Using consensus networks to understand poor roots

The standard way to root a tree is by outgroup rooting. Comprehensive outgroup sampling should minimize bias, such as ingroup-outgroup long-branch attraction (IO-LBA); but this may be impossible to avoid, when ingroup and all possible outgroups are very distant from each other. Using a recent all-Santalales up-to-7-gene dataset (Su et al. 2015) as an example, I will show how bootstrap consensus networks can illuminate topological issues associated with poorly supported roots.

These analyses should be obligatory whenever critical branches lack unambiguous support.

Some background: nothing to see, all is solved

The reason, why I had to re-analyse some of the data of Su et al., was that we dared to discuss alternatives to the accepted Loranthaceae (hereafter "loranth") root in our paper on loranth pollen (Grímsson, Grimm & Zetter 2017). Mainly for the artwork, I harvested gene banks for data on loranths in 2014 (re-checked in 2016, but no-one is studying this highly interesting group anymore). Earlier studies had used different taxon and gene sets, and produced cladograms (trees without branch lengths).

To assess the systematic value of loranth pollen, we needed to know how well resolved are intra-family relationships. Many deeper branches seen in the trees were not supported. What would be the competing alternatives? Unfortunately, one of our reviewers (#1), a veteran expert on plant parasites including loranths but not phylogenetics, was tremendously alienated by our tree, notably, the non-supported parts. He refused to understand the difference between a simple tree topology and branch support. Matrices producing ambiguous signals not-rarely lead to optimized trees that do not show the best-supported topological alternatives. Hence, for mapping our pollen, we did not use our tree, but the ML bootstrap consensus network (Fig. 1; which #1 refused even to look at). Fig. 2 shows the first plot focusing on the deepest, ambiguous relationships.

Fig. 1 The basis for our paper: a ML bootstrap consensus network, rooted under the commonly accepted assumption that the monotypic Nuytsia represents the first-diverging lineage.

Fig. 2 Example of what we did. My co-authors (re-)studied loranth pollen using high-res SEM microscopy; and then we plotted the pollen on the relevant part of the ML bootstrap consensus network (Fig. 1). Green background: the three surviving root parasites of the root-parasitic grade (not supported based on our data set) in outgroup rooted trees; orange background: the palynologically odd Tupeia. Note the lack of clear signal regarding root-proximal relationships, an indication for fast ancient radiation and diversification involving both root and aerial parasitic lineages.

Reviewer #1 pointed to the recent paper of Su et al., which (according to his interpretation) resolved the intrafamily relationships. Since our tree was topologically somewhat different, and did not provide the same level of support, it had to be wrong. My argument was that the genetic data are inconclusive regarding critical branches in the loranth subtree. This is obvious from our bootstrap network (not including any outgroup, to avoid ingroup-outgroup branching artefacts), and also from the earlier molecular phylogenies, including Su et al.’s. Plus, to focus on the loranths we included the best-sampled and most-divergent plastid region, a non-coding region, which was not included in Su et al. because it is unalignable across the order.

A particularly "absurd" notion (according to #1) was that we suggested using pollen morphology to pre-define an alternative root (the best-fitting alternative according to Bayes factors; Grímsson, Kapli et al. 2017). All loranths share a unique, easy to distinguish, triangular pollen morph (Fig. 1) that can be traced back till the Eocene, except for one monotypic genus: Tupeia (antarctica) from New Zealand (ie. at the margin of their modern distribution). Tupeia’s pollen is spheroidal (Fig. 1), the basic form found all over the Santalales tree (Fig. 3). Fig. 4 shows alternative rooting scenarios using Su et al.'s loranth subtree.

Fig. 3 Schematic drawings of Santalales pollen, mapped on the preferred tree of Su et al. (cf. Grímsson, Zetter & Grimm, 2017, pp. 36–41)

Fig. 4 I used this figure in one of the rebuttal letters to explain basic evolutionary concepts triggered by different rooting scenarios using the same tree, the one preferred by Su et al. (#1, and #3, did not realize trees are optimized unrooted). Note: aerial parasitism evolved independently several times in the Santalales (Vidal-Russell & Nickrent 2007), but the triangular loranth pollen is unique. Using Bayes Factors, we established that the pollen-based root is the best-fitting for the data set we used for node dating in Grímsson, Kapli et al. (2017).

