Among the three additional models considered, CAT + GTR_nt + Γ₄ 43 (see Methods) yielded the best fit to the nucleotide data set, and it outperformed GTR_nt + Γ₄ by 103 points of cross-validated likelihood (Additional file 4, Table S3). Moreover, posterior predictive tests showed that this model correctly anticipated the level of saturation of the nucleotide data set (p > 0.28, Additional file 5, Table S4). This suggests that the CAT + GTR_nt + Γ₄ model is not misled by site saturation. CAT + GTR_nt + Γ₄ strongly supported the monophyly of great ape and rodent parasites, considering either all codon positions (PP = 0.99, Table 1), first and second (see Additional file 6, Figure S2), or third codon positions (PP = 0.92 and PP = 0.65 respectively, Additional file 3, Table S2).

Third codon positions were compositionally heterogeneous (see above χ ² tests), and they carried 54% of variable sites. Hence, potential convergence of sequence compositions could have misled the previously used time-homogeneous models 50 51 52 . Interestingly, posterior predictive tests showed that the compositional heterogeneity across taxa of first and second codon positions was correctly anticipated under the time-homogeneous models GTR_nt + Γ₄ and CAT + GTR_nt + Γ₄ (p > 0.44, Additional file 5, Table S4), suggesting that these models are relatively robust to compositional changes in this data set.

The time-heterogeneous model GTR_nt + BP + Γ₄ 50 (see Methods) explicitly accounts for variations in composition across taxa. It correctly anticipated the observed compositional heterogeneity, considering either all, first and second, and third codon positions (p > 0.11, Additional file 5, Table S4), suggesting that this model is unlikely to be misled by compositional heterogeneity across taxa. The monophyly of great ape and rodent parasites was strongly supported under the GTR_nt + BP + Γ₄ model, considering either all codon positions (PP = 0.95, Table 1), first and second, or third codon positions (PP = 0.99 and PP = 0.72 respectively, Additional file 3, Table S2).

According to the analysis of the amino-acid data set, methodological bias may arise from the use of the universal replacement model JTT. The peculiar A+T rich composition of Haemosporidian genes could lead to slightly different estimations for the exchange rate parameters and hence alter the probability of clustering great ape and rodent parasites together. Accordingly, we used the GTR_aa model (where subscript aa stands for amino acids) which does not rely on a pre-estimated replacement matrix like JTT. The GTR_aa + Γ₄ model strongly supported the monophyly of great ape and rodent parasites (PP = 0.98, Table 1).

Cross-validations indicated that, among the 12 alternative models, the site-heterogeneous model CAT + JTT + Γ₄ 43 (see Methods) provided the best fit to the amino-acid data set (Additional file 4, Table S3). According to posterior predictive tests, this model correctly anticipated the saturation level observed in the data (p > 0.07, Additional file 5, Table S4). Moreover, the site- and time- heterogeneous model CAT + BP + Γ₄ 51 (see Methods) correctly anticipated the level of saturation of the amino-acid data set (p = 0.41). However, the posterior predictive test for compositional heterogeneity across taxa was rejected under CAT + BP + Γ₄ (p = 0.02), although as expected, this model anticipated compositional heterogeneity better than do time-homogeneous models (p = 0.001, Additional file 5, Table S4). Both the two last models moderately supported the monophyly of rodent and great ape parasites (PP = 0.80 and PP = 0.75 under CAT + JTT + Γ₄ and CAT + BP + Γ₄ respectively, Table 1). In both cases, few variable amino-acid positions are interpreted under highly parameter rich models, and moderate support is therefore to be expected.

Most importantly, all results in this section are congruent with our initial estimate. This suggests that measured model violations do not significantly bias the relationship of great ape parasites among mammal parasites. In other words, the monophyly of great ape and rodent parasites appears to be robust to the choice of the model, as well as to its assumptions and dimensionality.

