Dynamics and Equilibria of Ecological Predator-Prey Networks as Nature’s Supply Chains

Abstract

Ecological food webs in the form of predator-prey networks are nature’s supply chains. Here, we develop a dynamic network model of ecological food webs and prove that the set of stationary points of the projected dynamical system coincides with the set of solutions of a variational inequality governing the equilibrium of predator-prey networks. We also establish the relationship between the ecological models and supply chain network equilibrium models and highlight the connections to spatial price equilibrium problems. We propose an algorithmic scheme and provide convergence results. Finally, we apply the framework to a food web drawn from a fisheries application.

This paper is a contribution to the literature on the interfaces among economics, transportation and logistics, and biology/ecology through network models and methodologies.

Keywords: supply chains, food webs, predator-prey models, projected dynamical systems, variational inequalities, transportation and logistics