Time, t (generations) | Initial frequency, y | Time dependent probability of fixation | Error of the numerical result (%) | ||||
---|---|---|---|---|---|---|---|

Numerical result, c(t) | Kimura’s result | Wright–Fisher result | Relative to Kimura’s result | Relative to the Wright–Fisher result | |||

100 | 0.05 | 2.51× 10^{−4} | 2.70 × 10^{−4} | 2.88 × 10^{−4} | 6.9 | 12.7 | |

0.10 | 8.81 × 10^{−4} | 9.37 × 10^{−4} | 9.95 × 10^{−4} | 6.0 | 11.5 | ||

200 | 0.05 | 0.0076 | 0.0077 | 0.0079 | 1.3 | 3.8 | |

0.10 | 0.0177 | 0.0180 | 0.0184 | 1.7 | 3.8 | ||

300 | 0.05 | 0.0205 | 0.0207 | 0.0209 | 1.0 | 1.9 | |

0.10 | 0.0437 | 0.0440 | 0.0444 | 0.7 | 1.6 | ||

400 | 0.05 | 0.0312 | 0.0313 | 0.0315 | 0.3 | 1.0 | |

0.10 | 0.0644 | 0.0645 | 0.0649 | 0.2 | 0.8 | ||

500 | 0.05 | 0.0384 | 0.0385 | 0.0386 | 0.3 | 0.5 | |

0.10 | 0.0780 | 0.0781 | 0.0784 | 0.1 | 0.5 | ||

600 | 0.05 | 0.0429 | 0.0430 | 0.0431 | 0.2 | 0.5 | |

0.10 | 0.0866 | 0.0867 | 0.0868 | 0.1 | 0.2 |

This table gives results for the time-dependent probability of fixation at a neutral locus when the effective population size is

*N*_{e}= 100. It covers different values of the initial frequency,*y*, and different values of the time,*t*. The results were obtained from the numerical scheme of this work, Kimura’s expression for the time-dependent probability of fixation, which took the form of an infinite sum (Kimura 1955b), and the Wright–Fisher model. For the numerical calculations, we fixed the ratio*α*, Equation 5, at the value*α*= 500 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 final two columns of the table contain the magnitude of the error of the numerical approach, relative to Kimura’s result and the Wright–Fisher result.