First, we checked the influence on phylogenetic reconstructions of the selected great ape parasites. According to the initial taxon selection, this lineage includes P. falciparum, P. reichenowi and P. gaboni. Six additional combinations of these three taxa were devised (see Methods). The weakest (but still relatively high) support for the monophyly of great ape and rodent parasites was obtained when P. reichenowi was considered as the only representative of its lineage (PP = 0.93, SH = 0.78, BS = 0.68, Additional file 7, Table S5). Second, we devised six combinations of the three rodent parasites, P. berghei, P. yoelii and P. chabaudi. The data set with P. berghei as the only representative of its lineage yielded the weakest support for the monophyly of great ape and rodent parasites (PP = 0.56, BS = 0.52, Additional file 7, Table S5), and the ML tree weakly supported the alternative hypothesis of a monophyly of primate and rodent parasites (i.e. Figure 1B, SH = 0.05). Third, six combinations of primate parasites were considered. Only the combination with African primate parasites (P. gonderi and P. DAJ-2004) as the only representatives of their lineage supported the alternative hypothesis of a monophyly of primate and rodent parasites (i.e. Figure 1B, PP = 0.85, SH = 0.26, BS = 0.48, Additional file 7, Table S5). The five other combinations of primate parasites supported the monophyly of great ape and rodent parasites (PP > 0.96, SH > 0.60, BS > 0.71, Additional file 7, Table S5). Finally, we investigated the robustness to the taxon composition of the outgroup (i.e. mammal and saurian parasites were considered as ingroup and outgroup, respectively). All six devised outgroups yielded high support for the monophyly of great ape and rodent parasites (PP > 0.98, SH > 0.64, BS > 0.74, Additional file 7, Table S5).

Hence, with the exception of three taxonomic samples, in which (i) P. reichenowi, (ii) P. berghei and (iii) P. gonderi and P. DAJ-2004 were considered as the only representatives of their respective lineages, all other 21 combinations of taxa provided good support for the association of great ape and rodent parasites (PP > 0.96, SH > 0.60, BS > 0.71, Additional file 7, Table S5).

First, (i) 8 CytB genes from great ape parasites, (ii) 10 pairs of CytB and Cox1 genes from rodent parasites and, (iii) 27 pairs of CytB and Cox1 genes from Plasmodium species infecting a wide range of sauria hosts (Additional file 8, Table S6) were added in turn to the initial 33-taxon data set. The association of great ape and rodent parasites was still strongly supported (PP > 0.99, SH > 0.77, BS > 0.78, Additional file 7, Table S5), and the lineages of great ape, rodent, and mammal parasites were each still shown to be monophyletic (PP = 1).

Second, all previous taxa were analyzed together (33 taxa + 8 great ape + 10 rodent + 27 saurian parasites), yielding a 78-taxon tree. The monophyly of great ape and rodent parasites was still strongly supported (PP = 0.99, SH = 0.86, BS = 0.76, Additional file 7, Table S5).

Third, we added six Hepatocystis species to the initial 33-taxon nucleotide data set. These six parasites were monophyletic (PP = 1). They clustered within the clade of mammal parasites, which was then composed of four monophyletic main lineages. The monophyly of great ape and rodent parasites was weakly supported (PP = 0.40, SH = 0.05, BS = 0.38), but this low support was entirely due to high uncertainty with respect to the position of Hepatocystis within mammalian malaria parasites. Indeed, Hepatocystis were located, with weak support, in five positions on trees in which great ape and rodent parasites were located close together (e.g. Hepatocystis as a sister-group to great ape parasites: PP = 0.28, BS = 0.28, or to rodent parasites: PP = 0.31, BS = 0.29). We evaluated posterior and bootstrap support for the great ape being close to, but not necessarily monophyletic with, rodent parasites (i.e. the great ape plus rodent parasite lineage could also include Hepatocystis). When support was summed over the three possible positions of Hepatocystis relative to the association of great ape and rodent parasites, then parasites of great apes and of rodents were located close together with strong support (PP = 0.99 and BS = 0.87, Additional file 7, Table S5).

Fourth, the six Hepatocystis species were analyzed simultaneously with all the previous 78 taxa, yielding an 84-taxon tree (Figure 3). A strict monophyly of great ape and rodent parasites was weakly supported (PP = 0.28, SH = 0, BS = 0.31), due to high uncertainty with respect to the position of Hepatocystis (e.g. Hepatocystis as a sister-group to great ape parasites: PP = 0.36, BS = 0.25, or to rodent parasites: PP = 0.35, BS = 0.25). However, disregarding the exact position of Hepatocystis, great ape and rodent parasites were located close together with high support (PP = 0.99, BS = 0.75, Additional file 7, Table S5).

