Fast and Deterministic Computation of Fixation Probability in Evolutionary Graphs

Abstract

In evolutionary graph theory biologists study the problem of determining the probability that a small number of mutants overtake a population that is structured on a weighted, possibly directed graph. Currently Monte Carlo simulations are used for estimating such fixation probabilities on directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic algorithm for computing fixation probabilities for strongly connected directed, weighted evolutionary graphs under the case of neutral drift, which we show to be a lower bound for the case where the mutant is more fit than the rest of the population (previously, this was only observed from simulation). We also show that, in neutral drift, fixation probability is additive under the weighted, directed case. We implement our algorithm and show experimentally that it consistently outperforms Monte Carlo simulations by several orders of magnitude, which can allow researchers to study fixation probability on much larger graphs.

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Document Details

Document Type
Technical Report
Publication Date
Nov 07, 2012
Accession Number
ADA578231

Entities

People

  • Patrick Roos
  • Paulo Shakarian

Organizations

  • United States Military Academy

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Bayes Theorem
  • Computations
  • Convergence
  • Data Science
  • Extinction
  • Graph Theory
  • Monte Carlo Method
  • Network Science
  • Probability
  • Probability Distributions
  • Random Variables
  • Real Numbers
  • Simulations
  • Social Networks
  • Stochastic Processes
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Operations Research
  • Statistical inference.