Parameter Estimation
Once the best model for each species was identified, we used Fastsimcoal2 to estimate its demographic parameters and their 95% confidence intervals using the full, linked SNP datasets for each species and the monomorphic cell of the jSFS. We also estimated an additional parameter not included in the prior modeling: the mutation rate (\(\mu\)) in substitutions/site/million years. Fastsimcoal2 uses a modified expectation maximization algorithm, known as a conditional expectation maximization (ECM; Brent 1974, Meng and Rubin 1993) for maximum-likelihood optimization, which can get trapped in local optima of the likelihood surface. Therefore, we performed 100 independent parameter optimizations with different initial values, 100,000 simulations to estimate the expected folded jSFS, and 40 conditional EM cycles per optimization. Following the first optimization, we identified the global maximum likelihood and parameter estimates and performed an additional 100 independent optimizations using these maximum likelihood parameter estimates as the starting values.
To estimate confidence intervals, we simulated 100 parametric bootstrap replicates using the ML parameter estimates from the final optimizations of the empirical datasets. We then re-optimized parameters of the simulated datasets, initiating the parameters at the maximum-likelihood estimates from the original optimization. We used these parameter estimates to generated 95% high density confidence intervals for all parameters (Kruschke 2011).
All computational analyses were done using servers at the IBEST Computational Resources Core at the University of Idaho.