Three apicomplexans and three dinoflagellates were used as outgroups (Additional file 1: Table S2)44 (link). Maximum likelihood (ML) analyses were carried out using RAxML-HPC2 v7.6.6114 (link) on CIPRES Science Gateway115 . The DNA partition was analyzed with GTR + gamma. ProtTest 2.4116 (link) selected the MtArt + I + G + F amino acid replacement matrix as the best-fitting model for alpha-tubulin amino acid sequences. The alpha-tubulin amino acid partition was run under the MtArt + gamma model as this was the best-fitting model available in RAxML. Support for the best-scoring ML tree came from 1000 bootstrap replicates. Bayesian inference (BI) analysis was performed with MrBayes 3.2.2117 (link) on CIPRES Science Gateway using the GTR + I + G model for the DNA partition as selected by MrModeltest v.2.2118 and using mixed model for the alpha-tubulin amino acid partition. Markov chain Monte Carlo (MCMC) simulations were run with two sets of four chains for 4,000,000 generations with a sample frequency of 100 generations. The first 10,000 trees were discarded as burn-in. All remaining trees were used to calculate posterior probabilities using a majority rule consensus. Systematic schemes are mainly based on Lynn5 and Adl et al.44 (link), except for some revisions made in the present study.
The approximately unbiased (AU) test119 (link) was used to test the monophyly of the focal group against competing phylogenetic hypotheses (Table 1). Constrained ML trees enforcing the monophyly of the respective focal groups were generated based on SSU rDNA data. For all constraints, internal relationships within the constrained groups and among the remaining taxa were unspecified. The site-wise likelihoods for the resulting constrained topologies and the non-constrained ML topology were calculated using PAUP120 and were then analyzed in CONSEL121 (link) with standard parameters to obtain p-values.
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