Journal of Mathematical Biology

, Volume 2, Issue 3, pp 219–233 | Cite as

A selection-migration model in population genetics

  • W. H. Fleming


We consider a model with two types of genes (alleles) A1 A2. The population lives in a bounded habitat R, contained in r-dimensional space (r= 1, 2, 3). Let u (t, x) denote the frequency of A1 at time t and place x ɛ R. Then u (t, x) is assumed to obey a nonlinear parabolic partial differential equation, describing the effects of population dispersal within R and selective advantages among the three possible genotypes A1A1, A1A2, A2A2. It is assumed that the selection coefficients vary over R, so that a selective advantage at some points x becomes a disadvantage at others. The results concern the existence, stability properties, and bifurcation phenomena for equilibrium solutions.


Differential Equation Partial Differential Equation Stochastic Process Probability Theory Population Genetic 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • W. H. Fleming
    • 1
  1. 1.Lefschetz Center for Dynamical Systems Division of Applied MathematicsBrown UniversityProvidenceUSA

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