Thus, all six previous additions of mitochondrial genes did not alter the result indicating a likely close phylogenetic relationship of great ape and rodent parasites. Overall, statistical supports averaged over the 30 taxonomic samples considered in this section showed a robust relationship of great ape and rodent parasites . This suggests that this relationship does not depend solely on the selection of the taxa we considered here. However, the uncertainty concerning the exact position of Hepatocystis species within mammal parasites challenges the above mentioned monophyly of a clade only comprising parasites of great apes and of rodents, because it would be possible for Hepatocystis to cluster within that clade. Nonetheless, whatever the true position of Hepatocystis may be, it does not contradict our main result indicating that great ape parasites are unlikely to be a sister-group to all other mammal parasites 6 20 21 22 24 25 27 28 36 (Figure 1B), but instead, probably share a more recent common ancestor with rodent parasites 23 27 (Figure 1D).

As a general guideline, wider taxon sampling usually helps to resolve phylogenies more accurately, provided enough genes are available to overcome stochastic noise, and are also sufficiently conserved to avoid systematic errors 54 . In line with this idea, Martinsen et al. 36 analyzed four concatenated genes for a relatively wide sample of 40 taxa. Among the previous works, their experimental conditions are thus the closest to ours. But, intriguingly, our results do not confirm theirs. We suggest that the disagreement between the two studies is due to several factors, the first being the differences in the phylogenetic markers analyzed.

Both Martinsen et al. 36 and our study considered CytB and Cox1 mitochondrial genes. However, Martinsen et al. 36 additionally analyzed adenylosuccinate lyase (ASL) and caseinolytic protease C (ClpC) genes, whereas we analyzed the third mitochondrial gene Cox3. In order to compare global rates of evolution between these genes, we measured the total lengths of gene trees 55 , for a common sub set of eight taxa (P. falciparum, P. reichenowi, P. vivax, P. knowlesi, P. berghei, P. chabaudi, P yoelii and P. gallinaceum). Our values indicate that the ASL genes evolved 3 to 5 times faster than the slowest evolving genes: ClpC, Cox1 and Cox3 (Figure 4). The signal to noise ratio is expected to be higher for slowly evolving phylogenetic markers, and fast rates of evolution generally reduce the accuracy of inferred phylogenetic trees 49 56 . In addition, we considered ASL and ClpC genes of 18 and 27 taxa respectively, for taxonomic samples as close as possible to our originally selected 33 taxa (Additional file 9, Table S7). The rapidly evolving gene, ASL, did not support a monophyly of mammal parasites, suggesting strong systematic errors (Additional file 10, Figure S3). In contrast, the slow evolving gene, ClpC, supported this monophyly (PP = 0.99, SH = 0.94, BS = 0.51), but did not support any particular position of P. falciparum within mammal parasites (Additional file 11, Figure S4). However, a recent study of 14 ClpC genes supported a common ancestry of great ape and rodent parasites 57 .

Moreover, most CytB, ClpC and ASL sequences analyzed by Martinsen et al. 36 were partial CDS. Thus, even considering four genes, their alignment covered 2334 nucleotide sites, representing 70% of the 3308 nucleotide sites considered in the present study. Finally, they considered fewer mammalian malaria parasites than we did (11 taxa in the study of Martinsen et al. 36 , versus 20 to 44 taxa in our work), and they considered P. falciparum as the only representative of the lineage of great ape parasites, together with P. vivax and P. knowlesi as the only representatives of primate parasites. All these differences in experimental conditions (i.e. saturation of ASL gene, fewer sites, fewer mammal parasites close to P. falciparum) could together contribute to the difference between the results of Martinsen et al. 36 and ours.

