Description | Probability of Ultimate Fixation | Error of Numerical Result (%) | |||||
---|---|---|---|---|---|---|---|

Scenario | s | Numerical Result | Averaged Kimura Result | Simulation Result | Relative to the Averaged Kimura Result | Relative to the Simulation Result | |

Reference case: Constant population size, N = 100 | −0.001 | 0.0830 | 0.0830 | 0.0853 | 0.0 | 2.7 | |

0.000 | 0.1000 | 0.1000 | 0.1044 | 0.0 | 4.2 | ||

0.010 | 0.3358 | 0.3358 | 0.3365 | 0.0 | 0.2 | ||

Reference case: Constant population size, N = 200 | −0.001 | 0.0676 | 0.0680 | 0.0689 | 0.6 | 1.9 | |

0.000 | 0.0995 | 0.1000 | 0.0987 | 0.5 | 0.8 | ||

0.010 | 0.5508 | 0.5509 | 0.5513 | 0.0 | 0.1 | ||

Figure 4 (i): Population size discontinuously increases from N = 100 to N = 200 at t = 100 | −0.001 | 0.0747 | 0.0750 | 0.0713 | 0.4 | 4.8 | |

0.000 | 0.0996 | 0.1000 | 0.1000 | 0.4 | 0.4 | ||

0.010 | 0.3841 | 0.3841 | 0.3866 | 0.0 | 0.6 | ||

Figure 4 (ii): Population size continuously increases | −0.001 | 0.0731 | 0.0734 | 0.0711 | 0.4 | 2.8 | |

0.000 | 0.0996 | 0.1000 | 0.0998 | 0.4 | 0.2 | ||

0.010 | 0.4029 | 0.4030 | 0.4010 | 0.0 | 0.5 | ||

Figure 4 (iii): Population size discontinuously increases from N = 100 to N = 200 at t = 200 | −0.001 | 0.0763 | 0.0771 | 0.0768 | 1.0 | 0.7 | |

0.000 | 0.0997 | 0.1000 | 0.0952 | 0.3 | 4.7 | ||

0.010 | 0.3638 | 0.3638 | 0.3707 | 0.0 | 1.9 |

This table compares the effects of different scenarios of demographic change on the probability of ultimate fixation when the initial frequency is y = 0.1. It includes two reference cases (populations of constant size) and three cases where the population size changes over time, which are illustrated in Figure 4. For the long-time numerical calculations (column “Numerical result” in the table), we fixed the ratio

*α*, Equation 5, at the value*α*= 1000 and determined the probability associated with bin*K*at a sequence of progressively smaller values of the spacing of discrete frequencies,*ε*. Extrapolating a straight line through the data yielded the values given in the table (cf. Figure 3). The values in the column “Averaged Kimura result,” were obtained using the approach in*Appendix C*; these values used the entire distribution of the frequency and provide some evidence of its numerical accuracy. The simulations for this table were made within the framework of a Wright–Fisher model (Fisher 1930; Wright 1931). In such a framework, selection is treated as a deterministic process, and only the process of population thinning in the life cycle, corresponding to the random sampling of individuals without regard to type (*i.e.*, random genetic drift) is treated stochastically. The simulation results were obtained from 10^{4}replicate populations and simulations were continued until all populations either fixed or lost the*A*allele.