A novel analytical method for evolutionary graph theory problems

Paulo Shakarian, Patrick Roos, Geoffrey Moores

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.

Original languageEnglish (US)
Pages (from-to)136-144
Number of pages9
JournalBioSystems
Volume111
Issue number2
DOIs
StatePublished - Feb 2013
Externally publishedYes

Fingerprint

Graph theory
Fixation
Analytical Methods
Mutant
Graph in graph theory
Monte Carlo Simulation
Voter Model
Evolutionary Dynamics
Structured Populations
Directed graphs
Population Dynamics
Neurology
Directed Graph
Lower bound
Calculate
Computing
Experimental Results
Population
Framework
Monte Carlo simulation

Keywords

  • Complex networks
  • Evolutionary dynamics
  • Moran process

ASJC Scopus subject areas

  • Biochemistry, Genetics and Molecular Biology(all)
  • Applied Mathematics
  • Modeling and Simulation
  • Statistics and Probability

Cite this

A novel analytical method for evolutionary graph theory problems. / Shakarian, Paulo; Roos, Patrick; Moores, Geoffrey.

In: BioSystems, Vol. 111, No. 2, 02.2013, p. 136-144.

Research output: Contribution to journalArticle

Shakarian, Paulo ; Roos, Patrick ; Moores, Geoffrey. / A novel analytical method for evolutionary graph theory problems. In: BioSystems. 2013 ; Vol. 111, No. 2. pp. 136-144.
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