Large morphomatrices – trivial signal

In my last post about fossils, Farris and Felsenstein Zones, I gave an example of a trivial (signal-wise perfect) binary phylogenetic matrix, which will give us the true tree no matter which optimality criterion we use. In this post, we will look at a real world example, a huge bird therapods matrix.

S. Hartman, M. Mortimer, W. R. Wahl, D. R. Lomax, J. Lippincott, D. M. Lovelace
A new paravian dinosaur from the Late Jurassic of North America supports a late acquisition of avian flight. PeerJ 7: e7247.

What intrigued me about this particular paper (I have no idea about dinosaurs, but the documentation, pictures and data, and presentation seems impeccable) was the following sentence:

The analysis resulted in >99999 most parsimonious trees with a length of 12,123 steps. The recovered trees had a consistency index of 0.073, and a retention index of 0.589.

What can you possibly do with strict consensus trees (Losing information in phylogenetic consensus) based on an unknown number of MPTs that have a CI converging to 0 (but and RI of 0.6; The curious case[s] of tree-like matrices with no synapomorphies)? And isn't this a case for some networks-based exploratory data analysis?

The complete matrix has 501 taxa and 700 characters (the largest plant morphological matrices have hardly more than 100 characters) but also a gappyness of 72%. In this case, 255,969 of the 353,500 cells in the matrix are ambiguous or undefined (missing). The matrix is a (rich) Swiss cheese with very big holes. The high number of MPTs is hence not surprising, and neither is the low CI.

Why run elaborate tree-inferences on such a swiss cheese matrix? One answer is that (some) vertebrate palaeophylogeneticists are convinced that few taxa – many character matrices can lead to wrong clades (clades that are not monophyletic); and each added taxon, no matter how many characters can be scored, will lead to a better tree, by eliminating (parsimony) branching artifacts (see Q&A to the paper). At least 56 of the 501 taxa have 5% or fewer defined characters; still, with 700 characters, 5% equals up to 35 defined traits, which is more than we can recruit for most plant fossils. The median missing data proportion is 74% — more than half of the taxa are scored for less than 26% (< 182 out of 700) of the characters. Can such taxa really save the all-inclusive tree from branching artefacts, or is the high number of MPTs an indication for signal conflicts and data gaps issues?

For this post, we will just look at the tip of the iceberg. What is the signal from the 700 characters to start with?

The basic signal

Here's the heat map for the 19 taxa that have a gappyness of less than 15% (ie. at least 595 of 700 possible characters are defined). The taxon order is mostly the one from the original matrix, sorted by phylogenetic groups — for more orientation, I added next-inclusive superclass "Clades" from Wikipedia (so apologize any errors).

In my last post, I showed that evolutionary lineages (and monophyly) can be directly deduced from such a heat map following the simple logic: two taxa sharing a (direct) common origin are usually more similar to each other than to a third, fourth etc. taxon not part of the same lineage. Exceptions include fossils close to the last common ancestors lacking advanced traits.

The outgroup as used (in this taxon sample: Allosaurus to Tyrannosaurus) is most similar to each other but not monophyletic. One (Allosaurus) respresents the sister lineage of, the other an early split within the lineage that lead to the birds (Coelurosauria:Tyrannoraptora). The extinct (monophyletic) families (Tyrannosauridae, Ornithomimidae, Dromaesauridae) are, however, well visible, being defined by low intra-family and higher inter-family pairwise distances. The same is true for the direct relatives (Clade Ornithurae) of modern birds (class Aves).

Very typical for such datasets is the increasing distance between the (primitive?) outgroups and the most derived, modern-day taxa (living birds: Struthio – ostrich, Anas – duck, Meleagris – turkey). Closest relatives in the taxon set, phylogenetically and time-wise, are (much) more similar than distant ones. Allosaurus may be most similar to the tyrannosaurs, not because of common ancestry but because both are scored as being primitive with respect to the group of interest.

The only tree

This situation becomes very obvious from the only possible (single-optimal) tree that can be inferred from this matrix, when visualized as a phylogram (Stop using cladograms!)

The ML, MP and LS/NJ tree overlapped and scaled to equal root (first split within Tyrannoraptor) to tip (split between Anas and Meleagris) distance (phylogenetic distance, via the tree). Pink, the LS clade conflicting with ML and MP trees, and Wikipedia's tree(s).

No matter which optimisation criterion is used (here Least-Squares via Neighbor-joining, Maximum Parsimony, Maximum Likelihood), the result is the same. The only exception is that the NJ/LS tree places Archaeopteryx as sister to Dromaeosauridae; and the relative branch lengths of roots vs. tips also differ.

