![]() The most influential model of facilitation, stress-gradient hypothesis (SGH), which predicts dominance of facilitation over competition under intense stress 6, is conceptual instead of quantitative and there is still much debate about its generality 7, 8, 9, 10, 11, 12, 13, 14, 15. However, most facilitation research is about specific empirical case studies, while theoretical progress helping to generalize the findings has far lagged behind. For example, facilitation may affect species distribution and range shifts with climate change 3, 4 and/or plant diversity from local to large scales 5. Though competition dominates the literature, positive plant–plant interactions (facilitation) have been widely explored in the past two decades. Our model suggests that density-dependence must be considered for predicting plant–plant interactions under environmental change.Ĭompetitive interactions and environmental stress are crucial factors for structuring plant communities and shaping species distributions 1, 2. 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. 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. Here, we propose a conceptual model to incorporate density-dependence into theory about changes of plant–plant interactions under stress. However, recent empirical studies indicate that facilitation may be density-dependent too and peak at intermediate neighbor densities. Facilitation studies typically compare plants under differential stress levels with and without neighbors, while the density of neighbors has rarely been addressed. ![]()
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