Why I lacked confidence in the Su et al. tree(s)

Su et al.’s study establishes relationships within the Santalales using a quite gappy up-to-7-gene data set (3 nuclear + 3 plastid + 1 mitochondrial genes) to revisit the placement of an originally poorly defined family with extremely long-branching members, the Balanophoraceae s.l. They found two main clades, one – the resurrected Mystropetalaceae – reconstructed as sister of the loranths (see scheme in Fig. 3). From what the authors show (but do not discuss), there are a lot of signal issues with their data:

• The standard nucleotide tree (partition scheme unclear) in the main text differs in many critical aspects (branching patterns, root-tip length ratios, support values) from the two in the supplement (one based on removing the 3rd codon positions, and one amino acid based).
• Many branches have high posterior-probabilities but low ML bootstrap values (BS), a pattern typical for mixed-genome oligogene data sets with intrinsic conflict.

Regarding the loranth root question:

• The first three branches within the loranth subtree, defining a ‘root parasitic grade’, have low to high posterior probabilities (PP = 0.65 / 0.99 / 0.52) and consistently low ML bootstrap supports (BS = <50 / 53 / <50).
• The sister clades have extremely long branches, and the putative sister clade, the Mystropetalaceae, is only covered for nuclear and mitochondrial data. All probabilistic inference methods treat missing data and gaps as “N”; ie. the terminal probability vector p equals (1,1,1,1) for p(A,C,G,T). In case the signal from the best-sampled regions is clear, missing data is no issue; if there is conflict then missing data can be a problem.

In addition, I’m generally skeptical when it comes to “basal grades” and roots inferred by very distinct outgroups. Except for the three species forming the root-parasitic grade (one in South America, two in Australasia), all loranths are aerial parasites. Loranths are a ubiquitous, highly competitive tropical-subtropical group extending into temperate climates with proper summers and little snow. They have a very extensive and relatively old pollen record across all pieces of Gondwana and Laurasia (Grímsson, Kapli et al. 2017, and references therein). The main lineages are sorted continent-wise, and the shift from root to aerial parasitism is supposed to have happened several times within the Santalales and its families. But only once in loranths? And how could only one root-parasitic lineage survive in South America, and two more in Australasia; all with but a single species?

What’s behind the ambiguous bootstrap supports

For my head-to-head with the editor and reviewers (the editor had invited a #3 reviewer, an anonymous “expert on phylogeny”), I re-analysed Su et al.’s data subset on loranths plus sister groups. By reducing the outgroup sample to the sister clades only (Misodendraceae+Schoepfiaceae, Mystropetalaceae), I increased the BS support (100 / 62 / 60) for the root parasitic grade. This indicates either that Su et al.’s analysis was not comprehensive or that IO-LBA (ingroup-outgroup long-branch attraction) is prominent.

Large outgroup samples, all other Santalales + few non-Santalales in Su et al. vs. only loranths and sister clades in my re-analysis, may alleviate LBA to some degree (eg. Sanderson et al. 2000; Stefanović, Rice & Palmer 2004). Higher support with fewer outgroups than with many in the same dataset can be an alarm flag.

The ingroup-only bootstrap consensus network (Fig. 5) shows moderate, but unchallenged support for a split between root and aerial parasites, which agrees with Su et al.’s all-Santalales tree. The low support for the first and second branch in outgroup-rooted trees relates to an ambiguous signal between the root parasites — the signal from the combined data are ambiguous as to whether Atkinsonia (the second Australasian root parasite) or Gaiadendron (the South American root parasite) is the second diverging branch. Note that the position of our (pollen-based) alternative root candidate Tupeia is also unresolved (no split with a BS > 20; compare Figs 1 and 5), which could be expected for a potentially ancestral, relatively underived taxon — a taxon literally close to the family's root.

For most other deeper branches with high PP but low BS in Su et al.’s loranth subtree, the network shows two competing topological alternatives. There is thus an intrinsic signal conflict in Su et al.’s matrix, which explains the topological differences in earlier studies using different gene and taxon sets, preferring the one or other alternative in the final cladogram.