Because our matrix has favorable properties (few taxa, many defined characters), it's straightforward to establish branch support. This is a bit frowned upon in palaeontological circles, but having dealt with morphological evolution in cases where we have molecular data, I want to know how robust my clades are, and what may be the alternatives, before I conclude that they reflect monophyly. Bootstrapping coupled with consensus networks is a quick and simple way to test robustness and investigate ambiguous support (Connecting tree and network edges) .

The BS support consensus networks for NJ/LS and ML have only a single reticulation each.

Rooted support consensus networks based on the NJ/LS (10,000 pseudoreplicates, PAUP*) and ML bootstrap (100, number of necessary replicates determined by bootstop criterion implemented in RAxML) samples. Only splits are shown that ocurred in at least 15% of the BS pseudoreplicates.

The MP BS support consensus network is, however, has many more reticulations.

Rooted MP-BS support consensus network (10,000 BS pseudoreplicates, PAUP*). Green — edge bundles corresponding to clades in the all-optimal tree(s); orange — less supported conflicting alternatives; red – higher supported conflicting alternatives; pink – wrong clade in NJ/LS tree.

We can make two generally relevant observations here:

1. The wrong Archaeopterix-Dromaeosauridae clade (pink edge/branch) masks a split BS_NJ support: 68 for the wrong clade, 31 for the right one. While resampling under ML appears to be inert to this conflict, MP is not.
2. While the NJ- and ML support networks are very tree-like, all clades in the inferred tree have high to unambiguous support, and are near-congruent, the MP network is much more boxy. In some cases the split in agreement with the all-optimal tree has a lower BS support than an alternative (here usually in conflict with the gold tree).

Similar observations can be made with other data sets: although NJ/LS and ML optimisation are fundamentally different (distance- vs. character-based, equal change vs. varying probability of change), they show more agreement with each other when it comes to supporting a topology (or topological alternatives) than MP (character-based like ML, but all changes are treated as equal like NJ/LS). MP is a very conservative approach, highly dependent on possibly a few discerning characters. If they are missing from the BS pseudoreplicate, the backbone tree collapses or changes, and BS values may decrease rapidly. This is so even for a very data-dense matrix like the one used here (few taxa, many characters, low gappyness).

On the positive side, we can expect that MP will produce fewer false positives. On the negative side, it is also more dependent on character coverage, and will produce much more false negatives. Any fossil lacking the crucial characters (or showing too few of them) may be still resolved (placed and supported) under NJ/LS and ML but not using MP. When inferring trees, these fossils will quickly increase the number of MPTs and decrease branch support for the part of the tree they interact with. Personally, given how hard it can be to place a fossil per se with the data at hand, I always preferred a method that can give some result, and point towards possible alternatives (even risking including erroneous), rather than no result at all.

The simplest of networks

Naturally, we can use the distance matrix directly to infer a Neighbor-net, and explore the basic differentiation signal beyond trees but also with regard to the all-optimal tree.

Neighbor-net based on the pairwise distance matrix. Coloration highlights edges found (or not) in the optimised trees.

The Neighbor-net recovers the clades from the all-optimal tree (green, purple the NJ/LS-unique branch), but shows additional edges (orange). The principal signal in the data has, for instance, problems with placing Archaeopteryx, because it is (signal-wise) intermediate between the Avebrevicaudata, the lineage including modern birds, and the Dromaeosauridae, their sister lineage (note that the vertebrate fossil record is considered to be free of ancestors and precursors; all fossils represent extinct sister lineages – evolutionary dead-ends). Skeleton IGM 100042 (an Oviraptoridae), placed as sister to both in the all-optimal tree, also lacks obvious affinities: this is a taxon where the tree inference makes a decision that is not based on a trivial signal encoded in the matrix.

The central boxy part of the Neighbor-net correlates with the 2/3-dimensional part of the parsimony BS consensus network: to resolve these relationships, we need a large set of characters (under MP). On the other hand, recognizing the Ornithurae, members of an extinct family, or a relative of IGM 100042, should be straightforward even with a limited amount of defined characters. Based on the Neighbor-net, which is inferred in a blink no matter how large the matrix, we can also make a decision, as to which taxa interfere and which ones facilitate tree-inferences. The more tree-like the Neighbor-net graph becomes, the easier it is for a tree inference to be made.

