Evolutionary theory can be applied to improve agricultural yields and/or sustainability, an approach we call Evolutionary Agroecology. The basic idea is that plant breeding is unlikely to improve attributes already favored by millions of years of natural selection, whereas there may be unutilized potential in selecting for attributes that increase total crop yield but reduce plants’ individual fitness. In other words, plant breeding should be based on group selection. We explore this approach in relation to crop-weed competition, and argue that it should be possible to develop high density cereals that can utilize their initial size advantage over weeds to suppress them much better than under current practices, thus reducing or eliminating the need for chemical or mechanical weed control. We emphasize the role of density in applying group selection to crops: it is competition among individuals that generates the ‘Tragedy of the Commons’, providing opportunities to improve plant production by selecting for attributes that natural selection would not favor. When there is competition for light, natural selection of individuals favors a defensive strategy of ‘shade avoidance’, but a collective, offensive ‘shading’ strategy could increase weed suppression and yield in the high density, high uniformity cropping systems we envision.