Theory and experiments have demonstrated that negative plant-soil feedback (PSF) promotes coexistence between plant species. Plants and soils, however, face the challenge of an increasingly unpredictable environment due to multiple global change factors. Environmental stochasticity induces fluctuations that increase the variability and unpredictability of population dynamics, plant associations in the community and thus properties such as overall productivity. In this paper, we formulate a stochastic version of a classic PSF deterministic model, which describes the outcome of plant species competition in the presence of soil feedback. Especially when the soil feedback is negative, the deterministic expectation is that pulse perturbations to the system (e.g. a drought episode) cause plants and soil to move away from their equilibrium and then return to it. Environmental stochasticity alters this expectation: the system can either settle into a fluctuation regime around the deterministic expectation, or plant species may go extinct. Probability of extinction predictably increases with environmental stochasticity but the more negative the PSF, the more it can counteract the increase in extinction probability caused by increased environmental stochasticity. We stress that in nature the actual impact of PSF will depend on the interactions that link different types of soil organisms to plant species. We conclude that theory shows that plant communities with strong negative PSF are best placed to withstand the risk posed by increased environmental stochasticity but also that we still need more experimental evidence to validate theory and develop applications.
