Just try it for your data – a last first-of-its-kind Neighbor-net using FTIR data

This is likely to be my last post for this blog.

Some thoughts

When I joined the Genealogical World of Phylogenetic Networks three years ago, I didn't know how much fun it is to blog about science. Blogging, or writing essays, has several advantages against the traditional way to get a researcher's ideas out into the world — writing a scientific paper. The most important one is, one can just try out something without having to worry how this would get past the peer-reviewers and editors (or as I like to call them: the Mighty Beasts lurking in the Forest of Reviews). When I was still a (sort-of) career scientist (ie. paid by tax-payers to do science), I had my share of discouraging experiences, whenever we tried to leave the beaten (and worn out) paths to try something new; to look into the dark places and not right under the street-lights.

Before we submitted papers, we hence put a considerable effort into them, pondering what our peers may criticize, or what might alienate them (being likely unfamiliar with our methodological and philosophical approaches), and thus to minimize the chance all our work would be for nothing. In a couple of cases, where we expected fierce resistance, we opted for low-impact journals with no manuscript length restrictions and more welcoming editors and peers, to be able to put in everything that we had. Some of my best bits are buried in journals where you'd never expect them!

But it was increasingly annoying, nevertheless;. It was no fun anymore to formally publish research, and so I let my career as smoothly run out in the 2010s as it started in the Zeroes.

David's encouraging me to write blog-posts, just after I early retired, thus revitalized my interest in science, to "boldly go where no-one has gone before". The amount of effort is typically much lower, although some of my posts do involve the same work that I put into the papers that I co-authored. More importantly, there are no beasts in the World Wide Web that can bite you from the shadows; they have to do it in the open. It's an ideal way to get an idea out, without having to think about the consequences. None of the work I put into a post has been for vain. What a difference: before, for every graph / analysis result published, two ended in the bin, many devoured by the Mighty Beasts.

And, maybe somebody will find the work interesting enough to try it out; and eventually my idea finds a place in the sanctionized, peer-reviewed scientific world, anyway. Since I'm out-of-business, I can afford to not cash in the credit (no-one formally cites a blog post).

My last Neighbor-net for the Genealogical World

Neighbor-nets (NNets) and myself was love at the first sight (this was, in my case, ~2005, when my boss Vera Hemleben, a geneticist, sent me over to the new professor in our bioinformatics department, named Daniel Huson, who had just released a new software package, SplitsTree). These networks are...

• ... most versatile: any kind of data can be transformed into a distance matrix;
• ... quick-and-easy to infer.

And even if they are not phylogenetic networks in the strict sense – NNets are unrooted and their edge-bundles do not necessarily reflect evolutionary pathways – they more often than not point towards common origins and down-scale ± complex phylogenetic relationships more comprehensively than any phylogenetic tree (coalescent or not) that we could infer. The Genealogical World is full of examples, and the writers of this blog such as David [homepage], Mattis [GoogleScholar/ homepage], myself [GoogleScholar/ homepage], and like-minded researches have published quite a few of them (in high- and low-impact journals). For a comprehensive, permanently updated list see Philippe Gambette's Who's Who in Phylogenetic Networks page.

For my final post, I decided on a fascinating new data source in paleobiology: Fourier transformed infrared spectra (FTIR) of fossil cuticles.

The cuticle is a plant's skin, and it's composition and structure show a lot of variation, down to species level. Thus, their morphological-anatomical features have long been used as taxonomic markers to identify fossil material. Using infrared spectroscopy, one can look at the chemical composition of cuticles. Like any other spectrum, an FTIR-spectrum can be broken down in sets of quantitative (discrete, binned) or qualitative (continuous) characters; and one can then create a dissimilarity matrix for the investigated material. This is what Vajda, Pucetaite et al. (Nature Ecol. Evol. 1: 1093–1099, 2017) did for long-death (Mesozoic) but enigmatic seed plants and their equally enigmatic modern counterparts.

A UPGMA dendrogram based on FTIR data of fossil taxa (Vajda et al. 2017, fig. 4). Brackets to the right give the topology of the UPGMA dendrogram including extant material and data (Vajda et al. 2017, fig. 3).