Fig. 5 ML Bootstrap consensus network using Su et al.'s loranth data subset. A, the outgroup-inferred root; B, pollen-based root; C, a clock-based root inferred by Grímsson, Kapli et al. (2017). In contrast to Su et al.'s tree the network distinguishes between ambiguous and unambiguous relationships. Not too different from what we found using a more data-dense and divergent matrix (Fig. 1)

How to deconstruct a tree:

First step — single-gene trees and support networks

There are two main reasons for inferring single-gene trees and establishing single-gene support:

1. It is the only way assess the level of incongruence in the gene samples.
2. They inform about the amount of signal that each gene region contributes to the combined tree.

In case of Su et al.’s data set, it becomes clear that the combined topology is supported primarily by signal from the best-sampled (and most variable) plastid gene included in the data set: the plastid matK gene. The second, much less divergent, plastid gene (rbcL) partly reinforces the matK signal, or at least does not contradict it (except for a few odd-balls, which might be possible mix-ups during sequence generation).

It is also clear that the nuclear and plastid data fit aspect-wise, eg. both support or at least don’t reject potential clades, but not entirely. Particularly, the placements of the sister groups of the loranths within the loranth tree are unstable, ie. the position of the outgroup-inferred root.

Fig. 6 One-to-one comparison of trees inferred using the two most divergent nuclear and plastid genes included in Su et al.'s matrix: the matK (plastid) and 25S rDNA (nuclear-encoded ribosomal RNA gene; same scale). The root-parasitic grade and a loranth | sister clades split is moderately to well-supported using matK data, but not using 25S rDNA data. No plastid data were included for the assumed direct sister of loranths, the Mystropetalaceae. Note also the position of Tupeia (dark red) in both graphs, the only loranth without loranth-typical pollen.

Last, the single-gene trees and bootstrap networks illustrate a severe taxon sampling bias. The third nuclear marker, the RBS2 gene, is only covered for five ingroup taxa including Nuytsia but no other root parasite, and it fails to resolve the two aerial tribes, which are otherwise genetically distinct. Analysis of this small subset illustrates nicely the perils of taxon sampling (Fig. 7). The third plastid gene, the accD gene (7 ingroup representatives), supports Nuytsia as the first diverging lineage, but rejects the root parasite grade with equally high support (BS = 87)

Fig. 7 Some RPB2 trees, the new nuclear gene included by Su et al. (not included in our data set lacking taxonomic coverage). A, the tree including the sister clades of loranths. B, ingroup loranth-only tree, codon-positions treated as different data partitions; C, same, unpartitioned analysis. D, the "true tree" (according #1), ie. topology seen in Su et al. Green, splits in agreement with Su et al.'s tree, red, splits contrasting Su et al.'s tree.

The only mitochondrial gene included in the data set (matR) rejects the root-parasitic grade, in addition to the matK-only based Elytrantheae-Lorantheae clade seen in Su et al.’s tree, with nearly unambiguous support. However, it is in general low-divergent, and it may be that the authors relied on fragmentary (potentially pseudogene) data for some taxa. There are huge indels in the gene not found in any other angiosperm, and the two sequenced Loranthus are conspicuously distinct to the other loranths (Fig. 8).

Fig. 8 Neighbour-net based on Su et al.'s matR data. Numbers show the ML bootstrap support for (alternative) splits when sister groups are included or excluded. Note the position of the Mystropetalaceae, possible affected by IO-LBA with the Loranthinae (the latter's signal is in stark contrast to any other gene region). Two root-parasitic species are included: NuyFl = Nuytsia, GaiaPun = Gaiadendron; no matR for Tupeia.

One of the arguments of reviewer #1 was that Su et al. obtained a better resolved phylogeny because they sampled these extra gene regions. In fact, they obtained a better supported phylogeny because they added diffuse-signal or under-sampled gene regions. Hence, they enforced the dominant matK-preferred topology (high PP, low BS), while weaking locally conflicting signal from the nuclear 18S and 25S rDNA.

