Stable and unstable equilibrium states in a fishery-aquaculture model

This is the pre-peer reviewed version of the following article: Bergland, H., Pedersen, P.A. & Wyller, J. (2018). Stable and unstable equilibrium states in a fishery-aquaculture model. Natural Resource Modeling, which has been published in final form at https://doi.org/10.1111/nrm.12200. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.We study interactions between fishery and aquaculture using a 3D generalized Lotka–Volterra model, where we assume that the aquaculture production may affect the growth rate in the fish stock and the productivity in harvesting. In addition, input demands from both marine industries may result in effort competition. We identify conditions for the coexistence of a unique equilibrium state inside the first octant of the phase space and equilibrium states on its boundary. Conditions for stability and instability of these states are also given, thus showing the possibility of having bistability. The equilibrium point inside the first octant is stable if the growth impact on fishery from sea farming is below the potential productivity in harvesting. In the complementary case, we have an unstable interior equilibrium, and we may then end up in stable equilibrium states on the boundary, where either the fishery or the aquaculture is wiped out