Phylogenomic studies have resolved countless branches of the tree of life, but remain strongly contradictory on certain, contentious relationships. Here, we use a maximum likelihood framework to quantify the distribution of phylogenetic signal among genes and sites for 17 contentious branches and 6 well-established control branches in plant, animal and fungal phylogenomic data matrices. We find that resolution in some of these 17 branches rests on a single gene or a few sites, and that removal of a single gene in concatenation analyses or a single site from every gene in coalescence-based analyses diminishes support and can alter the inferred topology. These results suggest that tiny subsets of very large data matrices drive the resolution of specific internodes, providing a dissection of the distribution of support and observed incongruence in phylogenomic analyses. We submit that quantifying the distribution of phylogenetic signal in phylogenomic data is essential for evaluating whether branches, especially contentious ones, are truly resolved. Finally, we offer one detailed example of such an evaluation for the controversy regarding the earliest-branching metazoan phylum, for which examination of the distributions of gene-wise and site-wise phylogenetic signal across eight data matrices consistently supports ctenophores as the sister group to all other metazoans.
A well-resolved tree of life (ToL) is essential for understanding life’s history and the evolution of phenotypic diversity. The genomics revolution has allowed the assembly of many taxon-rich genome-scale data matrices for reconstructing the phylogenies of a wide diversity of lineages across the ToL1,
However, different phylogenomic analyses can sometimes strongly support branches that contradict one another. For example, concatenation analysis of a 1,233-gene, 96-taxon phylogenomic data matrix (609,899 amino acid sites) provided absolute clade support for the family Ascoideaceae as the closest relative of the families Phaffomycetaceae + Saccharomycodaceae + Saccharomycetaceae4; in contrast, concatenation analysis of a 1,559-gene, 38-taxon phylogenomic data matrix (364,126 amino acid sites) robustly placed the family Ascoideaceae as sister to a broader clade composed of the family Pichiaceae, the CUG-Ser clade, the family Phaffomycetaceae, the family Saccharomycodaceae and the family Saccharomycetaceae10. Contradictory branches can also be observed when different analytical approaches are used on the same data matrix. As an example, a phylogenomic analysis (maximum likelihood, homogeneous model, Opisthokonta as outgroup) of 406 genes from 70 taxa (88,384 amino acid sites) recovered ctenophores as sister to all other metazoan phyla11, whereas another analysis (Bayesian inference, heterogeneous model, Choanoflagellata as outgroup) of the same data matrix supported sponges, rather than ctenophores, as the sister to the rest of the metazoan phyla12.
Although both biological and analytical factors influence phylogenetic inference13,
Measuring phylogenetic signal
We defined phylogenetic signal as the difference in the log-likelihood scores between two alternative resolutions, T1 and T2, of a given branch (or internode or bipartition) in a phylogenetic tree18. For a given data matrix and branch in question, we defined T1 as the bipartition recovered by the phylogenetic tree obtained by maximum likelihood (ML) when the full data matrix is analysed by concatenation analysis; we defined T2 as a bipartition in the phylogenetic tree that shows substantial topological conflict with T1 (for example, in most cases, T2 was the most prevalent bipartition conflicting with T1) (Fig. 1a).
To calculate phylogenetic signal, we first calculated the site-wise log-likelihood scores for the unconstrained ML tree under concatenation (by definition, this topology contained the T1 branch and will be hereafter abbreviated T1) as well as for the ML tree constrained to recover the T2 branch (hereafter called T2) under the same substitution model and partitioning strategy (Fig. 1a). Next, we calculated the difference in site-wise log-likelihood scores (ΔSLS) between T1 and T2 for every site in a given data matrix. By summing the ΔSLS scores of all sites for every gene in a given data matrix, we then obtained the difference in gene-wise log-likelihood scores (ΔGLS) between T1 and T2 (Fig. 1b). By doing so, we were able to quantify the distribution of phylogenetic signal for T1 and T2 at the site and gene levels (Fig. 1c), as well as visualize the proportions of sites’ or genes’ support for T1 and T2 (Fig. 1d). This quantification and visualization of phylogenetic signal can be extended to the comparison of three alternative phylogenetic hypotheses (T1, T2 and T3), as shown in Supplementary Fig. 1.
