The downhill simplex method (Press et al., 1997) was employed to search for the maximum likelihood estimates (MLE) of the model parameters for each model.
Because PTP initiates the search for the maximum likelihood delimitation at the root of the input phylogeny, the tree has to be correctly rooted to obtain accurate estimates.
Our search for the maximum likelihood genealogy, in which 121 terminals had mtCR and mtATP (842 bp) concatenated, resulted in a tree with LnL −9497.713.
We ran 1000 searches and 2000 bootstrap replicates in Garli0.96 [ 17] to search for a maximum likelihood topology under the model TrN+I+G selected by Modeltest 3.7 [ 18] using the Akaike information criterion.
PAUP* was then used to search for the maximum likelihood (ML) tree, based on the best fit model and parameter estimates given by ModelTest (Table 1) and using a heuristic search with tree bisection reconnection (TBR).
The "-f a" option was used in RAxML for the simultaneous search for the best likelihood tree and rapid bootstrap analysis with "-# 1,000 1,00000 bootstrap replications) with default options of "-i" (automatically optimized SPR branch rearrangement for heuristic search) and "-c" (25 distinct rate categories).
A rapid bootstrap analysis [ 65] on 100 replicates followed by search for the maximum likelihood tree was performed using RAxML 7.2.6 (PTHREADS) with the GTR (General Time Reversible) amino acid substitution model with site-specific evolutionary rates (4 discrete GAMMA categories).
A heuristic search for a maximum-likelihood tree, under time reversible model of nucleotide substitution, with proportion of invariable sites and gamma rate distribution was made.
To search for the maximum-likelihood point over the parameter space, we applied the ECM (Expectation/Conditional Maximization) method (Meng and Rubin 1993), which was previously used in the demographic inference study by Excoffier et al. (2013).
Analytical solutions for the marginal likelihood do not exist; therefore, several methods were implemented approximating the marginal likelihood while searching for the maximum likelihood.
