Evotionary graph theory
Description:
The objective of this course is to give a fair introduction to evolutionary graph theory. Evolutionary graph theory is a an approach that studies how the topology of underlying network structure of population affects its evolution. It was introduced by Lieberman et al in 2005.
Lecture #1 : Evolutionary dynamics on graphs
(Wajid Ali, University of Liverpool)
In this lecture, we will briefly introduce the concept of evolution along with some early mathematical models for evolution such as Wright–Fisher model and Moran model. We will focus mainly on evolutionary graph theory models in which member of the population are placed on the vertices of graphs and the edges between the vertices determine where a focal individual will place its offspring. We will identify different network topologies that supress or amplify selection.
Lecture #2 : Evolutionary games on graphs
(Diogo Pires, City University of London)
Evolutionary game theory has proved to be a powerful tool to probe the self-organization of collective behaviour. Game-theoretic approaches look at social interactions through the lens of a game defined by the interacting players, their potential strategies, and the resulting payoffs. Considering populations of interacting individuals and their evolving strategies allows us to go beyond the assumption that everyone acts rationally, and instead understand the settings under which social behaviour emerges. These models often incorporate features of real complex systems, population structure being one of the most studied of those, due to its ubiquitous presence and long-known impact on emerging phenomena. In this session, we will provide an introduction to evolutionary games on graphs, how to model them, and possible extensions of the classic models.
Later in the course, we will discuss some recent research papers in this area.
References:
Lieberman, E., Hauert, C., & Nowak, M. A. (2005). Evolutionary dynamics on graphs. Nature, 433(7023), 312-316.
Szabó, G., & Fath, G. (2007). Evolutionary games on graphs. Physics reports, 446(4-6), 97-216.
Note: Certificates will be awarded to participants who completes 75% of homework. After the completion of this course, interested students can work on a short research project
Moran process:
<\rho> is the probability that the system will hit the state of all red (fixation probability)
Wright-Fisher Model:
The Wright–Fisher (WF) model describes a population with discrete, nonoverlapping generations.
Matrix representation of a graph.
Credit: Lieberman et al (2005)
Complete graph
Cycle graph
Star graph