A tiny amount of data can drive phylogenetic inference
For each of the 17 contentious branches and the 6 well-established branches (used as controls) in plants, animals and fungi, we first examined whether the unconstrained ML tree under concatenation (T1) had a significantly different log-likelihood score from the ML tree constrained to recover the T2 branch (T2) using the approximately unbiased (AU) test19,20. We found that T2 was significantly worse (P-value < 0.05) than T1 in 22/23 internodes (Table 1); the only exception was the neoavian branch in animals.
Examination of the distribution of ΔGLS values (that is, the difference in gene-wise log-likelihood scores between T1 and T2) in the 17 contentious and 6 control branches showed that the proportion of genes supporting T1 was generally greater than that of genes supporting T2 (Fig. 2; Supplementary Figs 2 and 3a; Supplementary Tables 1–3). The only exceptions were the angiosperm (plants), eutherian (animals) and Ascoideaceae (fungi) branches, for which the proportions of genes supporting T1 were slightly smaller than those supporting T2.
Examination of the distribution of ΔSLS values (the difference in site-wise log-likelihood scores between T1 and T2) showed that the proportion of sites supporting T1 was greater than that of sites supporting T2 for 18 of the 23 branches (Supplementary Fig. 3b); the remaining 5 branches (eutherian, lungfish and neoavian in animals, Ascoideaceae and ‘whole genome duplication’ (WGD) clade in fungi) had lower proportions of sites supporting T1 than T2 (Supplementary Fig. 3b). We observed the same pattern (Supplementary Fig. 4) when we considered only ‘weak’ sites17, whose absolute ΔSLS values were smaller than or equal to 0.5; as more than 95% of sites in each branch were weak ones (Supplementary Table 4), the similarity in results when considering all sites versus only weak sites is not surprising. Comparison of ‘strong’ sites17, whose absolute ΔSLS values were >0.5, with all sites for each branch showed that there was a higher proportion of strong (relative to all) sites favouring T1 in 13 branches and a lower proportion in the other 10 branches. Finally, 3 branches (eutherian and neoavian in animals, Ascoideaceae in fungi) had fewer strong sites supporting T1 than T2 (Supplementary Fig. 4).
Examination of the distribution of ΔGLS values also revealed that, in 6/17 contentious branches, a single or a handful of genes displayed very high ΔGLS values (Fig. 2 and Supplementary Figs 2, 5–30). Remarkably, we found that removal of the gene with the highest absolute ΔGLS value switched the ML tree’s support from T1 to T2 in 3 branches (angiosperm in plants, neoavian in animals, and Ascoideaceae in fungi) (Figs 2 and 3; Supplementary Figs 7, 17 and 23). In contrast, random exclusion of a single gene did not change support in any analysis (Fig. 4 and Supplementary Figs 5, 13 and 22); Similarly, removal of the gene with the highest ΔGLS value in our 6 control branches (Table 1) favoured T1 over T2 (Figs 2, 3, 4; Supplementary Figs 11, 12, 20, 21, 29 and 30).
The single genes whose removal caused the switch of the phylogenomic data matrices’ support from T1 to T2 in the angiosperm, neoavian and Ascoideaceae branches were orthologues of the Arabidopsis thaliana AT3G46220 gene (alignment id: 6040_C12), the Homo sapiens AUTS2 gene (alignment id: Pro_ENSG00000158321), and the Saccharomyces cerevisiae DPM1 gene (alignment id: BUSCOfEOG7W9S51), respectively. Plotting of the ΔSLS values (the difference in gene-wise log-likelihood scores between T1 and T2) for the three gene alignments showed that 14.4% of the 6040_C12 gene alignment, 11.0% of Pro_ENSG00000158321 and 47.9% of BUSCOfEOG7W9S51 had high ΔSLS values (>0.5); moreover, these strong sites were unevenly distributed in the 6040_C12 and Pro_ENSG00000158321 gene alignments (Supplementary Fig. 57). Further examination of the sequence alignments of these three genes did not identify apparently unusual sequences or columns (Supplementary Figs 58–60), while topological distances (measured by the normalized Robinson–Foulds tree distance, RFD, using RAxML with the option ‘-f r’) of their ML gene trees from the concatenation-based ML phylogenies (T1) inferred from the full data matrices were slightly higher than the corresponding means of topological distances of all individual gene trees from the concatenation-based ML phylogenies (Supplementary Tables 6–8). Finally, none of the three genes’ properties21 (see Supplementary Table 5) such as alignment length, alignment quality, compositional heterogeneity or disparity index, rate of evolution or single-gene tree resolution (for example, average bootstrap support across the maximum likelihood tree of a given alignment) could consistently explain why they exhibited such high ΔGLS values (Supplementary Tables 6–8).
