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NIMBioS Tutorial

Game Theoretical Modeling of Evolution in Structured Populations

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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:

  • Sergey Gavrilets, Ecology & Evoutionary Biology and Mathematics, Univ. of Tennessee, and Director of Scientific Activities, NIMBioS;
  • Alun Lloyd, Mathematics, North Carolina State Univ. Director of Biomathematics Graduate Program and Center for Quantitative Sciences in Biomedicine
  • Paulo Shakarian, Director of the Cyber-Socio Intelligent Systems Laboratory, Arizona State Univ.

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.

Tutorial objectives:

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.

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Playlist of online videos.



Cho E. Submitted (2017). A New Formula for the Volume of a Simplex. International Electronic Journal of Pure and Applied Mathematics.

A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Questions regarding diversity issues should be directed to You can read more about our Diversity Plan on our NIMBioS Policies web page. The NIMBioS building is fully handicapped accessible.

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From 2008 until early 2021, NIMBioS was supported by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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