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  • Numerical models

    Deterministic recursions are defined for single populations, or one-dimensional stepping-stone models.  There must be two alleles at each locus, but otherwise these recursions are fairly general.  They are designed for numerical iteration, and are reasonably fast for up to ~6 loci.

  • For example, this iterates a model of epistatic selection against heterozygotes, with 3 loci and 20 demes:

    • [Graphics:../Images/index_gr_18.gif]

  • Cline width reaches equilibrium at w=5.31 for all 3 loci within 200 generations 

    • [Graphics:../Images/index_gr_19.gif]
    0 1 1 1
    50 5.20775486910014517` 5.20775486910014695` 5.20775486910014695`
    100 5.29734636763913169` 5.29734636763913169` 5.29734636763913524`
    150 5.30619373083351941` 5.30619373083352208` 5.3061937308335203`
    200 5.30728884369828612` 5.30728884369828612` 5.30728884369828168`

    More loci can be followed if one can assume that all genotypes carrying x/n '1' alleles are equivalent.  Such 'symmetric' models can be iterated in one population or across a one-dimensional stepping sone model.  The stability of the symmetric solution can be determined.

  • For example, this gives the eigenvalues that describe the stability of the above model, with 3 genes and 20 demes:

    • [Graphics:../Images/index_gr_20.gif]
    [Graphics:../Images/index_gr_21.gif]

    Converted by Mathematica      April 16, 2002

    This site is no longer maintained and has been left for archival purposes

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