Voter model and biased voter model in heterogeneous environments

Nicolas Lanchier, C. Neuhauser

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

With the rapid adoption of transgenic crops, gene flow from transgenic crops to wild relatives through pollen dispersal is of significant concern and warrants both empirical and theoretical studies to assess the risk of introduction of transgenes into wild populations. We propose to use the (biased) voter model in a heterogeneous environment to investigate the effects of recurrent gene flow from transgenic crop to wild relatives. The model is defined on the d-dimensional integer lattice that is divided into two parts, Δ and ℤ d \ Δ. Individuals carrying the transgene and individuals carrying the wild type gene compete according to the evolution rules of a (biased) voter model on ℤ d \ Δ, while the process is conditioned to have only individuals carrying the transgene on Δ. Our main findings suggest that unless transgenes confer increased fitness in wild relatives, introgression of transgenes into populations of wild plants is slow and may even be reversible without intervention. Our study also addresses the effects of different spatial planting patterns of transgenic crops on the rate of introgression.

Original languageEnglish (US)
Pages (from-to)770-787
Number of pages18
JournalJournal of Applied Probability
Volume44
Issue number3
DOIs
StatePublished - Sep 2007

Fingerprint

Voter Model
Heterogeneous Environment
Biased
Gene
Pollen
Spatial Pattern
Fitness
Integer
Vote
Transgenic crops
Model

Keywords

  • Interacting particle systems
  • Random walk
  • Transgenic crops
  • Voter model interfaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Voter model and biased voter model in heterogeneous environments. / Lanchier, Nicolas; Neuhauser, C.

In: Journal of Applied Probability, Vol. 44, No. 3, 09.2007, p. 770-787.

Research output: Contribution to journalArticle

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