Placing fossils, quickly and easily

Using this backbone graph, it is easy to assess in which phylogenetic neighborhood a newly coded fossil falls, eg. the fossil newly described in Hartman et al. and scored for 267 unambiguously defined traits, Hesperornithoides.

Neighbor-net including Hesperornithoides.

Hesperornithoides is obviously a member of the Eumaniraptora (= Paraves), morphologically somewhat intermediate between the Avialae, the "flying dinosaurs", and Dromaeosauridae, but doesn't seem to be part of either of these sister lineages. The graph lacks a prominent neighborhood, the Archaeopteryx-Bambiraptor neighborhood may reflect local long-edge attraction (note the long terminal edges) or convergent evolution in both taxa and, possibly, also the Hesperornithoides lineage. Just based on this simple and quick-to-infer network, Hartman et al.'s title "A new paravian dinosaur from the Late Jurassic of North America supports a late acquisition of avian flight" appears to be correct (in future posts, we may come back to this morphological supermatrix to see what else networks could have quickly shown).

One should be willing to leave the phylogenetic beaten track – ie. relying on strict consensus parsimony trees as the sole basis for phylogenetic hypothesis. The Neighbor-net is a valuable tool for quick pre- and post-analysis because it can:

• visualize how coherent the clades in our trees are, 
• how easy it will be for the tree inference (especially MP) to find and support clades, 
• help to differentiate ambiguous from important taxa, and finally, 
• assess whether a new fossil really requires an in-depth re-analysis of the full matrix (and dealing with >99,999 MPTs) instead of using a more focussed taxon (and character) set.

Please stop using cladograms!

I really like the journal PeerJ, not only because it is open access and publishes the peer review process, but also because it's one of the few that adhere to strict policies when it comes to data documentation. In my last (on my own) 2-piece post (part 1, part 2), I showed what networks could have offered for historical and more recent studies in Cladistics, the journal of the Willi Hennig Society. In this one, I'll illustrate why paleontology in general needs to stop using cladograms.

An example

In a recent article, Atterholt et al. (PeerJ 6: e5910, 2018) describe and discuss "the most complete enantiornithine from North America and a phylogenetic analysis of the Avisauridae". I'm not a paleozoologist and "stuff of legend", but their first 17 figures seem to make a good point about the beauty of the fossil and its relevance; and it is interesting to read about it. This makes me envy paleozoologists a bit — the reason I exchanged chemistry for paleontology was my childhood love for the thunder lizards; I specialized in zoology not botany for graduate biology courses, and I fell in love with social insects, especially bees; but then more general circumstances pushed me into plant phylogenetics.

The result of Atterholt et al.'s phylogenetic analysis is presented in their figure 18, as shown here.

Figure 18 of Atterholt et al. (2018): "A cladogram depicting the hypothetical phylogenetic position of Mirarce eatoni." [the beautiful fossil is highlighted in bold font]

This looks very familiar — graphs like this can be seen in many paleontological studies, not only those in Cladistics. However, this is a phylogeneticist's "nightmare" (but a cladist's "dream").

First, phylogenetic trees, especially those that were weighted post-analysis several times to get a more or less resolved tree, should be depicted as phylograms — trees with branch lengths. Phylogenetic hypotheses are not only about clades, and what is sister to what, but about the amount of (inferred) evolutionary change between the hypothetical ancestors, the internal nodes, and their descendants, the labelled tips. For example, we may want to know how long is the root of the clade (Avisauridae, Avisaurus s.l.) comprising the focus taxon compared to the lengths of the terminal branches within the clade. Prominent roots and short terminals are a good sign for monophyly (inclusive common origin), or at least a fossil well placed, whereas short roots and long terminals are not.

The above tree as phylogram (using PAUP*'s AccTran optimization). The beauty of cladistic classification is that the new specimen could have just been described as another species of Avisaurus (but read the author's discussion).

In this example, we seem to be on the safe side, although one may question the general taxonomic concept for extinct birds. Are the differences enough to erect a new genus for every specimen? This is hard to decide based on this matrix.

