Understanding how vegetation structure and productivity arise from plant photosynthetic traits entails scaling up from leaf to canopy. Simple optimization has commonly been used to this end, with traits being assumed optimal when productivity of a vegetation stand is maximized. This ignores the fact that plants interact with each other; their leaves and roots influence each other’s light and nutrient availability. In such cases game theory (competitive optimization) is more appropriate. Focusing on leaf area, I will show that stands with an optimal structure for maximum productivity are not evolutionarily stable and can be invaded by a ‘cheating’ mutant that overinvests in leaf area. As a result natural plant communities are less than maximally productive. But while the structure and productivity of vegetation can now reasonably be predicted analyzing genetic and species diversity is still a major challenge. I will present some advances in this direction.