Dávalos and Perkins 53 extracted a set of 104 putative orthologous nuclear genes from the eight complete genomes of Plasmodium species sequenced to date (P. falciparum, P. reichenowi, P. vivax, P. knowlesi, P. berghei, P. chabaudi, P yoelii and P. gallinaceum). Their phylogenetic analyses of individual genes displayed discrepancies with respect to the inferred trees. Approximately half the 104 genes supported a monophyly of primate and rodent parasites (Figure 1B) 6 20 21 22 24 25 27 28 36 . Alternative hypotheses of a monophyly of great ape and primate parasites (Figure 1C) 14 , and of great ape and rodent parasites (Figure 1D) 23 27 , were each supported by nearly a quarter of these 104 genes. Interestingly, for the same reduced sample of eight taxa, our phylogenetic analyses of mitochondrial genes, taken separately, displayed comparable discrepancies (Table 2). Moreover, the supports obtained showed a near-random resolution of the internal branch of the 8-taxon individual gene trees. This suggests that, rather than showing a global preference of individual genes for the monophyly of primate and rodent parasites, the analysis of individual genes by Dávalos and Perkins 53 might have been strongly influenced by stochastic noise.

Increasing the amount of signal by concatenating genes helps to alleviate the effects of stochastic noise. The analysis of the three concatenated mitochondrial genes, for the eight taxa, supported the monophyly of great ape and rodent parasites (PP = 0.97, SH = 0.58, BS = 0.65; Table 2). In contrast, the concatenation of the 104 nuclear genes yielded strong support for the monophyly of primate and rodent parasites 53 (Figure 1B). We estimated the total tree lengths of each of these 104 genes, as well as of their concatenation. First, mitochondrial genes evolved as slowly as the fraction of the 104 nuclear genes which displayed the slowest rate of evolution (Figure 4). Second, total tree length estimated for the 104 gene concatenation indicated a fast average rate of evolution, about two times faster than that of the three mitochondrial genes. These observations confirm the fact that mitochondrial genes are well conserved, and corroborate the conclusion of Dávalos and Perkins 53 indicating that most of their 104 genes are highly saturated and evolved relatively fast. Thus, the monophyly of primate and rodent parasites (Figure 1B), obtained by the latter authors from a large concatenation of 104 genes, most likely results from systematic errors that may be due to the high saturation level of most genes 53 58 , but also presumably to the small sample of only eight taxa 54 .

In contrast, our results support a common origin of great ape and rodent parasites (Figure 1D). This corroborates results of a recent study published by Perkins 23 who, to the best of our knowledge, was the first to mention this hypothesis. This author sequenced seven new mitochondrial genomes and reconstructed the phylogeny of a sample of 24 taxa. A similar phylogeny was also obtained from 38 partial CytB sequences 27 . However, the two previous studies did not discuss the robustness of this result, but instead suggested it should be considered with caution 23 27 , as most previous studies of mitochondrial genes supported a monophyly of primate and rodent parasites (Figure 1B) 6 21 22 24 24 25 27 28 35 .

However, in our results, this hypothesis never obtained significant statistical support: at most, it reached PP = 0.35 and BS = 0.57 with the 33-taxon amino-acid alignment (Additional file 3, Table S2, column "Primate+Rodent"), and it obtained averaged supports of and over the 30 additional taxon samples considered (Additional file 7, Table S5, column "Primate+Rodent").

Interestingly, each time the monophyly of great ape and rodent parasites (Figure 1D) was not significantly supported, the only alternative hypothesis which could not be statistically rejected was the monophyly of primate and rodent parasites (i.e. support for "Primate+Rodent" in Additional files 3 and 7, Tables S2 and S5, where PP > 0.05). Moreover, nine additional samples of 19 taxa were drawn so that trees would display long branches, and we obtained five trees in which great ape parasites were shown to be a sister-group to primate and rodent parasites (Additional file 12, Table S8). This suggests that the monophyly of primate and rodent parasites (Figure 1B), rather than the monophyly of great ape and rodent parasites (Figure 1D), might result from the effect of long branch attraction. Thus, the slight tendency of mitochondrial genes to weakly support a monophyly of primate and rodent parasites, along with differences in taxon sampling and gene selection, could explain the disagreements between our results and most previous studies.

