2.4 | Tests of population history by coalescent simulations
We used fastsimcoal2 ver. 2.6.0.3 (Excoffier et al., 2013) to perform coalescent simulations in pre-defined models to infer the demographic histories associated with speciation for François’ langur and White-headed langur. A two-dimensional joint SFS (2D-SFS) estimation was constructed using only intergenic regions. In splitting an ancestral langur population into François’ langur and White-headed langur, we simulated four models in total: Model 1 assumed that no gene flow occurred after the divergence of François’ langur and White-headed langur; Model 2 assumed constant gene flow between François’ langur and White-headed langur after their divergence; Model 3 assumed that there was secondary contact with asymmetric gene flow; and in Model 4, as a modification of Model 3, we assumed a reverse process, with gene flow at the beginning, then without gene flow at time T1 and with gene flow again at time T2 (Figure 4).
The software used in our analysis and the number of simulation runs has been shown to produce robust results in previous studies (for example, Westbury et al., 2020 publication titled “Hyena paleogenomes reveal a complex evolutionary history of cross-continental gene flow between spotted and cave hyena” used 100,000 simulations per cycle). For each model, we performed a total of 100,000 coalescent simulations to estimate of the expected 2D-SFS and we computed log-likelihoods based on simulated and observed 2D-SFS matrices. Global maximum-likelihood estimates for each model were obtained from 50 independent runs, with 20-50 conditional maximization algorithm cycles. The relative fit of the different demographic models to the data was evaluated using the Akaike Information Criterion (AIC) and the model with the maximum Akaike’s weight value was chosen as the optimal one. A parametric bootstrapping approach was used to construct the 95% confidence intervals with 40 independent runs in each bootstrap.