Population genetics on islands connected by an arbitrary network: An analytic approach

George W.A. Constable, Alan J. McKane

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30 Citations (SciVal)


We analyse a model consisting of a population of individuals which is subdivided into a finite set of demes, each of which has a fixed but differing number of individuals. The individuals can reproduce, die and migrate between the demes according to an arbitrary migration network. They are haploid, with two alleles present in the population; frequency-independent selection is also incorporated, where the strength and direction of selection can vary from deme to deme. The system is formulated as an individual-based model and the diffusion approximation systematically applied to express it as a set of nonlinear coupled stochastic differential equations. These can be made amenable to analysis through the elimination of fast-time variables. The resulting reduced model is analysed in a number of situations, including migration-selection balance leading to a polymorphic equilibrium of the two alleles and an illustration of how the subdivision of the population can lead to non-trivial behaviour in the case where the network is a simple hub. The method we develop is systematic, may be applied to any network, and agrees well with the results of simulations in all cases studied and across a wide range of parameter values.

Original languageEnglish
Pages (from-to)149-165
Number of pages17
JournalJournal of Theoretical Biology
Early online date1 Jun 2014
Publication statusPublished - 7 Oct 2014


  • Fast-mode reduction
  • Metapopulation
  • Migration
  • Moran model
  • Selection

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • General Biochemistry,Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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