Data sets were analyzed under various probabilistic models of molecular evolution. We applied the JTT 45 replacement model to the amino-acid data set. We applied the most general time reversible model GTR_nt , where subscript nt denotes nucleotides, to the nucleotide data sets 41 . These substitution models were run using both maximum-likelihood (ML) and Bayesian inference (BI) methods. This allowed for the use of different statistical supports with different meanings, and comparison of the phylogenies estimated with the two approaches.

ML phylogenetic reconstructions were performed using PhyML 3.0 47 . Irrespective of the substitution model (GTR_nt , JTT) used for the analysis, the phylogenetic model additionally involved four discrete categories of gamma distributed rates across sites (denoted + Γ₄, 42 ), plus an invariant site category (denoted +I). The proportion of invariant sites and the shape parameter of the gamma distribution were estimated from the data. When the nucleotide data sets were analyzed, all eight free parameters of the GTR_nt substitution models were estimated from the data (GTR_nt + Γ₄ + I, 10 degrees of freedom). In the case of the amino-acid alignment analyzed under JTT, stationary probabilities were set to empirical frequencies of amino acids measured over the whole data set (JTT + Γ₄ + I + F, 21 degrees of freedom). Note that these models were identified as the available ML models that best fit the sequence alignments, according to the AIC criterion 40 .

Bayesian phylogenetic reconstructions were performed using PhyloBayes 3.0 43 . For all Bayesian experiments performed in this study, two independent MCMC chains - each starting from a random point - were run for up to 100, 000 cycles. One MCMC sample was saved every 10 cycles, and the first 500 samples were discarded as "burnin". The eight free parameters of GTR_nt and the amino-acid frequencies of JTT (19 free parameters), were estimated from the data.

We also applied more general and parameter rich models of evolution, implemented in a Bayesian framework. We used GTR_aa , where subscript aa indicates a GTR model dedicated to amino-acid sequences. This model directly estimates the exchange rate parameters from the data (208 degrees of freedom). Models JTT and GTR_aa homogeneously apply a single substitution model to the whole data set. However, in some cases, this parameterization is prone to violations by the data, resulting in wrong phylogenetic inferences 51 . Consequently, we applied the site-heterogeneous mixture model CAT to the amino-acid alignment, which implements a mixture of stationary probability vectors across sites 48 . The CAT model was combined with free (+GTR_nt ) or empirical (+JTT) relative exchange rates, applied to the nucleotide and amino-acid alignments, respectively. Both CAT + GTR_nt and CAT + JTT models were combined with discretized gamma rates across sites (+ Γ₄). Finally, we analyzed both nucleotide and amino-acid alignments under time-heterogeneous models of evolution. The BP model component allows for changes over time of the substitution model stationary probabilities and hence, estimates the compositional drift of the sequences 50 . We applied the GTR_nt + BP + Γ₄ 50 and the CAT + BP + Γ₄ 51 models to the nucleotide and the amino-acid alignments, respectively.

Additional models with Bayesian implementations were compared using cross-validation (see below). In addition to the + Γ₄ model of rate variation across sites, we applied a covarion model (+COV) which enabled us to estimate site specific rate variations (i.e. heterotachy) 71 . In addition to JTT and GTR_aa , we considered the MtREV 72 empirical rate matrix. Finally, in addition to the mixture model CAT, we considered the empirical mixture models UL2 and UL3 73 . These components allowed 13 and 3 models of evolution to be derived and applied to amino-acid and nucleotide alignments, respectively.

The fit of the models implemented in a Bayesian framework was estimated by cross-validation, as implemented in PhyloBayes 3.0 43 . Ten replicate data sets were randomly drawn. The learning part of each replicate data set comprised 90% of the sites of the whole alignment. The 10% of remaining sites were used to compute the cross-validated likelihood. The tree topology was considered as a free parameter. Note that, for computational reasons, fits of time-heterogeneous models GTR_nt + BP + Γ₄ and CAT + BP + Γ₄ were not evaluated.

