Reference: chapter 3 of “A history of world agriculture from the neolithic era to the current crisis” by Marcel Mazoyer and Laurence Roudart.
With the disappearance of forests, slash-and-burn agriculture was no longer possible, and new forms of agriculture were developed. This is an extremely simplified overview of some of these new forms:
Pastoralism in arid regions
In arid regions with little vegetation, the cultivation of crops impossible; there was not enough water, and the lack of vegetation meant that the soil lacked fertilizing nutrients as well. In these regions a nomadic, pastoral lifestyle arose. People kept herds of animals which provided them with milk and meat. When the animals had grazed a particular area the people would move with their herds to greener pastures.
Flood-based agriculture in river valleys
A very different form of agriculture arose in river valleys such as the Indus, the Tigris, the Euphrates, and the Nile. Although surrounded by arid scrubland or desert, these valleys benefited from annual flood waters, so that cultivation based on flood water, rather than rainwater, was possible. The floods also provided fertilizer in the form of alluvial deposits; soil carried by the flood waters and deposited on the valley floor. Crops (mainly wet rice, which grows when submerged in water) were planted just before or during the flood, to benefit from the water and nutrients.
Wet rice cultivation in humid tropic regions
In humid tropical regions, valleys and low-lying regions are often flooded during the rainy season, and under these conditions, like in the river vallyes, wet rice cultivation was practised.
Cultivation with fallowing and animal manure in temperate regions
In temperate regions, (including the Mediterranean and most of Europe) cereal crops such as wheat and rye were grown. Only the most fertile areas were used for crop-growing. The most fertile land was mostly found in the low-lying areas; not only were these regions wetter, but they benefited more from deposits of nutrient-rich sediments carried by rainwater. By contrast, in the hilly regions after deforestation there was a lot of soil erosion, with the top layer of soil being carried by wind and rain to the low-lying areas. These hilly areas of poor fertility were used to graze animals such as sheep or cows. The animals provided meat and milk, and one other very important resource: manure.
Fallowing was practised: a field would be planted with a cereal crop one year, would be allowed to grow grasses the next in order to restore some fertility to the soil. Further fertilization was provided by the animals, which were allowed to graze the hilly pasture areas during the day, and at night were put on the fallow land, so that they would deposit fertilizing manure there.