Theory predicts plants grow roots to compete with only their closest neighbours.

The combination of individual-based selection with shared access to resources drives individuals to invest more than necessary in taking up their share of resources due to the threat of other individuals doing the same (competitive overinvestments). This evolutionary escalation of investment is common, from deer antlers and peacock feathers to tree height and plant roots. Because plant roots seem to be well intermingled belowground, the simplifying assumption that belowground resources are perfectly well mixed is often made in models-a condition that favours maximal fine-root overinvestments. Here, I develop simple models to investigate the role of space in determining the overlap among individuals belowground and resulting fine-root biomass. Without costs of growing roots through space, evolutionary optimization leads individuals to intermingle their fine roots perfectly and to invest just as much in these roots, whether there are two individuals competing or many. However, if there are any costs of sending roots through soil, investment in fine roots is constrained in amount and spatial extent. Dominant individuals are those that keep their roots in the soil closest to their own stem and the stems of their closest neighbours. These results highlight the importance of space in determining individual strategies as well as competitive networks.