3.4 | Neural-Network ABC parameter inference accuracy for the ACB and ASW populations
For the ACB under the AfrDE-EurDE scenario (Figure 4A ,Table 2 ), we found that the two recent admixture intensities from Africa and Europe (s Afr,20 ands Eur,20, respectively) and the steepness of the European recurring introgression decrease (u Eur) had sharp posterior densities clearly distinct from their respective priors. Note that the cross-validation error on these parameters in the vicinity of our real data were low (average absolute error 0.02744, 0.0044, and 0.1084, respectively for s Afr,20,s Eur,20, and u Eur) (Table 3 ), and lengths of 95% CI reasonably accurate (96.4%, 94.4%, 94.1% of 1,000 cross-validation true parameter values fell into estimated 95% CI, Supplementary Table S4 ).
Furthermore, the two ancient admixture intensities from Africa and Europe at generation 1 (s Afr,1 ands Eur,1, respectively), also had posterior densities apparently distinguished from their prior distributions, but both had much wider 95% CI (Figure 4A , Table 2 ). Consistently, we found a slightly increased posterior parameter error in this part of the parameter space for both parameters, with average absolute error equal to 0.121 and 0.095 respectively fors Afr,1 and s Eur,1(Table 3 ). Nevertheless, note that 95.8% and 94.7% of 1,000 cross-validation true values for those two parameters fell into the estimated 95% CI (Supplementary Table S4) . This shows a reasonably conservative behavior of our method for these estimations, albeit indicating that information is lacking in our data or set of summary statistics for a more accurate estimation of these parameters, rather than an inherent inaccuracy of our approach.
Interestingly (Figure 4A , Table 2 ), we found that accurate posterior estimation of the steepness of the African recurring introgression decrease (u Afr) is difficult. Indeed, the posterior density of this parameter showed a tendency towards small values only slightly departing from the prior, indicative of a limit of our method to estimate this parameter (Figure 4A ,Table 2 ). Finally (Figure 4A , Table 2 ), we found that we had virtually no information to estimate the founding admixture proportions from Africa and Europe at generation 0, as our posterior estimates barely departed from the prior and associated mean absolute error was high (0.2530, Table 3 ). Nevertheless, our method seemed to be performing reasonably conservatively for these two latter parameters (95.6% and 95.3% of 1,000 cross-validation true parameter values fell into estimated 95% CI, Supplementary Table S4 ). This indicates that information is strongly lacking in our data or summary statistics for successfully capturing these parameters, rather than inherent inaccuracy of our approach.
For the ASW under the AfrDE-EurDE model, our posterior parameter estimation results were overall less accurate compared to those obtained for the ACB population, as indicated by overall larger CI and cross-validation errors (Figure 4B , Table 2 ,Table 3 , Supplementary Table S4 ). This was consistent with the more ambiguous RF-ABC model-choice results obtained for this population (Figure 3 ).
Note that, we conducted the above analyses under the loosing scenario Afr2P-Eur2P instead, for comparison. We find, as expected, that parameters and 95% CI are very poorly estimated for all parameters under this model (Supplementary Table S3 and S5 ). This indicates, consistently, that no information is available in the ACB or ASW data for accurate and conservative estimation of the loosing scenario Afr2P-Eur2P parameters using ABC.