Thursday, March 24, 2011

Ecological Predator-Prey Networks as Nature's Supply Chains

With the heart-breaking disasters in Japan, and the tremendous human and economic impacts, and, now, with the radiation spreading and various foods from the area surrounding the damaged Fukushima nuclear plant banned for consumption, plus even the water in Tokyo affected, I thought it time to step back and to reflect on nature.

Interestingly, we are increasingly seeing calls for "robustness" and "resiliency" in the context of supply chains since so many from automobile to airline to high tech component ones, including chips, have been adversely affected and seriously disrupted, including the biggest auto manufacturing company in the world, Toyota, because of the triple earthquake-tsunami-nuclear plant disaster that hit Japan, beginning on March 11, 2011, a date that I have sealed in my memory. In addition, journalists are making analogies of supply chains to biological organisms and even the human body and noting how resilient such systems are.

So what are the relationships between biological networks in nature and supply chains? If we can rigorously establish the connections, we should be able to learn how to design more resilient and robust systems, including supply chain networks.

In a recent study, entitled, Dynamics and Equilibria of Ecological Predator-Prey Networks as Nature’s Supply Chains, that I co-authored with the "other" Professor Nagurney, we were able to establish the equivalence between predator-prey ecological networks (think of food chains, for example, as in fisheries, to start) and multitiered supply chains consisting of "agents" who are manufacturers, retailers, or consumers, respectively. What I found fascinating is that in "product" or, shall I say, "corporate" supply chains, one explicitly considers various decision-makers' objective functions, which tend to include the maximization of profits, at least for the manufacturers and the retailers. Moreover, the various decision-makers "compete," whereas in predator-prey ecological networks, competition is clear, but, until now, no-one really quantified prices or value in that context.

In our paper, we established, using a dynamic model of predator prey interactions, that the stationary points or equilibria coincide precisely with those of the equilibria in supply chain networks! The general supply chain model that we used to show this equivalence, which was previously unexplored, was the supply chain network equilibrium model that I developed with Professors June Dong and Ding Zhang and which was published in Transportation Research E in 2002. That model has served as the foundation for numerous extensions; for just a few, click here.

Hence, amazingly, predator-prey interactions have an underlying economics, whereas supply chain networks, in a sense, are ecological predator-prey systems.

The study, Dynamics and Equilibria of Ecological Predator-Prey Networks as Nature’s Supply Chains, expanded on our earlier work that showed the equivalence between bipartite predator-prey networks and classical spatial price equilibrium problems going back to the work of the Nobel Laureate, Paul Samuelson. That paper, "Spatial Price Equilibrium and Food Webs: The Economics of Predator-Prey Networks," I will be presenting at the 2011 IEEE International Conference on Supernetworks and System Management
Shanghai, China, May 29-30, 2011, and it is in press in the Proceedings of that conference.

We became interested in this area of research due to a truly original paper, entitled "NEATS: A Network Economics Approach to Trophic Systems," published in the journal Ecological Modelling, co-authored by a group of researchers based in France: Mullon, Shin, and Cury. The paper applies some of the results in my Network Economics: A Variational Inequality Approach book to formulate and determine equilibria in predator-prey complex webs. One reads regularly about the impact of science on economics but this paper demonstrates how economics and, especially, network economics, can be used to combine both biological constraints that couple biomass balance equations with complementarity principles using Walras' law. The authors investigate the solutions to simple food chains, bilayer networks, complex food webs, and even to cannibalism (the links loop back to the specific nodes in such networks)!