Friday, April 27, 2012

Game Theory, Network Economics, Predators and Prey, and Ecology

I am fascinated by math modelling, networks, and the world.

Although I teach in a business school and have appointments in engineering I have always enjoyed biology and ecology and, as a freshman at Brown University, even took botany and ecology.

I have written about how I became interested in conducting research in ecological modelling, which was due to the intriguing work being done by Dr. Christian Mullon and his colleagues in France. Their research was integrating network economics (and used my book on the topic) with predator prey networks, focusing on fisheries, and used real data. They were exploring climate change and fisheries as well as supply chains.

Inspired by their work, I went on to co-write two articles on the topic, including the paper, "Dynamics and Equilibria of Ecological Predator-Prey Networks as Nature's Supply Chains," that was published in Transportation Research E.

Last Fall, in glorious Paris, where I gave a plenary talk at NetGCoop,  I had a chance to meet Dr. Mullon and spent a day with him and his lovely wife.

This morning, he shared the wonderful news with me.

Our paper, "A Game Theoretical Approach to the Vertical Coexistence of Small and Big Fish," has now been accepted for publication in the journal Ecological Modelling.

In the paper we construct an abstract model of a pursuit-evasion game using tools from network economics. Animal moves are represented as human migrations: people move to destinations that they find agreeable to migrate to and the associated decision-making depends on the specific characteristics of the location that they come from, the place that they migrate to, the distance between both, but also on the density and the characteristics of the other members of the human population living there. This competitive behavior results in a simple non-cooperative game. The repetition of this game, in turn,  yields a dynamical system, the equilibrium of which may be computed using variational inequality tools. These ideas are implemented in the model of a vertical marine ecosystem in which big fish pursue small fish that try to evade, with the small fish preferring to live in surface and with the big fish preferring to reside in depth. The theoretical and computational results suggest that the specific trade-offs for both pursuers and evaders are important for the stability and the permanence of ecosystems. We then discuss how this quite simple model could be a first step towards a game theoretical formalization of the connectivity of marine ecosystems, which is an important and open question in marine ecology.

Our paper cites several of my previous papers with Jie Pan, who was one of my former doctoral students, and had attained promotion and tenure at St. Joseph's University in Philadelphia, after receiving his PhD in Math at UMass Amherst. He died of an undiagnosed illness, after even seeking treatment in China, while I was living with my family in Stockholm, Sweden. The paper:  Pan, J., Nagurney, A., 1994. Using Markov Chains to Model Human Migration in a Network Equilibrium Framework, Mathematical and Computer Modelling 19 (11), 31-39 is cited as well as a paper that we wrote that was published in the European Journal of Operational Research.  We had even published in Operations Research together with Sten Thore.

Research is fascinating -- years after you may be applying results to an entirely different discipline and the good work of those who have passed on lives on through the world of ideas!