PCA plots of the first and second (a), and first and third (b) coordinates, with the main seed plant lineages indicated (modified after Vajda et al. 2017, suppl.-fig. 4)

PCA and UPGMA are not phylogenetic inference methods, but there is obviously some phylogenetic signal encoded in these FTIR spectra, as shown above.

When I first saw the paper, I contacted the authors (including former colleagues of mine at Naturhistoriska riksmuseet in Stockholm), and the first author gave the second author, Milda Pucetaite (a Ph.D. student), a green light to share and convert her FTIR data into a simple distance matrix for me to run a NNet, as shown below.

Neighbor-net based on the combined distance matrix provided by Milda (pers. comm. July 2017).

Note that this NNet is a partly impossible graph, phylogenetically. The chemical composition naturally changes after the foliage (in this case) gets buried in sediment, and its cuticle is then conserved for millions of years by various taphonomic and diagenetic processes. As pointed out by the experienced biochemist among the authors during our correspondence: it is hence pointless to combine the data from extant and extinct taxa.

Well, since this is a post and not a paper, I combined them anyway. I find the result quite compelling, supporting the paper's conclusions including more speculative follow-up ones. The NNet reflects every aspect that these kind of data can provide for phylogenetic and systematic purposes.

The prominent central edge bundle reflects the taphonomic-diagenetic change separating the living from fossil samples. The basic sequence within the subgraphs is the same: gingkoes are closest to cycads, and cycads bridge to Araucariaceae, which is a relict lineage of the "needle" trees, the conifers (many of which don't have needles but leaves). Bennettitales and Nilssoniales are extinct groups of seed plants, which are here resolved as a distinct lineage. Especially, the Bennettitales have been have long puzzled scientists. They may represent a third major lineage of seed plants that are neither angiosperms (flowering plants) nor gymnosperms (ginkgoes, cycads, conifers, gnetids), or perhaps an early side lineage of either one (or lineages, as their two main groups are quite different).

As for pretty much any kind of data, just try it out for yourself. This is exploratory data analysis (EDA), particularly useful to get a first, fast impression of the primary signal in your data. This is true even if you keep it to yourself, having to watch out for the Mighty Beasts of the Forest of Reviews (especially the ones that call themselves "cladists"). Who are quick in telling you, what you can't do, but not so straightforward, when it comes pointing you to other options for analyzing your data.

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My dive-in list for some more (im-)possible NNets

• "Man gave name to all those animals": cats and dogs — a joint post with Mattis, where we just mapped the names on a NNet of world languages. Cormac Anderson joined for the second part dealing with goats and sheep.
  
• Should we try to infer trees on tree-unlikely matrices — my first post for the Genealogical World of Phylogenetic Networks about a NNet that, at the time I made it, was impossible to publish.
  
• Stacking networks based on sign language manual alphabets — NNets based on hand-shapes historically used for sign letters.
• To boldy go where no one has gone before – networks of moons — a joint post with Timothy Holt, who scored celestial bodies of our stellar system for classification.
• Visualizing U.S. gun laws — inferring NNets based on serious issues can be fun. Related post: The 2nd Amendment does more than keep King George away.

With David retiring, the Genealogical Worlds of Phylogenetic Networks will fall dormant, the next and final post will be a farewell from David. Like Mattis (Von Wörtern und Bäumen), I will keep on science-blogging (in spite of the new buggy Blogger-editing interface forcing me to draft directly in HTML) for a little while (and irregularly) on my Res.I.P. blog, which also includes a tag for "phylo-networks" for any future NNets and the like.

Fossils and Networks 3 – (deleting and) adding one tip

In the last Fossils and Networks post, we explored the use of SuperNetworks to identify both safe and problematic branching patterns by removing one OTU and re-evaluating the analysis. Here, we'll take the opposite approach, and see what we can learn from adding one OTU to our analysis.

Breaking and supporting wrong branches

We start again with the artificial Felsenstein Zone matrix that results in a wrong AB clade. Here's the original true tree used to generate the matrix.

