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Table 3: Prior and posteriors parameter estimates for AC, RI, ACS and RIS models.

Validation of model selection and parameter estimation

When comparing all five simple models simultaneously, the cross-validation method was not able to discriminate them. The ED and AC models were consistently easiest to identify. However, in the pairwise model comparisons, and in the simultaneous evaluation of the four models (i.e. AC and RI models with and without structure), cross-validation support improved substantially (Supplementary Tables S2c). However, the method was not able to distinguish between the simple and the structured version of the same model (i.e. between AC, and ACS, RI and RIS), which could be because these models (with and without structure) are very similar. Altogether, this cross-validation provided confidence in the model choice results and further support to the high posterior probability values obtained for the AC model using the model choice procedure.

We estimated the posterior distributions for the parameters in the best-supported model (i.e. the AC model with wide prior on mutation rate for all microsatellite loci; Table 3 shows that the posterior density curves of the current (N_Cur), and ancestral effective population size (N_Anc), differ noticeably from the priors. This indicates that these posterior values were informative as being derived from the genetic data rather than being driven by the prior values.

Figure 3

Posterior (black solid lines) and prior (dashed grey lines) distributions of demographic parameters for Bornean elephant estimated through ABC analysis and according to the best-fitting model (ancient colonization). Point estimates and 95% credibility intervals for all key parameters obtained through simulations are also given. Note that in (a) and (b) values were converted from log to linear scale. See Fig. 3 for further details on the demographic parameters.

Examining the influence of prior assumptions

For our initial ABC simulations, we chose prior distributions tightly bounded around values based on the available historical data. However, to explore sensitivity to these assumptions, we conducted additional simulations with broader prior assumptions on effective population sizes and the time of bottleneck (see supporting materials). In all cases, the same demographic model (AC) was the most supported as in the initial simulations. For comparison, we note that the supplementary simulations based on fixed mutation rate value (i.e. 10?3) and broader prior assumptions on N_Anc and T_shrink yielded lower posterior estimates than in our initial simulations. Notably, the time (T_shrink) in this model exhibits a posterior which was again different from the prior with a mean estimate of 11,400 years before present. Additionally, the T_shrink parameter was insensitive to the mutation rate, whereas, as expected, the ancestral and current population sizes were (see Fig. S6). Therefore, the dating of the founder event in the AC scenario is robust and relatively ancient. This is not necessarily as surprising as 1 mg blue ksalol xanax may seem since genetic diversity after a bottleneck event is mainly driven by genetic drift, and does not depend so much on mutation rates.

We further tested the impact of mutation rate on our inferences by simulating the AC and RI demographic models a second time, using fixed mutation rates of 10?3, 10?4, and 10?5. Simulation of the two models using different mutation values still favoured the AC model (with mean mutation rate 10?3 for all loci) over RI and revealed similar estimates for the dating of the founder event (18,000 years before present, Fig. S7).

(ii) mtDNA simulations

The results from the simulations using mtDNA data showed the AC model to have the highest number of simulations (64,344 out of 100,000) with zero diversity, as observed in present-day Bornean elephants, consistent with the results obtained using microsatellite data (Supplementary Table S5). However, two other models (RI and TI) also yielded a high proportion of zero diversity (49,451 and 54,564), making 1 mg blue ksalol xanax difficult to distinguish the three models (AC, RI and TI) using mtDNA data alone.

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