To investigate the impact of model of sequence evolution in the proportions of sites supporting T1 versus T2, we used Seq-Gen22 version 1.3.3 to simulate alignments of the plant (290,718 sites), animal (1,806,035 sites) and fungal (609,772 sites) phylogenies using exactly the same ML trees and model parameters (that is, state frequency, rates and alpha parameter: the shape for the gamma rate heterogeneity among sites) used in the original three phylogenomic studies as well as in our analyses. Comparison of the differences in the proportions of strong, weak and all sites supporting T1 between biological and simulated data showed that differences were small for the 6 control branches but much larger for the 17 contentious branches (Supplementary Fig. 61); this trend was especially noticeable when only the strong sites were considered. Furthermore, the differences in the proportion of sites supporting T1 between biological and simulated data were especially pronounced in the angiosperm, neoavian and Ascoideaceae branches (Supplementary Fig. 61), suggesting that the site- and gene-specific patterns of support for T1 or T2 are a poor fit to those predicted by the models of sequence evolution employed.
To quantify the effect of gene removal, we next investigated the effects of excluding 5, 10, 50 and 100 genes with the highest absolute ΔGLS values, as well as of excluding the genes with outlier ΔGLS values (see equations (3) and (4) in the Methods section). Our results showed that these gradual removals of genes had the same effect as single gene removal (a switch from T1 to T2) for the angiosperm and Ascoideaceae branches, whereas the neoavian branch was unstable, switching between T1, T2 and other topologies (Fig. 3). Interestingly, the results on single or few gene removals were very similar to the results obtained when outlier genes were removed (Fig. 3). Furthermore, when the number of removed genes was equal to or greater than 50, a switch from T1 to T2 or other hypotheses was also observed for the eutherian and neoavian branches in animals and the Hyphopichia branch in fungi (Fig. 3).
Coalescence-based species tree approaches23,24, by taking into account each gene tree’s history, are less likely to be influenced by a single gene or handful of genes in a phylogenomic data matrix. However, these approaches can be sensitive to errors and biases in estimating individual gene trees25,
Among the branches strongly influenced by the removal of the single site with the highest absolute ΔSLS value from every gene were the bryophyte branch in plants, the eutherian, lungfish, neoavian and teleost branches in animals, and the Ascoideaceae and WGD clade branches in fungi. Interestingly, the neoavian and Ascoideaceae branches were sensitive both to the removal of the gene with the highest absolute ΔGLS value and to that of the site with the highest absolute ΔSLS value from every gene. Exclusion of the 1% of sites with the highest absolute ΔSLS values28 from every gene showed that the coalescence-based topology based on the full data matrix was no longer supported for 13/17 contentious branches (Fig. 4 and Supplementary Figs 31–56).
Although some of these 17 contentious relationships seem to be driven by a tiny subset of data and should effectively be considered unresolved, the quantification of ΔGLS and ΔSLS values for a specific branch of a phylogeny can also augment the support for one of the alternative hypotheses. For example, similar to the well-established branch associated with the monophyly of amniotes on the vertebrate phylogeny that we used as a control (Figs 2, 3, 4), examination of the evolutionary placement of turtles (Table 1 and Figs 2, 3, 4) showed very strong support for the hypothesis that turtles are the sister group to archosaurs (birds + crocodiles). Specifically, the ΔGLS values of 74% (3,466 out of 4,682) of the genes in the data matrix favour this hypothesis over the second best alternative (turtles as sister group to crocodiles) (Supplementary Fig. 2a); the same is true for ΔSLS values (88% or 1,588,738 out of 1,806,035 sites favour turtles as the sister group to archosaurs rather than to just crocodiles; Supplementary Fig. 3b).
