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Supplementary file for Bessho and Otto, \[OpenCurlyDoubleQuote]Fixation \
probability in a haploid-diploid population\[CloseCurlyDoubleQuote].\
\>", "Section"],
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Here we put supplementary information for our manuscript, \
\[OpenCurlyDoubleQuote]Fixation probability in a haploid-diploid population\
\[CloseCurlyDoubleQuote].
Note that, you might have to reset the variables as necessary because we \
reuse same variables in the different sections.\
\>", "Text"]
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Deriving the fixation probability in the haploid-diploid Moran model\
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The relevant solution is the second one. Calculating the probability of \
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Diffusion Approximation (First Moment / Separation of Time Scale)\
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We first derive the first moment of change in mutant allele frequency appying \
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EqOrder1pM (pM)
EqOrder1\[Delta]p (pM, \[Delta]p)
EqOrder1\[Rho]H (pM, \[Rho]H)
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We next derive the second moment of change in mutant allele frequency\
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Explicitly tracking the genotypes of the deaths, deaths occur in proportion \
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or diploid (i.e., assuming that the allele frequencies will remain near each \
other) and ignoring the slight fluctuations that would occur around the \
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In the following, we keep track of changes in the allele frequency, pM:\
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Conclusion:
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EqOrder1\[Delta]p(p, \[Delta]p)
EqOrder1\[Rho]H(p, \[Rho]H)
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Conclusion:
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As ploidally antagonistic selection becomes stronger, however, the M allele \
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We next derive the selection coefficient of allele R, reversing the effects \
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This is when M stops being selected when common.
We next ask when R can actually invade a population fixed on M, according to \
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We first plot the fixation probability of allele M when allele M is rare.\
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We next derive the invasibility of allele R, reversing the effects of allele \
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To consider this fixation probability, we now define the rare allele as m \
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As ploidally antagonistic selection becomes stronger, however, the M allele \
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This is when M stops being selected when common.
We next ask when R can actually invade a population fixed on M, according to \
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We first plot the fixation probability of allele M when allele M is rare.\
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We next derive the invasibility of allele R, reversing the effects of allele \
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