Plant–soil feedback is recognized as a causal mechanism for the emergence of vegetation patterns of the same species especially when water is not a limiting resource (e.g. humid environments) (Cartenì et al. in J Theor Biol 313:153–161, 2012. https://doi.org/10.1016/j.jtbi.2012.08.008; Marasco et al. in Bull Math Biol 76(11):2866–2883, 2014. https://doi.org/10.1007/s11538-014-0036-6). Nevertheless, in the field, plants rarely grow in monoculture but compete with other plant species. In these cases, plant–soil feedback was shown to play a key role in plant-species coexistence (Mazzoleni et al. in Ecol Model 221(23):2784–2792, 2010. https://doi.org/10.1016/j.ecolmodel.2010.08.007). Using a mathematical model consisting of four PDEs, we investigate mechanisms of inter- and intra-specific plant–soil feedback on the coexistence of two competing plant species. In particular, the model takes into account both negative and positive feedback influencing the growth of the same and the other plant species. Both the coexistence of the plant species and the dominance of a particular plant species is examined with respect to all model parameters together with the emergence of spatio-temporal vegetation patterns.

植物-土壤反馈被认为是同一物种的植被格局出现的原因机制，尤其是在水不是限制性资源（例如潮湿环境）的情况下（Cartenì等人，J Theor Biol 313：153-161，2012）。 https://doi.org/10.1016/j.jtbi.2012.08.008; Marasco等人在Bull Math Biol 76（11）：2866–2883，2014. https://doi.org/10.1007/s11538-014 -0036-6）。然而，在田间，植物很少在单一栽培中生长，而是与其他植物种类竞争。在这些情况下，植物-土壤反馈被证明在植物-物种共存中起关键作用（Mazzoleni等人，Ecol Model 221（23）：2784–2792，2010. https://doi.org/10.1016/j （ecolmodel.2010.08.007）。使用由四个PDE组成的数学模型，我们调查了两种竞争植物物种共存的种间和种内植物土壤反馈机制。特别地，该模型考虑了影响同一植物和其他植物物种生长的负反馈和正反馈。相对于所有模型参数以及时空植被格局的出现，都检查了植物物种的共存和特定植物物种的优势。