Example posteriors for uniform (A) and discontinuous (B) priors. The model is the same as in Figure 1. Posterior estimates using ABC–GLM and ABC–REG for S_obs = 16 were based on 5000 simulations with dist(S, S_obs) < 10. ABC–REG posteriors were smoothed with a bandwidth of 0.4, and the width of the Dirac peaks in the ABC–GLM approach was set to 10⁻⁵.

Comparison of rejection (A and D), ABC–REG (B and E), and ABC–GLM (C and F) posteriors with those obtained from analytical likelihood calculations. We estimated the population–mutation parameter θ = 4Nμ of a panmictic population for different observed numbers of segregating sites (see text). Shades indicate the L₁ distance between the inferred and the analytically calculated posterior. White corresponds to an exact match (zero distance) and darker gray shades indicate larger distances. If the inferred posterior differs from the analytical more than the prior does, squares are marked in black. The top row (A–C) corresponds to cases with a uniform prior θ ∼ Unif([0.005, 10]) and the bottom row (D–F) to cases with a discontinuous prior with “gap.” The tolerance ε is given as the absolute distance in number of segregating sites. Shown are averages over 25 independent estimations. To have a fair comparison, we adjusted the smoothing parameters (bandwidths) to get the best results for all approaches.

Bayes factor for the island relative to the panmictic population model for different acceptance rates (logarithmic scale). For very low acceptance rates we observe large fluctuations whereas the Bayes factor is quite stable for larger values. Note that A_ε ≤ 0.005 corresponds to ≤500 simulations, too small a sample size for robust statistical model estimation.