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.