Because of convergent/parallel evolution in the modern taxa (genera O, A and B) and primitive characters of their fossil sisters, any phylogenetic inference method will find the wrong, tree with a A + B | rest split.

In the Felsenstein Zone, parsimony will always get the wrong tree due to long-branch attraction (LBA), while Maximum likelihood has a 50:50 chance to escape LBA. To break down the LBA between A and B, we need a fossil that is, from an evolutionary point of view, intermediate between D and B.

If we add a fossil E that features 1 out of 3 derived traits found in the BD lineage (including the only synapomorphy of BD), we end up with two alternative parsimony trees: one with a wrong topology and the other the correct topology, as shown here.

By adding a fossil F featuring 2 out of 3 derived traits, we increase the number of most-parsimonious trees (MPTs) to three alternatives, all of which fall prey to A-B+F LBA, as shown next.

Convergent evolution is a problem for tree inference but selection bias and homoiologies are worse, involving accumulation of the same advanced trait within some but not all members of a lineage (Has homoiology been neglected in phylogenetics?). This is worse because the characters will enforce attraction between long-branching, highly evolved (more modern) taxa. A and B are siblings, but by enforcing an ABF clade, we will inevitably misinterpret the most primitive members of the ingroup, C and D. Hence, we may draw wrong conclusions about evolution in the A–F lineage.

Because E is virtually half-way evolved between D and F, and F is the next step towards B, the all-inclusive tree gets it right. We infer a single optimal tree, shown here.

PS: Also, in this case we could use any other optimality criterion (Maximum Likelihood, Least-squares, Minimum Evolution) and we would end up with the same tree.

Missing the important bits

That last observation is encouraging: the more fossils we include in our matrix and the better they reflect the evolutionary trends within a group (here from a D-like ancestor via E to F and B), the greater the chance of ending up with the true tree. There's only one drawback: in real-world data sets, we may miss exactly those traits in the fossil sample that are needed in order to infer (or stabilize) the true tree.

(Paleo-)Parsimonists have frequently argued that missing data are unproblematic, which is true in one sense, as shown in the above example. The commonly used strict consensus tree has no wrong branches, because it only has one, which is the trivial ingroup-outgroup split. The much less commonly used Adams consensus tree has one more branch, which is wrong: the ABF clade.

As always in such cases, the strict Consensus network visualizes the MPT sample best (again exemplifying why we should stop using cladograms).

The price for not having false positives is that we cannot infer a most-parsimonious tree or a few alternative trees any more, but could easily end up with scores of them. Here, we have 41 MPTs for a 8-taxon dataset that include fairly wrong trees*, although some of them are closer to the true tree (green and olive edges in the strict Consensus network above). For large matrices, or matrices lacking tree-like signals, the number of MPTs can easily reach tens or hundreds of thousands. Lacking critical traits in E (14 out of 46 characters missing) and F (7 missing), we may escape LBA at the cost of decisiveness. If we do have those traits only in F but not E, we will enforce LBA between A and B.

Plus-1-trees (and SuperNetworks)

Before adding a taxon as an additional leaf to our tree, we may be interested in what that taxon does to our tree: can it trigger a topological change or does it fall in line? We will again take the dinosaur-to-bird-matrix of Hartman et al. (2019, PeerJ 7: e7247) as a real-world example. This includes everything from well-covered highly derived and most primitive taxa, to those that lack discriminatory signal in general (ie. are unresolved), plus the one or two rogue taxa, with ambiguous phylogenetic affinities creating topological conflict. (Note: the commonly reported strict consensus trees cannot distinguish between those two alternatives.)

The best-covered 15 taxa provide us with a single optimal tree that is in agreement with current opinion (shown below). However, this struggles to resolve the clade of modern birds because the extinct Lithornis is being attracted by Anas, the duck. When we remove Dromiceiomimus (as shown in Fossil and Networks 2), we end up with a putatively wrong Dromaeosauridae grade, because of LBA between the most distinct Dromaesauridae, Velociraptor and Bambiraptor, and the distantly related (to flying dinosaurs) Allosaurus, Tyrannosaurus and the IGM 10042 skeleton.

Two of the Minus-1 trees generated for the last post of this series.

