Evolutionary graph theory revisited: when is an evolutionary process equivalent to the Moran process?

Pattni, K., Broom, M., Rychtar, J. & Silvers, L. J. (2015). Evolutionary graph theory revisited: when is an evolutionary process equivalent to the Moran process?. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471, e2182. doi: 10.1098/rspa.2015.0334

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Abstract

Evolution in finite populations is often modelled using the classical Moran process. Over the last 10 years, this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such population is whether a rare mutant has a higher or lower chance of fixating (the fixation probability) than the Moran probability, i.e. that from the original Moran model, which represents an unstructured population. As evolutionary graph theory has developed, different ways of considering the interactions between individuals through a graph and an associated matrix of weights have been considered, as have a number of important dynamics. In this paper, we revisit the original paper on evolutionary graph theory in light of these extensions to consider these developments in an integrated way. In particular, we find general criteria for when an evolutionary graph with general weights satisfies the Moran probability for the set of six common evolutionary dynamics.

Item Type: Article
Additional Information: Copyright The Royal Society 2015
Uncontrolled Keywords: finite population, evolutionary dynamics, Moran process, fixation probability
Subjects: G Geography. Anthropology. Recreation > G Geography (General)
Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/13209

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