Although the importance of group selection in nature is highly controversial, several researchers have argued that plant breeding for agriculture should be based on group selection, because the goal in agriculture is to optimize population production, not individual fitness. A core hypothesis behind this claim is that crop genotypes with the highest individual fitness in a mixture of genotypes will not produce the highest population yield, because fitness is often increased by "selfish" behaviors, which reduce population performance. We tested this hypothesis by growing 35 cultivars of spring wheat (Triticum aestivum L.) in mixtures and monocultures, and analyzing the relationship between population yield in monoculture and individual yield in mixture. The relationship was unimodal, as predicted. The highest-yielding populations were from cultivars that had intermediate fitness, and these produced, on average, 35% higher yields than cultivars with the highest fitness. It is unlikely that plant breeding or genetic engineering can improve traits that natural selection has been optimizing for millions of years, but there is unutilized potential in traits that increase crop yield by decreasing individual fitness.