What is the earliest branch of the metazoan phylogeny?
To further illustrate how the quantification of phylogenetic signal for a specific branch of a phylogeny can augment the resolution of contentious branches, we next examined the support for three alternative hypotheses regarding the earliest-branching lineage of the Metazoa (T1: Ctenophora-sister; T2: Porifera-sister; and T3: Porifera + Ctenophora-sister)11,12,29 (Fig. 5a). Specifically, we collected eight phylogenomic data matrices from three recent studies11,29,30, comprising different data types (genomic data or ‘transcriptomic + genomic data’) and different outgroups (Opisthokonta or Choanoflagellata).
Examination of ΔGLS values between T1, T2 and T3 (see Methods for full details) showed that T1 had the highest proportions of supporting genes, ranging from 42.5% to 69.7%, across the eight data matrices (Fig. 5a and Supplementary Table 9). In addition, the ΔGLS values of genes favouring T1 were higher than those favouring either T2 or T3 across all eight data matrices (Supplementary Table 9 and Supplementary Fig. 62). This is most easily observed by examining the distribution of ranked ΔGLS values for each data matrix (Supplementary Fig. 63). Moreover, all concatenation ML analyses of the removal of one single gene and the genes with outlier ΔGLS values still supported Ctenophora-sister hypothesis (T1) (Supplementary Fig. 65a–h).
Examination of ΔSLS values between T1, T2 and T3 (see Methods for full details) showed that T1 also had the highest proportions of supporting sites, ranging from 39.8% to 56.9% (Fig. 5b). Importantly, comparison of the proportions of strong, weak and all sites supporting T1 showed that this hypothesis received its highest support in all eight data matrices from the strong sites; their proportions in favour of T1 ranged from 52.2% to 85.3% (Supplementary Fig. 64). Thus, examination of ΔGLS and ΔSLS values in eight phylogenomic data matrices shows robust support for the Ctenophora-sister hypothesis.
In this study, we examined the distribution and strength of phylogenetic signal on contentious branches of the ToL. For some contentious branches, our approach clarified the nature of the phylogenetic incongruence and, by quantifying the support for alternative hypotheses at the site and gene levels, illuminated their resolution. For other contentious branches, however, we found that tiny amounts of data — in what are otherwise very large phylogenomic data matrices — exerted decisive influence in their resolution.
There are two potential explanations for why this is so. One explanation is that the evolution of these genes may have been shaped by positive selection31, which can give rise to convergent evolution that misleads phylogenetic inference17,32,
Our proposed framework for quantifying and visualizing phylogenetic signal could be used to analyse any branch of the tree of life, irrespective of how contentious they are; our examination of six control branches (Figs 2 and 3) is a good case in point. However, our approach is most likely to be useful in cases of branches showing a high degree of conflict (for example low scores of internode certainty-related measures39,
Quantifying and visualizing the distribution of phylogenetic signal at the level of sites or genes would also be helpful for the identification of any sites or genes that might be exerting a disproportionate amount of influence on the resolution of a given contentious branch. The undue influence of one or a few genes or a few sites on phylogenetic inference has been previously observed in smaller data matrices17,28,44,
How are we then to interpret inferred relationships that rest on the presence of tiny amounts of data in phylogenomic studies? The history of life abounds with examples of ancient evolutionary radiations. Previous theoretical as well as empirical studies6,14,48,49 indicate that the resolution of relationships within such series of closely spaced species divergences in deep time can be extremely challenging. It is our view that the branches of the ToL that exhibit this behaviour (that is, their resolution rests on the presence of a tiny subset of genome-scale data) should effectively be considered unresolved. Of course, this does not mean that these branches will never be fully resolved, but rather that we are unable to do so with our current methodology and sampling of genes and taxa. Clear demarcation of such unresolved branches would provide a more accurate account of the phylogenetic hypotheses supported by the available data.
