Catastrophic or sustainable scenarios might occur when the carrying capacities of a tourism‐based socioecological system vary

Abstract

In this work, we propose a socioecological model to describe the effects of visiting tourists in biological attractive sites. We model conditioned interactions between the forest resources and the wildlife with the tourists. This allows us to describe the net benefits–costs rates that the species and their habitats receive from the interaction with tourists. We show that when a scenario of sustainable tourism exists, it is always at risk. This occurs because there is at least a component of the socioecological system that can go to zero when the initial conditions belong to the basin of attraction of a border equilibrium. However, a sustainable equilibrium can be reached when the initial conditions belong to the basin of attraction of a positive attractor. The analysis of the model shows that increasing the tourism carrying capacities can lead to different dynamical patterns. Sometimes, these patterns describe scenarios of unsustainable tourism. When this is the case, by decreasing the negative impact due to the nature and wildlife‐based tourism industry, a tourism sustainability can be reached. Among the scenarios of unsustainable tourism, there are scenarios without wildlife and/or tourists or without both; scenarios in which the ecological and the social variable show sustained oscillations, or scenarios with chaotic patterns for these variables. We show numerical solutions of the model to display different scenarios when the touristic carrying capacities are varied.