Modelling competitive interactions and plant–soil feedback in vegetation dynamics

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.