For our experiment, we will take this (partly) wrong tree, and add every other taxon included in the Hartman et al. (2019) matrix as 15th tip. We can then perform a branch-and-bound search to infer these 14-Plus-1 tree(s). When we browse through the inferred MPTs, we can see that many taxa fall in line with the wrong topology, including a few that, in addition, increase uncertainty for branches correctly resolved in the minus-Dromiceiomimus tree.

Out of the 485 candidate trees, only 10** have a set of characters that can compensate for the missing Dromiceiomimus, leading to Plus-1 trees that show a Dromaesauridae clade, as shown here.

Two of the ten Plus-1 trees, where the added tip saves the inference from LBA. Numbers give the amount of defined characters (scored traits). Both Halszkaraptor and Zhenyuanlong are classified as Dromaeosauridae, however only the better covered taxon is placed as sister to the Dromaeosauridae included in the original 14-taxon tree.

The presence of the deep-branching Compsognathus (Tyrannoraptora: ... :Neocoelurosauria: †Compsognathidae) triggers an Archaeopteryx-Dromaesauridae clade.

In the case of relative deep-branching Garudimus (... :Neocoelurosauria: Maniraptoriformes: †Ornithomimosauria: †Deinocheiridae) and Epidexipteryx (... : Maniraptoriformes: ... : : ... : Paraves: †Scansoriopterygidae) one or two of the two or three MPTs show the wrong grade except the last the clade.

Note: the relative low number of scored traits for Epidexipteryx can avoid LBA leading to a Dromaeosauridae grade but misplace the taxon within the Plus-1 MPTs: its family, the Scansoriopterygidae, are considered to represent the sister lineage (Wikipedia, referring to Godefroit et al. 2013 Nature 498: 359–362) of the Eumaniraptora which include the Dromaeosauridae as first-diverging branch.

We can also summarize the outcome, a collection of 640 Plus-1 MPTs, in form of a z-closure SuperNetwork, as we did for the Minus-1 trees in the previous Fossils and Networks post (shown next).

This SuperNetwork is quite boxy, and may be only semi-comprehensive (I used only 20 runs, which took half a day). Matching 485 tips into a 14-taxon backbone tree is not the kind of tree sample that the SuperNetwork has originally been designed for!

Only four edges, fat and blue, are without alternatives. In all other cases, the added tip triggered the creation of several alternatives: the highest dimension for the boxes is five, but most have four or less dimensions. Regarding our problem of saving the Dromaeosauridae clade, we can see that the topological change depends on very few characters, with Microraptor being very close to the divergence but a bit more bird-like (in a very broad sense), while the other two are much more derived.

Close-up on the Dromaeosauridae part of the network, with all tips labeled. Pie charts give the percentage of scored traits/missing data. * – Tips that saved the inference from LBA (see above).

Note the length of some of the colored edges, especially the light green which represent edges reflecting a Dromaeosauridae clade. Other Dromaeosauridae taxa increase not only the diversity but also may create substantial topological ambiguity (bluish and greenish edge bundles; same color = same split) and branching bias.

Take-home message

Creating morphological supermatrixes makes a lot of sense, because it ensures normalization and facilitates universal comparability, which is crucial also for paleobiology. However, even more than molecular phylogenies, paleophylogenies are affected by character and taxon sampling. This is nothing new, and much debate has dealt with which parsimony strict consensus cladogram is the better one.

I suggest taking a new route. Instead of using morphological supermatrixes to infer trees – for this matrix, Hartman et al. found millions of equally optimal parsimony trees further filtered by post-analysis, initial tree topology informed character weighting (as implemented in TNT) – we should use it to generate subsets and engage in exploratory data analysis. This will pinpoint strengths and weaknesses of the data and its individual taxa. Rather than producing evolutionary meaningless soft polytomies, one should study the reasons for any topological ambiguity. After all, one simple reason for unstable branching patterns may be that all so-far inferred trees are biased, only differently.

The SuperNetwork can assist us in putting together taxon sets that could allow not only a simple tree inference but also topology testing.

