Topic: Game Theoretical Modeling of Evolution in Structured Populations
Meeting dates: April 25-27, 2016.
Location: NIMBioS at the Univ. of Tennessee, Knoxville
Mark Broom, Mathematics, City Univ. London
Jonathan Rowell, Mathematics and Statistics, Univ. of North Carolina, Greensboro
Jan Rychtar, Mathematics and Statistics, Univ. of North Carolina, Greensboro
Jeremy Van Cleve, Biology, Univ. of Kentucky
Recent models of evolution have begun to study structured populations using evolutionary graph theory. These models embed standard games such as the Prisoner’s Dilemma or the Hawk–Dove game within a graph structure that dictates allowable interactions. One limitation of this otherwise quite general framework is that interactions in these models typically are restricted to those of a pairwise nature, despite the fact that animal interactions can involve many actors. The next phase in the development of this model system is to include such multi-player interactions. An alternative to this approach is an area of research that has instead explored spatially structured populations competing over continuously varying resource environments. In these models, interactions occur between an individual and the rest of the community with both relative trait frequency and absolute population levels influencing payoffs. In this tutorial, we explored both discrete and continuous game theoretical models of evolution in structured populations that address both pairwise and multi-player interactions.
The tutorial format included interactive lectures with quick exercises on each topic, followed by structured hands-on activities during which participants worked in small groups on exercises and projects. During these sessions, participants learned simple machine learning algorithms, MATLAB® programming, and intuitive analytic tools. The tutorial also featureed research lectures by:
This tutorial was appropriate for both mathematics and biology faculty as well as advanced graduate students. In particular, it targeted those working in evolutionary and behavioral ecology, economics and game theory, and evolutionary anthropology, linguistics, psychology, and sociology.
Participants were introduced to the discrete graph theory methods and models of structured population as well as classical continuous models based on differential equations. They learned how to use such methods and/or build and analyze models in the context of the tutorial's topics and worked in small groups to experience how to use the methodology to describe, simulate, and analyze the relevant biological systems.
Participants were exposed to software that implements the mathematical methods, aids visualization, and facilitates computations and analyses.
Participants learned how the tutorial materials may fit into mathematics and biology courses or be used as an introduction to independent studies or undergraduate research.
Cho E. Submitted (2017). A New Formula for the Volume of a Simplex. International Electronic Journal of Pure and Applied Mathematics.
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