Towards a theoretical framework for analysis and intervention of random drift on general networks

Shaolin Tan, Jinhu Lu, David John Hill

Research output: Contribution to journalArticleResearchpeer-review

49 Citations (Scopus)

Abstract

It is well known that evolution is a fundamental phenomenon driving nature. And random drift is a basic force for population evolution. This technical note aims at constructing a unified theoretical framework for analyzing and intervening in random drift of binary states on general networks. In detail, a general methodology is developed for calculating the fixation probability with different dynamics, including the Wright-Fisher (WF), birth-death (BD), and death-birth (DB) processes. In particular, we prove that the fixation probability of a mutant at node $k$ corresponds to the $k$-th element of stationary distribution of a stochastic matrix deduced from the weight matrix of the networks. Intuitively, it provides an effective way to discover the invasion hubs of structured population and further to intervene in random drift on networks. Finally, a typical example is then given to validate the above theoretical results.

Original languageEnglish
Article number6826557
Pages (from-to)576-581
Number of pages6
JournalIEEE Transactions on Automatic Control
Volume60
Issue number2
DOIs
Publication statusPublished - Feb 2015
Externally publishedYes

Keywords

  • Evolutionary dynamics
  • fixation probability
  • general networks
  • random drift

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