We used three taxon- and gene-rich phylogenomic data matrices representing three eukaryotic kingdoms of the tree of life: plants (103 plant species × 620 nuclear genes; Fig. 2 in original study1), animals (58 jawed vertebrate species × 4,682 nuclear genes; Fig. 1 in original study50) and fungi (86 yeast species × 1,233 nuclear genes; Fig. 3 in original study4). Although these studies constructed several different data matrices, we used only the full data matrix in each study.
Topological hypothesis testing
We investigated a total of 17 contentious branches present in three phylogenomic data matrices from plants, animals and fungi (Table 1). These branches were deemed contentious either because they were considered as such in the original papers1,50 or because they were incongruent between the concatenation- and coalescence-based phylogenies4. As a control, we also investigated two well-established branches from each of the three phylogenomic data matrices (see Table 1 for full details). For each branch, the unconstrained ML tree under concatenation (T1) and the ML tree constrained to recover the T2 branch were examined (Table 1). In most cases, T2 was the most prevalent bipartition conflicting with T1. The ML tree constrained to recover the T2 branch was obtained by enforcing the topological constraint option (option -g) in RAxML51, version 8.2.3. All ML searches were performed by using the same models and partitioning strategies as the original studies; the ML phylogeny was obtained by conducting five separate tree searches using five different random seeds (option -p). To test whether the T2 topology was statistically worse than the T1 topology for each of the 17 branches, we applied the approximately unbiased (AU)19 test in the software package CONSEL20, version 0.20. The AU test was conducted using the multi-scale bootstrap technique based on the site-wise log-likelihood scores, which were calculated in RAxML (option -f G). Notably, the difference between the RAxML software51, version 8.2.3, and the IQ-TREE software52, version 1.5.1, in calculating log-likelihood scores for our 17 contentious branches was very small (Supplementary Table 10).
A schematic workflow for the calculation and visualization of phylogenetic signal is shown in Fig. 1. For a given data matrix and branch in question, we defined T1 as the bipartition recovered by the phylogenetic tree obtained by maximum likelihood (ML) when the full data matrix is analysed by concatenation analysis; we defined T2 as a bipartition in the phylogenetic tree that shows substantial topological conflict with T1 (for example, in most cases, T2 was the most prevalent bipartition conflicting with T1) (Fig. 1a). For a given data matrix and branch in question, using the ML framework18, we here defined phylogenetic signal as the difference in the log-likelihood scores for the unconstrained ML tree under concatenation (by definition, this tree contained the T1 branch) against the ML tree constrained to recover the T2 branch (T2). Briefly, we first estimated the site-wise log-likelihood values for both T1 and T2 based on the concatenation data matrix and the same models using RAxML (option -f G). We then calculated the difference in site-wise log-likelihood scores (ΔSLS) between T1 and T2 using the equation: where T1 is the unconstrained ML tree obtained by concatenation analysis of the full data matrix and T2 is the ML tree constrained to recover the T2 branch. ΔSLSi is the difference in site-wise log-likelihood scores under T1 and T2 for the ith site (Si) in the full data matrix. Similarly, we also calculated the difference in gene-wise log-likelihood scores (ΔGLS) for T1 versus T2 for every gene according to: where T1 is the unconstrained ML tree obtained by concatenation analysis of the full data matrix and T2 is the ML tree constrained to recover the T2 branch. ΔGLSj is the difference in gene-wise log-likelihood scores under T1 and T2 and can be calculated as the sum of ΔSLS values of all sites within the jth gene (Gj).
Effect of removing a tiny amount of data on phylogenetic inference
To examine the influence of tiny amounts of data on phylogenetic inference, we generated six reduced data matrices by excluding 1, 5, 10, 50 and 100 genes with the highest absolute ΔGLS values (the difference in gene-wise log-likelihood scores between T1 and T2), as well as all genes whose ΔGLS values were outliers, from the full data matrix for each of the 17 contentious branches and 6 well-established control branches. Outlier genes were defined as those whose absolute ΔGLS values were greater than the upper whisker or smaller than the lower whisker of a boxplot in the R programming environment53:
where max(x) and mix(x) are the maximum value and minimum value for a set of absolute ΔGLS values, respectively, Q1 and Q3 are the first quartile and the third quartile, respectively, and IQR (interquartile range) is the difference in value between Q3 and Q1 (Q3 – Q1).
