I'm not sure if I buy this theory, since the collapse of the Roman empire was presaged by the collapse of the taxation system by several generations, especially in Hispania. Regardless, the nutrition and health of Rome in particular was ravaged by the Justinian invasion of Italy and the subsequent Lombard war, which reset the agricultural production of Italy to a significantly lower level for the next 800 years or so until the 1400s and the rise of the Italian city-states.