The only constant is that, no matter which gene region, Nuytsia is always the most distinct taxon of all species close to the root node. With respect to the very distant sister clades, IO-LBA may be inevitable. The BS consensus networks favor a closer relationship of the root parasites, and there is relatively strong signal for a root parasitic clade in the matK (Fig. 5), so that the biased outgroup-root then becomes a proximal (‘basal’) grade (Fig. 6, left).

Data effects of the LBA-missing sort also challenge the placement of the Mystropetalaceae as sister to the loranths. The plastid data establish that Misodendraceae and Schoepfiaceae (M+S) are distinct from the loranths. They provide unambiguous support for a loranth versus M+S split. Having no data on any plastid gene, the extremely long-branched Mystropetalaceae fall in line. Being very distinct from both M+S and loranths in the nuclear (Fig. 5) and mitochondrial (Fig. 8) genes, the tree places them next to the loranths, because the latter's root node and many of its members are much more distant from the all-ancestor than those of the M+S clade (compare with Su et al.'s trees; keep in mind that missing data may increase branch-lengths).

Second step—remove a taxon, or two, or a gene region

If the hypothesis of a root-parasitic grade holds, then one should be able to remove the first diverging taxon (Nuytsia in this example) from the dataset, and still have the position of the second (Atkinsonia) and third diverging (Gaiadendron) remain the same. Furthermore, the support for the corresponding branches should at best increase, and at least not decrease. Atkinsonia is relatively distinct, but Gaiadendron is not (as reflected by their pollen morphology, Fig. 2).

In the case of Su et al.’s data, removal of Nuytsia collapses the root-proximal part of the ingroup tree (Fig. 9). ML-tree inferences select a sub-optimal topology, because the signal weakens for the splits {Atkinsonia + outgroups | all other Loranthaceae} and {root parasites + outgroups | aerial parasites}. The competing alternative (BS = 23) is a first-diverging Atkinsonia-Gaiadendron clade. When both Nuytsia and Atkinsonia are removed, Gaiadendron is placed within the aerial parasites, and the Elytrantheae, a low-diverged Australasian tribe, are favored as first-diverging loranth clade (BS increases from 15 to 39; any alternative BS is < 20; see also their placements in Fig. 5).

Fig. 9 ML tree and bootstrap (top-right) consensus network using Su et al.'s data with the putative first-branching Nuytsia eliminated from the equation (see above). The tree is rooted according to Su et al.'s tree.

Equally disastrous for the support of a root parasitic grade is the elimination of matK from the combined data set. This is a major advantage of BS or support consensus networks: one can estimate whether taxon or gene sampling increases or decreases support for competing topologies; and not only the combined trees’ topologies.

Support consensus networks should be obligatory when studying non-trivial or suboptimal data sets

When it comes to extremely long-branching roots and sister groups, one should generally be careful with combined-data roots defined by outgroups (see also our discussion of the outgroup-inferred Osmundaceae root in Bomfleur, Grimm & McLoughlin 2015). But when the crucial branches in addition lack consistent support, one should actually be alarmed.

In the case of gappy oligogene (as used by Su et al.) or multigene data, one should always test the primary signal in the combined gene regions. Fast and efficient ML implementations make it very easy to infer and compare single-gene trees, and thus establish differential branch support patterns, which can be visualized and investigated using support consensus networks. As biologists working with complex systems and, likely, non-trivial evolutionary pathways, we should not be afraid of conflicting splits patterns, but deal with them!

It can also be useful to plot (tabulate) competing support values from different analysis. RAxML has an option that allows testing the direct correlation between two bootstrap (or Bayesian) tree samples, without being restricted to any particular tree. The Phangorn library for R includes functions to map trees into networks, and transfer support from networks to trees. In my experience, many nuclear and plastid incongruences are:

1. tree-based, meaning the trees are different, but the supports for topological alternatives are not conflicting;
2. resolution-based, meaning the nuclear data illuminate different parts of the evolutionary history compared to the plastid data;
3. rogue-based, meaning there are only a few taxa with strongly conflicting signals in the tree.