Second, a tree without branch support is just a naked line graph, telling us nothing about the quality (strengths and weaknesses) of the backing data. Neontologists are not allowed to publish naked trees. In molecular phylogenetics, we are not uncommonly asked by reviewers to drop all branches (internodes) below an arbitrary threshold: a bootstrap (BS) support value < 70 and posterior probability (PP) < 0.95. In palaentology, it has become widely accepted to not show support values at all. The reason is simple: the branch support is always low, because of data gaps and homoplasy. This is a problem the authors are well aware of:

The modified matrix consists of 43 taxa (26 enantiornithines, 10 ornithuromorphs) scored across 252 morphological characters [the provided matrix lists 253], which we analyzed using TNT (Goloboff, Farris & Nixon, 2008a). Early avian evolution is extremely homoplastic (O’Connor, Chiappe & Bell, 2011; Xu, 2018) thus we utilized implied weighting (without implied weights Pygostylia was resolved as a polytomy due to the placement of Mystiornis) (Goloboff et al., 2008b); we explored k values from one to 25 (see Supplemental Information) and found that the tree stabilized at k values higher than 12. In the presented analysis we conducted a heuristic search using tree-bisection reconnection retaining the single shortest tree from every 1,000 replications with a k-value of 13. This produced six most parsimonious trees with a score of 25.1. These trees differed only in the relative placement of five enantiornithines closely related to the Avisauridae, forming a polytomy with this clade in the strict consensus tree (Consistency Index = 0.453; Retention Index = 0.650; Fig. 18).

I've seen much worse CI and RI values in the paleophylogenetic literature (some of them are plotted in this post). For a phylogenetic inference, homoplasy equals internally incompatible signals — many characters show different, partly or fully conflicting, taxon bipartitions; or, in other words, they prefer different trees. The signal in the matrix is thus not tree-like — it doesn't fit a single tree. That's why we have to choose one using TNT's iterated reweighting procedures. (Note: an alternative "phenetic" Neighbor-joining tree has a computation time < 1s, and produces the same tree for the Ornithumorpha and the root-proximal, 'basal' part of the tree, except that Jeholornis is moved two nodes up; but it shuffles a lot in the Longirostravis–Avisauridae clade.)

Another point is that the more homoplasy we have, then the higher must have been the rate of change (here: visible anatomical mutation). The higher the rate of change, the higher the statistical inconsistency of parsimony.

In short, paleontologists (Atterholt et al. just follow the standard in paleophylogenetic publications) use data with tree-unlike signal to infer trees (see also David's last post on illogicality in phylogenetics) under a possibly invalid optimality criterion, which are then used to downweight characters (eliminate noise due to homoplasy) to infer less noisy, "better" trees.

The basic signal

We can't change the data, but we can explore and show its signal. And the basic signal from the unfiltered matrix is best visualized using a Neighbor-net splits graph.

Neighbor-net based on mean pairwise taxon distances. Thick edges correspond to branches in the published tree.

Some differentiation patterns that explain the clades in the tree can be traced, but it becomes difficult in the group that is of most interest: the (inferred) clade(s) comprising the newly described fossil. In the Neighbor-net this is placed close to another member of the Avisauridae, but not all. The matrix is not optimal for the task at hand.

The data properties

The matrix is a multistate matrix with up to six states in the definition line (although only five are used, as state "5" is not present). The taxa have variable gappyness (i.e. the proportion of completely undetermined cells), between 2% (extant birds: Anas and Gallus) and 94% (Intiornis, an Avisauridae) — the median is 56%, and the average close to it (54%). The "hypothetically" placed fossil Mirarce eatoni (in the matrix it is under its old designation: "Kaiparowits") lacks a bit more of the scored characters (61%). That may strike one as a lot, but note that the matrix has 253 characters! However, we may well ask: if I want to place a fossil for which I can score 99 characters, why bother to include another ~150 that tell me nothing about its affinity? (Note: paleobotanists struggle hard even to get such numbers, we usually have at best 50 characters.)

Its closest putative relatives, the Avisaurus s.l., lack 90% of the characters; leaving us with max. 25 characters supporting the relevant clade (assuming that the 10% are all found in Mirarce as well). Coverage is not much better in the next-closest relatives (phylogenetically speaking).

Data coverage in the phylogenetic neighborhood of Mirarce eatoni

The missing data percentage may have mislead the Neighbor-net a bit, because we will have fed it with unrepresentative or highly ambiguous pairwise distances. In the the network, the focus fossil comes close to Neuquenornis, the only other Avisauridae with some data coverage. Looking at the heat map below, we see that missing data is indeed a problem in this matrix — we have zero distances between several pairs that show different distances to the better-covered taxa.

The distance matrix drawn as a heat map: green = similar, red = dissimilar (values range between 0 and 0.8). Red arrows: taxa with too many (and ambiguous) zero pairwise distances.

