Density-dependence tips the change of plant–plant interactions under environmental stress

Facilitation studies typically compare plants under differential stress levels with and without neighbors, while the density of neighbors has rarely been addressed. However, recent empirical studies indicate that facilitation may be density-dependent too and peak at intermediate neighbor densities. Here, we propose a conceptual model to incorporate density-dependence into theory about changes of plant–plant interactions under stress. To test our predictions, we combine an individual-based model incorporating both facilitative response and effect, with an experiment using salt stress and Arabidopsis thaliana. Theoretical and experimental results are strikingly consistent: (1) the intensity of facilitation peaks at intermediate density, and this peak shifts to higher densities with increasing stress; (2) this shift further modifies the balance between facilitation and competition such that the stress-gradient hypothesis applies only at high densities. Our model suggests that density-dependence must be considered for predicting plant–plant interactions under environmental change.