Based on the definition that M. Altieri and Pierre Rabhi have given to agro-ecology, agro-ecology is practically synonymous with organic farming. Organic farming doesn't simply mean farming "without chemical or synthetic products." It was clearly defined in the 1930s-1940s as a farming system that sees humans, the natural ecosystem, and the crop and livestock agro-system as forming a complex organism. Organic farming aims to weave farming into the natural cycles and give farming societies the means to become technically and financially autonomous.
Agro-ecology is therefore a modified version of organic farming. You can think of it as an improved version of the original form of organic farming (as opposed to industrial organic farming, which is sometimes encouraged by multinationals or excessively relaxed regulation), particularly the form practiced by smallholders in tropical areas.
The negative impacts that conventional farming has on the environment and our health are obvious. But conventional farming has negative social impacts as well: the over-mechanized monoculture systems encourage land-grabbing by large estates and lead to mass unemployment. Almost all of the 12 million Brazilians suffering from hunger are former agricultural employees forced into unemployment by the over-mechanization of the export-oriented soy and biofuel sectors.
But the purported benefits of conventional farming are just an illusion. Chemistry does not lead to higher yields per hectare and will not be able to feed the whole planet! Chemical monoculture obtains worse yields than intercropping. Moreover, conventional monoculture only works in temperate climates - but 3/4 of the world's farms are in non-temperate regions. In these conditions, conventional agriculture is unstable, inefficient, and leads to indebtedness.
Because of the misunderstandings that persist about this mode of production. Many agronomists think that "organic farming" is the same thing as "conventional farming without chemical or synthetic products." They notice that when you stop using chemical products in conventional systems, yields fall. But that's not organic farming!
A farmer who grows varieties that are specifically seleted to be sustained by chemistry, who doesn't make use of hedges, who grows his vegetables as clones in monoculture, etc. obviously will not be able to obtain good yields without relying on chemical products.
Developing organic farming systems requires reconstituting farming ecosystems and putting smallholder know-how to use. Better yields per hectare are achieved through the intensification of intercropping, but chemical products must not be used because chemical fertilizers destroy the life of the soil and pesticides destabilize the farming ecosystem. With intercropping, all of the different plants protect one another mutually, and if intercropping is combined with livestock farming (or if trees are grown in the crop fields), it will ensure the long-term fertility of the fields.
A few different large-scale studies have tried to predict what would happen if organic farming were practiced accross the entire planet: they have all come to the conclusion that yields would drop slightly in Europe and North America but increase considerably throughout the rest of the world...and that the overall result would be a very large net increase.
Organic farming is the best way to feed the planet, whose population could reach 9 to 12 billion.