Approximating Fixation Probabilities in the Generalized Moran Process

Mertzios, G.B.

doi:10.1007/978-3-642-27848-8_596-1

Approximating Fixation Probabilities in the Generalized Moran Process

Mertzios, G.B.

Authors

Dr George Mertzios george.mertzios@durham.ac.uk
Associate Professor

Contributors

Ming-Yang Kao
Editor

Abstract

Problem Definition Population and evolutionary dynamics have been extensively studied, usually with the assumption that the evolving population has no spatial structure. One of the main models in this area is the Moran process [17]. The initial population contains a single “mutant” with fitness r > 0, with all other individuals having fitness 1. At each step of the process, an individual is chosen at random, with probability proportional to its fitness. This individual reproduces, replacing a second individual, chosen uniformly at random, with a copy of itself. Lieberman, Hauert, and Nowak introduced a generalization of the Moran process, where the members of the population are placed on the vertices of a connected graph which is, in general, directed [13, 19]. In this model, the initial population again consists of a single mutant of fitness r > 0 placed on a vertex chosen uniformly at ...

Citation

Mertzios, G. (2014). Approximating Fixation Probabilities in the Generalized Moran Process. In M. Kao (Ed.), Encyclopedia of algorithms (1-6). Springer Verlag. https://doi.org/10.1007/978-3-642-27848-8_596-1

Acceptance Date	Oct 3, 2013
Publication Date	Nov 26, 2014
Deposit Date	Mar 13, 2015
Publisher	Springer Verlag
Pages	1-6
Book Title	Encyclopedia of algorithms.
DOI	https://doi.org/10.1007/978-3-642-27848-8_596-1
Keywords	Evolutionary dynamics, Moran process, Fixation probability, Markov-chain Monte Carlo, Approximation algorithm.