Evolutionary graph theory
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An area lying at the intersection of graph theory, probability theory, and mathematical biology, evolutionary graph theory is an approach to studying how topology affects evolution of a population. That the underlying topology can substantially affect the results of the evolutionary process is seen most clearly in Lieberman, Hauert and Nowak (2005).
In evolutionary graph theory, individuals propagate from vertex to vertex on a graph; fitter types propagate more readily. Evolutionary graph theory may also be studied in a dual formulation, as a coalescing random walk.
Closely related stochastic processes include the voter model, which was introduced by Clifford and Sudbury (1973) and independently by Holley and Liggett (1975), and which has been studied extensively.
[edit] Bibliography
1. Holley, R., and Liggett, T. (1975) Ergodic theorems for weakly interacting systems and the voter model. Ann. Prob. 4, 195–228
2. Lieberman, E., Hauert, C., and Nowak, M.A. (2005) Evolutionary dynamics on graphs. Nature. 433, 312–316 [1]
3. Liggett, T.M. (1999) Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Springer, New York
4. Clifford, P. and Sudbury, A. (1973) A model for spatial conflict. Biometrika. 60, 581–588
[edit] External links
A virtual laboratory for studying evolution on graphs:[2]
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