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.