City Research Online

An analysis of the fixation probability of a mutant on special classes of non-directed graphs

Broom, M. & Rychtar, J. (2008). An analysis of the fixation probability of a mutant on special classes of non-directed graphs. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 464(2098), pp. 2609-2627. doi: 10.1098/rspa.2008.0058

Abstract

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.

Publication Type: Article
Subjects: H Social Sciences > HA Statistics
Q Science > QH Natural history
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
[thumbnail of lines8.pdf]
Preview
PDF
Download (265kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login