rome, the less grain available to local Egyptians.
Sure, likewise, the more grain is shipped from Iowa, the less grain is available to local Iowans, theorectically . . . however, the same amount of grain would support far more people with far more sophisticated economies in, say, Chicago or New York, than say in the plains of Iowa, whose population would be limited for reasons other than the absolute amount of grain the land could turn out, and the same amount of grain would be left to rot or not grown to begin with in the absence of the export demand. On top of that, due to the geographic limitations along the Nile valley, narrow strip of fertile soil in the flood zone, then hostile desert immediately outside, building residential houses along the Nile to accommodate more grain eating mouths would automaticly cut into acreage available for farming . . . a situation similar to the land use problem in East China. The magic of trade is that it can solve many of these problems and elevate the production to a higher level of equilibrium in the grain production area, meanwhile allowing the emergence of a far more sophisticated commerce center where the export grain is consumed.
The Egyptian plough was like Greek ploughs. It barely disturbed the surface of the soil and pushed stones aside. Hoes and digging sticks were still needed.
Whatever it was, it apparently used draft animals according to the vast numbers of wall paintings. Because these farms were for profit, not latter day communist "model farms," it can be safely assumed that the draft animals were productive in what they were doing for their owners.
BTW, it's not my idea that Aztec was at the same integration level with early Roman republic. Sanders & Price mentioned the civilization in Mesoamerica resembled a certain civilization in Europe but never gave out the name. I believe I have every reason to assume what they had in mind was early Roman republic. In a way, I'm just speaking out what they had in mind but didn't speak out for various reasons.
Early Roman Republic can be 500BC, and no one is claiming Rome had 50 million people in 500BC. Also, in latter times, the production method of a food import zone does not reflect the state of art for grain production. For example, if we examine farming/gardening practices in Manhatten over the past 200 years, we'd be baffled at how the handicraft human labor approach to farming/gardening could possibly support a large city, much less a metropolis with over 8 million. The answer is in trade. Manhatten doesn't need to import combines; a large combine can be put to much better use in Iowa, with only the resulting corn (or even corn fed beef from somewhere else) imported into Manhatten. Likewise, if plough pulling draft cattles were expensive in Roman times, I'd imagine the Roman banks would be financing such a cattle-plough "combine" in Egypt intead of in the suburbs of Rome. The bankers in Rome would be earning their food by collecting interest on financing that cattle-plough "combine" in Egypt, and the Egyptian farmer who took out the loan would be producing more food than would be the case without the trade/commerce link to Rome.