The closest relative of Mirarce is, indeed, Avisaurus/Gettya gloriae, but the latter has zero distances to various other poorly covered taxa from the phylogenetic neighborhood, in contrast to the much better-covered Mirarce. Neighbor-nets are very good at getting the obvious out of a morphological matrix, but they don't perform miracles. However, why should we include poorly known taxa at all during phylogenetic inference? Wouldn't it be better to infer a backbone tree (or network showing the alternative hypotheses) based on a less gappy matrix, and then find the optimal position of the poorly known taxa within that tree (network)?

Estimating the actual character support

Some characters cover just 10–20% of the taxa, whereas others are scored for most of them — more than half of the characters are missing for more than half of the taxa. Using TNT's iterative weight-to-fit option means that we infer a tree, ideally one fitting the well-covered data (taxon- and character-wise), and then downweight all conflicting characters elsewhere to fit this tree. We then end up with a tree where we have no idea about actual character support. Since the matrix is a Swiss cheese, we only can re-affirm the first-inferred tree.

Let's check the raw character support, using non-parametric bootstrapping and maximum likelihood as the optimality criterion (corrected for ascertainment bias, as implemented in RAxML).

ML-BS Consensus Network (using Lewis' 2-parameter Mk+G model). Edge lengths are proportional to the BS support values of taxon bipartitions (= phylogenetic splits, internodes, branches in phylogenetic trees). Only splits are shown that occurred in at least 10% of 900 BS pseudoreplicates (number of necessary BS replicates determined by the Extended Majority Rule Bootstrap criterion), trivial splits collapsed. Thick edges correspond with branches in Atterholt et al.'s iterative parsimony tree; coloring as before.

The ML bootstrap Consensus Network bears not a few similarities to the distance-based Neighbor-net. The characters do not support the Avisauridae subtree, as depicted in the published TNT tree, but there are faint signals associating some of them to each other, despite the missing data. Keep in mind: a BS support of 20 for one alternative and < 10 for all others means (ideally) one fifth of the characters support the split, and the rest have no (coherent) information. Some sister pairs have quite high support (for this kind of data set), and Gettya gloriae is resolved as sister of Mirarce (unambiguously, with a BS support = 67). But, the matrix hardly has the capacity to resolve deeper relationships within the group of interest, the Enantiornithes — the polytomy with the next relatives seen in the tree and the corresponding clade dissolve. This confirms what we saw in the Neighbor-Net (despite missing data distortion).

The matrix and the tree show something that could have been deduced directly from the distance matrix: the poorly known Gettya (Avisaurus) gloriae is (literally) the closest relative of the enigmatic new genus / species Mirarce (morphological distance of 0.08 compared to 0.1–0.64 for all other taxa). But is this overall similarity enough to conclude Avisaurus, Gettya and Mirarce are a monophyletic group within the Avisauridae?

What the authors (and all paleontologists doing phylogenetics) should have done

(I would have skipped all trees, naturally, but peer reviewers and most readers probably need to see them.)

• Trimmed the matrix to include only those characters preserved in the fossil of interest, in order to minimize missing data artefacts during inference.
• Shown the Neighbor-net to visualize the primary signal situation, including and excluding poorly covered taxa. From the Neighbor-net it is already obvious that the fossil is an Enantiornithes, so any subsequent optimization / inference could have focussed on this group alone.
• Then inferred a backbone tree excluding poorly covered taxa, and shown the resulting phylogram. In case one needs to test the Enantiornithes root (the Neighbor-net gives us two alternatives for the Enantiornithes root: Pengornis + Eopengornis or Protopteryx + Iberomesornis), there is no point in including the poorly covered Enantiornithes or the worst-covered taxa outside this clade.
• Then optimized the position of the poorly covered taxa in the backbone tree. I recommend using RAxML's evolutionary placement algorithm (EPA) for this, but you can also do this in a parsimony framework if you wish. (EPA can also be used to test outgroup roots: here, one would search the branch at which all non-Enantiornithes fit best.)
• Shown the resulting phylogram including all taxa — that is, read in the topology to the analysis, and then re-optimize branch lengths.
• Shown a Support Consensus Network to illustrate the support for the branches in the preferred tree and their competing alternatives. (There may be one or more, as there are many options to estimate branch support.) How sure can we be about relationships within the Avisauridae and their relationships to other Enantiornithes?

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Postscriptum. For those who are curious about how the ML tree would look like, here it is:

I have no idea about birds, but from a methodological point of view this is an equally (if not more, because unforced) valid hypothesis for the data set. And demonstrating its limitations: note the relatively long branches with very low support making up the backbone of the Enantiornithes clade. This is typical for matrices lacking coherent discriminatory signal and/or struggling with internal conflict.