As a control, we also randomly excluded a single gene from the full data matrix and repeated this process five times in each of the three data matrices. For each reduced data matrix (we examined a total of 153 data matrices), the ML tree was inferred, as implemented in the IQ-TREE software52 using the same substitution models (plant: GTR + GAMMA; animal: LG + GAMMA + F; fungi: LG + GAMMA) and partitioning strategies (plant: eight partitions; animal: one partition; fungi: one partition) as described in the original papers. Branch support for each internode was evaluated with 100 rapid bootstrapping replicates54 using RAxML51 (option -x). Since the bootstrapping analysis of such large data matrices in RAxML is computationally very expensive (each plant data matrix takes ~150 CPU hours; each animal data matrix takes ~4,200 CPU hours; each fungal data matrix takes ~2,900 CPU hours), we performed bootstrapping on only two (those associated with removal of a single gene and removal of all outlier genes) of the six reduced data matrices for each of the 17 contentious branches and 6 well-established branches.
Similarly, we excluded the site with the highest absolute ΔSLS value (that is, the difference in site-wise log-likelihood scores between T1 and T2) from every gene for each branch. As a control, we also created reduced individual gene alignments where one site was randomly excluded for each data matrix. Maximum likelihood analysis of each reduced individual gene alignment was performed in RAxML by conducting 100 rapid bootstrapping replicates and 10 separate ML searches. Finally, the resulting RAxML ML trees and their 100 rapid bootstrapping trees were used to infer the coalescence-based species phylogeny with the ASTRAL software55, version 126.96.36.199. In addition to removal of a single site with the highest absolute ΔSLS value, we also excluded the 1% of sites with the highest absolute ΔGLS values from every gene for each branch, as implemented in previous work28.
The root of the Metazoan phylogeny
To investigate the distribution of phylogenetic signal in studies aiming to elucidate which was the first-branching metazoan phylum11,12,29,30,56,
We examined three hypotheses: Ctenophora-sister (T1; Fig. 5a), Porifera-sister (T2; Fig. 5a) and Porifera + Ctenophora-sister (T3; Fig. 5a). For each hypothesis, its corresponding constraint ML phylogeny and its site-wise log-likelihood scores were estimated for each of eight data matrices using RAxML, as described above. We then calculated the mean of all pairwise absolute differences in site-wise log-likelihood scores (ΔSLSi) between T1, T2, and T3 for the ith site (Si) in the full data matrix using equation (5):
Similarly, we calculated the mean of all pairwise absolute differences in gene-wise log-likelihood scores (ΔGLSj) between T1, T2 and T3 (see Supplementary Fig. 1 for full schematic representation) using equation (6):
Finally, we examined whether removal of a single gene with the highest absolute ΔGLS value or removal of the genes with outlier ΔGLS values (see equations (3) and (4)) altered the hypothesis favoured by concatenation analysis.
All data matrices, all resulting phylogenies and the custom scripts can be found in the Figshare data repository at http://doi.org/10.6084/m9.figshare.3792189.
How to cite this article: Shen, X.-X., Hittinger, C. T. & Rokas, A. Contentious relationships in phylogenomic studies can be driven by a handful of genes. Nat. Ecol. Evol. 1, 0126 (2017).
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We thank members of the Rokas laboratory, and in particular X. Zhou, for discussions and comments. We also thank M. Chen for providing the animal phylogenomic data matrix and J. Leebens-Mack for providing further information about the plant data matrix. This work was conducted in part using the resources of the Advanced Computing Center for Research and Education (ACCRE) at Vanderbilt University, of the UW-Madison Center for High Throughput Computing, and of the CIPRES Science Gateway. This work was supported by the National Science Foundation (DEB-1442113 to A.R.; DEB-1442148 to C.T.H.), in part by the DOE Great Lakes Bioenergy Research Center (DOE Office of Science BER DE-FC02- 07ER64494), the USDA National Institute of Food and Agriculture (Hatch project 1003258 to C.T.H.), and the National Institutes of Health (NIAID AI105619 to AR). C.T.H. is a Pew Scholar in the Biomedical Sciences, supported by the Pew Charitable Trusts.
Supplementary Tables 1–10