Roots in space: a spatially explicit model for below-ground competition in plants

Game theory provides an untapped framework for predicting how below-ground competition will influence root proliferation in a spatially explicit environment. We model root competition for space as an evolutionary game. In response to nutrient competition between plants, an individual's optimal strategy (the spatial distribution of root proliferation) depends on the rooting strategies of neighbouring plants. The model defines and predicts the fundamental (in the absence of competition) and realized (in the presence of competition) root space of an individual plant. Overlapping fundamental root spaces guarantee smaller, yet still overlapping, realized root spaces as individuals concede some but not all space to a neighbour's roots. Root overlap becomes an intentional consequence of the neighbouring plants playing a nutrient foraging game. Root proliferation and regions of root overlap should increase with soil fertility, decline with the distance cost of root production (e.g. soil compactness) and shift with competitive asymmetries. Seemingly erratic patterns of root proliferation and root overlap become the expected outcome of nutrient foraging games played in soils with small-scale heterogeneities in nutrient availability.