Agriculture was one of the areas where things really innovated following the fall of the Empire, even if it was out of necessity.

The Imperial agricultural system had been dominated by Latifundia; large, intensive farm systems centred on villa complexes and worked largely by slave labour to feed the ever-hungry Roman cities. The scale of the Empire and its vast logistical capabilities meant that each province of the Empire could specialise in specific produce, including lucrative cash crops; Italy, for example, largely didn't produce grain, specialising instead in olive oil, wine and (in coastal regions) garum fish sauce for export. Instead, the grain for the cities of Italy was imported entirely from North Africa, in particular Egypt.

You can see already the vulnerability in this system which devolved rapidly into a crisis with the collapse of the Empire. As the Empire fell into infighting, instability, invasion and recession upon recession, so the logistical networks which underpinned the Imperial economy also crumbled. Without reliable trade to provide staple foodstuffs, provinces could no longer rely on cash crops and exports, and could also not maintain the vast array of slaves necessary to underpin the Latifunfa system. In Britain in particular, a series of virulent plagues and an increase in raiding led to a population collapse and a general abandonment of the cities by the sixth century. These changes left the Latifunda system as it had been largely untenable in much of Northern Europe. Combined with this, intensive Roman agricultural practices frequently led to depleted soil.

With the collapse of Imperial logistics and authority, regional populations fell back largely on local, often pre-Roman, power structures and settlement patterns. This largely required communities to be self-sufficient, or at least to an extent that could be reached within the more diminished trade capacity with neighbouring communities. This in turn meant a return to, essentially, subsistence agriculture, with surplus then being used for local trade. The demands of this system, the desire to produce a surplus for trade, and the problems of soil depletion, led to a series of highly important innovation. The early medieval period saw the widespread introduction of crop rotation systems, greatly improving yields over time. It also saw the introduction of the heavy plow, which allowed for a much greater exploitation of the heavy soils of Northern Europe.