Dynamics and equilibria of ecological predator–prey networks as nature’s supply chains

• Published in: Transportation research. Part E, Logistics and transportation review Logistics and transportation review, 2012, Vol.48 (1), p.89-99
• Main Authors: Nagurney, Anna, Nagurney, Ladimer S.
• Format: Article
• Language: English
• Subjects: Convergence; Dynamical systems; Dynamics; Ecology; Fisheries; Food webs; Foods; Networks; Predator–prey models; Projected dynamical systems; Supply chains; Transportation; Transportation and logistics; Variational inequalities
• ISSN: 1366-5545; 1878-5794
• DOI: 10.1016/j.tre.2011.07.007

► We develop new static and dynamic models of predator–prey networks. ► The equilibria are shown to coincide with those of multitiered supply chains. ► In the bipartite case, the equilibria are as in classical spatial price problems. ► A real world fisheries application illustrates the model and the proposed algorithm. ► This work rigorously shows that ecological food webs are nature’s supply chains. In this paper, 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 equivalence between the ecological models and supply chain network equilibrium models and highlight the connections to spatial price equilibrium problems. We propose an algorithmic scheme, provide convergence results, and apply it to a food web drawn from a fisheries application. This paper is a contribution to the interdisciplinary supply chain network literature.