A theoretical model of plant species competition: The case of invasive Carpobrotus sp. pl. and native Mediterranean coastal species

Abstract

In this paper we introduce and study a new mathematical model that describes the interaction between invasive and native plants in competition for resources and space. The first are represented by Carpobrotus sp. pl. while the second by the native coastal area species. Following the terminology used in modeling, we have used the term “population” to refer to the set of plants, i.e. native and alien invasive. Differently than in a classical Lotka–Volterra competition model, here we assume that the invasive species grow following a generalized logistic growth law while the native population a logistic one. Moreover, in the competition term we take into account the fact that the two populations of plant interact in a 3D space and the interaction occurs on the borders of the vegetation patch and/or volume, meaning that both densities will be characterized also by two exponents. A complete mathematical analysis of the proposed model was done by studying also some particular cases of it. The model is characterized by the presence of different equilibrium points such as the trivial equilibrium point, where both populations get extinct, the Carpobrotus-free equilibrium, the native-plant-free equilibrium and the coexistence, where both plant populations coexists. Computational simulations show that different bistability scenarios exist but also the tristability of the last three equilibrium introduced above was studied. The obtained results suggest that external factors, due to human intervention, that leads to a decrease in the initial population of Carpobrotus sp. pl. and/or increase of the native population might help in having the stability of the Carpobrotus-free equilibrium or the coexistence equilibrium.