An analysis of the fixation probability of a mutant on special classes of non-directed graphs
By Mark Broom, Jan Rychtár. Proceedings of the Royal Society A, 2008
200 citations recorded by the source corpus.
There is a growing interest in the study of evolutionary dynamics on populations with some non-homogeneous structure. In this paper we follow the model of Lieberman et al. (Lieberman et al. 2005 Nature 433, 312–316) of evolutionary dynamics on a graph. We investigate the case of non-directed equally weighted graphs and find solutions for the fixation probability of a single mutant in two classes of simple graphs. We further demonstrate that finding similar solutions on graphs outside these classes is far more complex. Finally, we investigate our chosen classes numerically and discuss a number of features of the graphs; for example, we find the fixation probabilities for different initial starting positions and observe that average fixation probabilities are always increased for advantageous mutants as compared with those of unstructured populations.
Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/833300745c21528d968eb4a0453818413e6ec86b
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Citations in the corpus
- Evolutionary Dynamics on Graphs - the Effect of Graph Structure and Initial Placement on Mutant Spread (2011, background): “There is an equality in (4.1) for star graphs (Broom and Rychtář, 2008).”
- Two results on evolutionary processes on general non-directed graphs (2010, methodology): “The paper Broom & Rychtář (2008) analytically investigated the probability for mutants to fixate in an otherwise uniform population on two types of heterogeneous graphs (lines and stars) by evolutionary dynamics.”
- Martingales and fixation probabilities of evolutionary graphs (2014, background): “Some graphs are sufficiently symmetric to allow inductive evaluation of recursive equations, but this results in complex expressions for fixation probabilities [4,11].”
- Evolutionary dynamics on small-order graphs (2009, background): “∗E-mail: M.Broom@sussex.ac.uk †E-mail: rychtar@uncg.edu ‡E-mail: btstadle@uncg.edu ——————————– Journal of Interdisciplinary Mathematics Vol. 12 (2009), No. 2, pp. 129–140 c© Taru Publications”
- Evolutionary games on graphs and the speed of the evolutionary process (2010, background): “(2.17) We note that in the case where mutant individuals have fixed fitness equal to r and resident individuals’ fitness is equal to 1 we recover the formula of the fixation probability from Broom & Rychtář (2008).”