Figure 4.

Accuracy of fixation probability formula. Here we compare the approximate fixation probabilities computed with Equation 1 to Monte Carlo (MC) simulations for N = 1000. In parts A - I, θ varies by row, and s by column. The MC estimates for p_fix (m, θ) and p_fix (θ, m) are indicated by squares and circles respectively, and the vertical bars through these symbols indicate the standard error based on 10⁶ trials. Equation 1 sometimes becomes inaccurate when θ and m are large, particularly for intermediate values of sN ≈ 10, for which selection is important but fairly slow. This is most noticeable in part H. Note that m̂_opt ≈ θ for s = 1, but switching probabilities smaller than θ are favored for s = 0.0001. The gray shaded areas indicate the regions between p̂_fix from Equation 1 and the heuristic bound for p_fix described in Appendix C. The heuristic bound for p_fix (m₁, m₂) is typically a lower-bound when m₁ < m₂ and an upper-bound when m₂ < m₁. (The shaded areas are often too narrow to be seen.)