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. 2011 Aug;188(4):975–996. doi: 10.1534/genetics.111.128876

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Copyright © 2011 by the Genetics Society of America

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Figure A1 — Asymptotic behavior of the survival probability for the communal and infinitesimal recombination models. (A) The survival probability Φ(τ), obtained by numerical solution of Equation A1 for the communal recombination model, exhibits the predicted asymptotic behavior $\sqrt{- 2 {\tilde{r}}^{2} \log Φ} \sim W ({\tilde{r}}^{3} τ e^{- 1 - {\tilde{r}}^{2} / 2})$ (Equation 5). (B) The survival probabilities in the infinitesimal model (IM) and the communal model (CM), determined by simulating the branching process, exhibit a similar scaling collapse, indicating that the dependence on parameters is similar. (C) The first passage time, T_fp, to allele copy number νN, is well described by the branching process approximation for the dynamics of alleles in a finite population as long as the frequency $ν ≪ 1$ . This is confirmed here by plotting $\sqrt{2 {\tilde{r}}^{2} \log σ ν N}$ vs. $W ({\tilde{r}}^{3} σ T_{fp} e^{- 1 - {\tilde{r}}^{2} / 2})$ . The collapse of data for different $\tilde{r}$ and different ν confirms the predicted parameter dependence (Equation 7), while the concordance with the branching process results confirms the branching process model. Deviation from the branching process prediction is apparent for ν = 0.5. Recombination rates in C follow the same color code as in A and B, while black symbols correspond to $\tilde{r} = 1$ .

Figure A1 — Asymptotic behavior of the survival probability for the communal and infinitesimal recombination models. (A) The survival probability Φ(τ), obtained by numerical solution of Equation A1 for the communal recombination model, exhibits the predicted asymptotic behavior $\sqrt{- 2 {\tilde{r}}^{2} \log Φ} \sim W ({\tilde{r}}^{3} τ e^{- 1 - {\tilde{r}}^{2} / 2})$ (Equation 5). (B) The survival probabilities in the infinitesimal model (IM) and the communal model (CM), determined by simulating the branching process, exhibit a similar scaling collapse, indicating that the dependence on parameters is similar. (C) The first passage time, T_fp, to allele copy number νN, is well described by the branching process approximation for the dynamics of alleles in a finite population as long as the frequency $ν ≪ 1$ . This is confirmed here by plotting $\sqrt{2 {\tilde{r}}^{2} \log σ ν N}$ vs. $W ({\tilde{r}}^{3} σ T_{fp} e^{- 1 - {\tilde{r}}^{2} / 2})$ . The collapse of data for different $\tilde{r}$ and different ν confirms the predicted parameter dependence (Equation 7), while the concordance with the branching process results confirms the branching process model. Deviation from the branching process prediction is apparent for ν = 0.5. Recombination rates in C follow the same color code as in A and B, while black symbols correspond to $\tilde{r} = 1$ .