Model violations were measured by posterior predictive experiments, as implemented in PhyloBayes 3.0 43 . We applied a test statistic measuring the compositional heterogeneity across taxa. The test statistic "composition" was defined as the maximum of the χ ² distances separating each sequence composition from the composition of the whole data set 52 . We applied two test statistics to measure site saturation. The test statistic "site diversity" measures the mean state diversity across sites 48 (e.g. a constant site has a diversity of 1). The test statistic "homoplasy" considers the averaged number of convergence and reversion events per site, as displayed by inferred stochastic mapping 49 . A posterior predictive test compares the value V_O of a test statistic measured given the observed data, to the distribution of that test statistic measured over simulated replicate data sets. Each replicate data set was simulated given an a posteriori drawn sample of parameters. The p-value indicates the probability of observing a test statistic as extreme as V_O , under the null hypothesis stating that the model assumptions are true. Failure to reject a posterior predictive test indicates that the model assumptions allow to realistically reproduce the observation V_O based on real data.

Saturation of the phylogenetic signal of each codon position was illustrated by a saturation plot 74 . For each pair of taxa in an alignment, we plotted their "pairwise similarity distance" (i.e. y-coordinates: number of sites displaying different states, normalized by the alignment length), versus the distance separating these two taxa along the tree branches (i.e. x-coordinates: the sum of branch lengths from the two taxa to their common ancestor). We used a fixed tree topology estimated from all codon positions (Figure 2). Branch lengths and other model parameters were evaluated according to separate codon positions.

Under ML analysis, statistical support of tree branches was estimated from 1000 bootstrap replicates and, in addition, using the Shimodaira-Hasegawa-like test (SH) implemented in PhyML 3.0 47 75 . Bayesian analysis classically provides a collection of samples drawn from the a posteriori distribution. The posterior probability of observing a given phylogenetic association between two lineages is then approximated by its frequency among sampled trees. Given a monophyletic target lineage A (e.g. great ape parasites), we extracted from a tree collection the list of all its N different sister-groups B_n (e.g. rodent parasites). We then computed the frequency : the posterior support of clade A + B_n (e.g. great ape plus rodent parasites). The same approach was used for the bootstrap support, but not for the SH support which applies only to clades that belong to the ML tree.

Let A and B each be a monophyletic lineage within a phylogenetic tree, and let them form a well-supported monophyletic clade A + B according to an initial sample of taxa. To ensure that the target relationship between A and B does not result from stochastic noise (lack of signal) or systematic error (model violation), we checked its robustness to taxon sampling (e.g. 49 ). Given a lineage C (possibly equal to A or B) including k taxa, we checked that every combination of 1 to k - 1 taxa of C yielded a congruent phylogeny with respect to the phylogenetic relationship A + B. If lineage C was composed of too many taxa, we selected only a few relevant taxon combinations among all those available.

We focused on the robustness of the association of lineage A: great ape parasites, with lineage B: rodent parasites. Each of these two lineages was considered in turn as a sampled lineage C. According to our initial selection of 33 taxa, both these lineages were composed of 3 taxa and, 6 combinations of single or pairs of representatives were considered. We also considered in turn the group of primate parasites (14 taxa) and the saurian parasite outgroup (13 taxa) as sampled lineages C. For each of these sampled lineages, only 6 combinations of single or pairs of sub-groups were considered. For the 14 primate parasites, the 3 sub-groups were: (a) P. malariae and P. ovale (infecting humans), (b) P. gonderi and P. DAJ-2004 (African primate parasites), and (c) 10 Plasmodium species infecting Asian primates (Additional file 1, Table S1). For the 13 saurian parasites, the 3 sub-groups were (a) the 5 Plasmodium species, (b) the 4 Haemoproteus and Parahaemoproteus species, and (c) the 4 Leucocytozoon species (Additional file 1, Table S1). All these 24 sub data sets were obtained from the nucleotide alignment by simply discarding the relevant sequences without renewed aligning.

Finally, up to 51 malaria parasites were added to the initial selection of 33 taxa. We aligned all 84 taxa following the alignment procedure described above. Note that for CytB, 38 of the 51 additional sequences were partial CDS (see Additional file 8, Table S6). In order to retain more sites, complete and partial CytB genes were filtered separately with Gblocks, and then manually reassembled into an 84-gene alignment. All 6 additions of taxa to the 33-taxon data set were obtained from the whole concatenation of genes of the 84 taxa by discarding the relevant sequences.