The network of woodpeckers, etc

The world continues on its merry way, searching for fragments of the Tree of Life. That is, research papers continue to be published that give no credence to the possibility of reticulate evolutionary history, especially in zoology.

A recent case in point is this one:

Matthew J. Dufort (2016) An augmented supermatrix phylogeny of the avian family Picidae reveals uncertainty deep in the family tree. Molecular Phylogenetics and Evolution 94: 313–326.

The author constructed a supermatrix for 26 loci for 78 taxa of the bird family containing woodpeckers, piculets, and wrynecks. The author used an array of phylogenetic techniques, including the construction of maximum-likelihood "gene" trees, several different maximum-likelihood species trees, plus time trees. All of these methods pre-suppose that the evolutionary history of the species was strictly tree-like.

We can use an exploratory data analysis to evaluate how probable is this fundamental assumption. I constructed a SuperNetwork based on the 26 gene trees produced by the author, using the SplitsTree program, as shown here. The network is basically tree-like, with one major exception.

I have labeled only one taxon, which seems to be the culprit for the major non-tree-likeness. This species appears in 10 of the gene trees, being part of the Leiopicus group (as expected) in 7 of the rooted trees. It is unexpectedly related to the Picus group in two of the other rooted trees, and is close to Dryocopus in the remaining tree.

This network EDA does not, of course, imply the existence of reticulate evolution. It does, however, highlight a pattern of incongruence that requires explanation, if the history of these birds is to fully elucidated. Reticulate evolution remains one of the possible explanations, pending further investigation.

For an example of a network view of bird evolution, see:

Antonio Hernandez-Lopeza, Didier Raoult, Pierre Pontarotti (2013) Birds perching on bushes: networks to visualize conflicting phylogenetic signals during early avian radiation. Comptes Rendus Palevol 12: 333-337.

Conflicting avian roots

A couple of years ago, I noted that genomic datasets have not helped resolve the phylogeny at the root of the placentals, because each new genomic analysis produces a different phylogenetic tree (Conflicting placental roots: network or tree?). It appears that the results depend more on the analysis model used than on the data obtained (Why are there conflicting placental roots?), and it is thus likely that the early phylogenetic history of the mammals was not tree-like at all.

Recently, a similar situation has arisen for the early history of the birds. In the past year, three genomic analyses have appeared involving the phylogenetics of modern birds (principally the Neoaves):

Erich D. Jarvis et alia (2014) Whole-genome analyses resolve early branches in the tree of life of modern birds. Science 346: 1320-1331.

Alexander Suh, Linnéa Smeds, Hans Ellegren (2015) The dynamics of incomplete lineage sorting across the ancient adaptive radiation of Neoavian birds. PLoS Biology 13: e1002224.

Richard O. Prum, Jacob S. Berv, Alex Dornburg, Daniel J. Field, Jeffrey P. Townsend, Emily Moriarty Lemmon, Alan R. Lemmon (2015) A comprehensive phylogeny of birds (Aves) using targeted next-generation DNA sequencing. Nature 526: 569-573.

The first analysis used concatenated gene sequences from 50 bird genomes (including the outgroups), and the second one used 2,118 retrotransposon markers in those same genomes. The third analysis used 259 gene trees from 200 genomes. The second analysis incorporated incomplete lineage sorting (ILS) into the main analysis model, while the other two addressed ILS in secondary analyses. None of the analyses explicitly included the possibility of gene flow, although the second analysis considered the possibility of hybridization for one clade.

These three studies can be directly compared at the taxonomic level of family. I have used a SuperNetwork (estimated using SplitsTree 4) to display this comparison. The tree-like areas of the network are where the three analyses agree on the tree-based relationships, and the reticulated areas are where there is disagreement about the inferred tree.

The network shows that some of the major bird groups do have tree-like relationships in all three analyses (shown in red, green and blue). However, the relationships between these groups, and between them and the other bird families, is very inconsistent between the analyses. In particular, the basal relationships are a mess (the outgroup is shown in purple), with none of the three analyses agreeing with any other one.

Thus, the claims that any of these analyses provide a "highly supported" phylogeny or "resolve the early branches in the tree of life of birds" seem to be rather naive. ILS is likely to have been important in the early history of birds, as this is usually considered to have involved a rapid adaptive radiation. However, I think that models involving gene flow need to be examined as well, if progress is to be made in unravelling the bird phylogeny.

This analysis was inspired by a similar one by Alexander Suh, which appeared on Twitter.