Support consensus networks can pinpoint all three scenarios. In the case of scenarios 1 and 2, a combined analysis still works, as also in the case of scenario 3 when the rogues are eliminated (from the combined analysis, not from the study, which unfortunately still a tradition in phylogenetics)

Uploading a matrix and the optimized tree to (eg.) TreeBase is just the first step (although many TreeBase submissions include only naked trees). In the case of ambiguous branch support (BS < 80 or 85, depending on the proportion of nuclear vs. mitochondrial and plastid gene regions; PP < 1.00), much more important would be to document the bootstrap replicate and Bayesian tree samples.

Furthermore, reviewers and editors should not encourage the publishing of trees where low support is masked by cut-offs (eg. BS < 50, PP < 0.95). Which is, unfortunately, the editorial policy of the journal that published the Su et al. study, and the reason for the scarcity of studies showing support consensus or other networks that can illuminate signal issues (but see eg. Denk & Grimm 2010, Wanntorp et al. 2014, and Khanum et al. 2016, published in Taxon). The latter a common feature in plant molecular data sets, independent of the taxonomic hierarchical level.

Further reading, and data

The full details of my re-analysis of Su et al.’s data subset, including loranths and sister clades, can be found in File S6 [PDF] to Grímsson, Grimm & Zetter (2017), included in the Online Supporting Archive (9.5 MB; journal hompage/mirror]. The relevant data and analysis files can be found in subfolder "Su_el_al." of the archive.

References

Bomfleur B, Grimm GW, McLoughlin S (2015) Osmunda pulchella sp. nov. from the Jurassic of Sweden — reconciling molecular and fossil evidence in the phylogeny of modern royal ferns (Osmundaceae). BMC Evolutionary Biology 15: 126. http://dx.doi.org/10.1186/s12862-015-0400-7

Denk T, Grimm GW. 2010. The oaks of western Eurasia: traditional classifications and evidence from two nuclear markers. Taxon 59:351–366. — Includes neighbour-nets based on inter-individual and uncorrected p-distances, with ML branch support mapped and tabulated.

Grímsson F, Grimm GW, Zetter R (2017) Evolution of pollen morphology in Loranthaceae. Grana DOI:10.1080/00173134.2016.1261939. http://dx.doi.org/10.1080/00173134.2016.1261939

Grímsson F, Kapli P, Hofmann C-C, Zetter R, Grimm GW (2017) Eocene Loranthaceae pollen pushes back divergence ages for major splits in the family. PeerJ 5: e3373 [e-pub]. https://peerj.com/articles/3373/ Don't miss reading the peer review documentation, which includes some interesting discussion. (If you agree that the peer review should be transparent in general, then you can sign up here for fighting the windmills.)

Khanum R, Surveswaran S, Meve U, Liede-Schumann S. 2016. Cynanchum (Apocynaceae: Asclepiadoideae): A pantropical Asclepiadoid genus revisited. Taxon 65:467–486. — Includes trees, median-joining and bootstrap consensus networks [I really enjoyed working on this, but retreated from co-authorship to protest against Taxon's editorial policies.]

Sanderson MJ, Wojciechowski MF, Hu J-M, Sher Khan T, Brady SG (2000) Error, bias, and long-branch attraction in data for two chloroplast photosystem genes in seed plants. Molecular Biology and Evolution 17: 782-797.

Stefanović S, Rice DW, Palmer JD (2004) Long branch attraction, taxon sampling, and the earliest angiosperms: Amborella or monocots? BMC Evolutionary Biology 4: 35. http://biomedcentral.com/1471-2148/4/35

Su H-J, Hu J-M, Anderson FE, Der JP, Nickrent DL (2015) Phylogenetic relationships of Santalales with insights into the origins of holoparasitic Balanophoraceae. Taxon 64: 491-506.

Vidal-Russell R, Nickrent DL (2008) The first mistletoes: origins of aerial parasitism in Santalales. Molecular Phylogenetics and Evolution 47: 523-537.

Wanntorp L, Grudinski M, Forster PI, Muellner-Riehl AN, Grimm GW. 2014. Wax plants (Hoya, Apocynaceae) evolution: epiphytism drives successful radiation. Taxon 63:89–102. — Includes trees and a "splits rose" [The editors forced us do drop some quite nice bootstrap consensus and median-joining networks; see also this post]