Dynamics and Equilibria of Ecological Predator-Prey Networks as 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.

[1]  M. Florian,et al.  A new look at static spatial price equilibrium models , 1982 .

[2]  F. Egerton.  Changing Concepts of the Balance of Nature , 1973, The Quarterly Review of Biology.

[3]  A. Nagurney,et al.  Projected Dynamical Systems and Variational Inequalities with Applications , 1995 .

[4]  Walter C. Labys,et al.  SPATIAL PRICE EQUILIBRIUM AS A FOUNDATION TO UNIFIED SPATIAL COMMODITY MODELING , 2005 .

[5]  Anna Nagurney,et al.  Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations , 2007, Comput. Manag. Sci..

[6]  A. Nagurney.  Network Economics: A Variational Inequality Approach , 1992 .

[7]  Qiang Qiang,et al.  Fragile networks: identifying vulnerabilities and synergies in an uncertain age , 2012, Int. Trans. Oper. Res..

[8]  A. Nagurney.  Supply Chain Network Economics: Dynamics of Prices, Flows and Profits , 2006 .

[9]  Jose M. Cruz,et al.  Multiperiod effects of corporate social responsibility on supply chain networks, transaction costs, emissions, and risk , 2008 .

[10]  Anna Nagurney,et al.  Projected dynamical systems modeling and computation of spatial network equilibria , 1995, Networks.

[11]  Anna Nagurney,et al.  Stability of spatial price equilibrium modeled as a projected dynamical system , 1996 .

[12]  S. Neira,et al.  Trophic interactions and community structure in the upwelling system off Central Chile (33-39°S) , 2004 .

[13]  A. Nagurney,et al.  A supply chain network equilibrium model , 2002 .

[14]  C. Mullon,et al.  NEATS: A Network Economics Approach to Trophic Systems , 2009 .

[15]  P. Zusman.  Spatial and temporal price and allocation models , 1971 .

[16]  Patrizia Daniele,et al.  Evolutionary variational inequalities and applications to complex dynamic multi-level models , 2010 .

[17]  Anna Nagurney,et al.  Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation , 2007 .

[18]  Ding Zhang.  A network economic model for supply chain versus supply chain competition , 2006 .

[19]  Fan Yang,et al.  Day-to-day stationary link flow pattern , 2009 .

[20]  Anna Nagurney,et al.  Sensitivity Analysis for the General Spatial Economic Equilibrium Problem , 1984, Oper. Res..

[21]  Anna Nagurney,et al.  Dynamics of Supply Chains: A Multilevel (Logistical–Informational–Financial) Network Perspective , 2002 .

[22]  A. Nagurney,et al.  Spatial price equilibrium and food webs: The economics of predator-prey networks , 2011, 2011 International Conference on Business Management and Electronic Information.

[23]  Sergio Neira,et al.  Comparative analysis of trophic structure of commercial fishery species off Central Chile in 1992 and 1998 , 2004 .

[24]  E. Odum.  Fundamentals of ecology , 1972 .

[25]  Anna Nagurney,et al.  On the stability of an adjustment process for spatial price equilibrium modeled as a projected dynamical system , 1996 .

[26]  K. Cuddington.  The “Balance of Nature” Metaphor and Equilibrium in Population Ecology , 2001 .

[27]  S. Carpenter,et al.  Catastrophic regime shifts in ecosystems: linking theory to observation , 2003 .

[28]  Roy Szweda,et al.  In an uncertain world , 2006 .

[29]  A. Doan.  Balance of Nature , 2002 .

[30]  Anna Nagurney,et al.  Dynamical systems and variational inequalities , 1993, Ann. Oper. Res..

[31]  David Ben-Arieh.  Network Economics: A Variational Inequality Approach , 2012 .

[32]  Stephen Enke,et al.  Equilibrium among Spatially Separated Markets: Solution by Electric Analogue , 1951 .