• If we want to test the stability of, e.g., the Dromaeosauridae clade against taxon sampling, it will be of little use to include the most primitive (anything outside Maniraptora) and much more advanced taxa (Avialae including modern birds) of the 501-taxon matrix. On one had, the most primitive taxa will only increase the computational load, because our inferred tree not only optimizes branches we are interested in, but also irrelevant ones, using taxa that largely lack discriminative signal for the branches of interest or at all. On the other hand, the most derived taxa may bias the tree inference by providing strong terminal signals outcompeting potentially conflicting weak basal signals.
• If we want to test the stability of the backbone phylogeny against adding taxa and entire lineages, we may prefer short-branched over long-branched taxa, in order to avoid (local) LBA (especially when we want to stick to parsimony). The terminal edges in the SuperNetwork indicate the minimum number of unique changes for each tip added to the 14-taxon tree. As seen also in our hypothetical example: E and F only break down the wrong AB clade because both are either identical (or very similar) to the last common ancestor of E+F+B and F+B, respectively.

In a future post, I'll come back to the issue of identifying taxa that are game changers, using a simple and quick tree-based approach: the so-called "evolutionary placement algorithm", first implemented in RAxML.

PS.
For any of you who really don't like networks, but still find no comfort in comb-like strict consensus cladograms either: just tick the SuperTree option when inferring the SuperNetwork. But only if your input trees converge to a shared topology. Otherwise the result may look like this:

A SuperTree based on the 640 Plus-1 MPTs.

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* Somebody familiar with Consensus networks and morphological data partitions providing complex signal, can extract a phylogenetic hypothesis from this boxy network for the included taxa. In general, the distance along the network edges represents a phylogenetic distance, and thus gives a direct measure of how derived a taxon is.

For example, C, D are closer to the ougroup and placed close to the centre of the graph, which is exactly where a primitive ingroup taxon, with an ancestral morphology, would be placed. F is most likely a sister of B. The olive EF | rest split supports a potential common origin of E, F, and B (long green edge bundle). Hence, A can only represent a distant, strongly evolved sister lineage (both the alternative AB and ABF clade have less character support). Also, since the graph depicts E as least derived of the four (irrespective of the topological alternatives), its affinity to F and B has more value than the affinity between A and B, both being long-branched, and hence susceptible to LBA. D fits into the picture, the olive DE edge either: (1) represents a common origin, which would make D an early member of the red lineage; or (2) has similarity due to shared primitive traits within the ingroup, which would make D an early member of an ABEF lineage. C, in contrast to D, has no clear affinities with any other ingroup member, and so can only be interpreted as an early, very primitive form with uncertain phylogenetic relationships. The (true tree) mutual monophyly of the red and blue ingroup lineages has very little character support in the matrix, and hence cannot possibly be resolved.

** Systematically they cover a range of maniraptoran ('hand hunters') families 'below' the Avialae ('flying' dinosaurs) including, in addition to two Dromaeosauridae (Halszkaraptor, Zhenyuanlong, trees shown above), members of †Alvarezsauroidea (Haplocheirus), †Caudipteridae (Caudipteryx), †Sinovenatorinae (Sinovenator), †Therizinosauroidea or related (Beipiaosaurus, Jianchangosaurus) and †Troodontidae (Gobivenator, Sinornithoides). Caihong is a member of the †Anchiornithidae, which Wikipedia flags as "Avialae ?". These OTUs show data coverage far above the median (74% missing), with 278 (Caihong) to 558 (Caudipteryx) defined characters (out of a total of 700).

Fossils and networks 2 – deleting (and adding) one tip

A general assumption in phylogenetics is: the more the better. The more data my matrix includes, the better will be my tree. The more taxa I include, the better will be my phylogenetic analysis. But is this true when we include (or rely on) fossils? After all, there is an old saying: less is more; and in this post I will show you that it is often true here, too.

Perfect data – how to recognize unproblematic topologies

In the first post of this series (Farris and Felsenstein), I introduced two matrices, a Farris Zone matrix and a Felsenstein Zone matrix, with the same set of tip taxa: three extant genera and three early fossils, one for each generic lineage.

The Farris Zone matrix provides a perfect signal. No matter which inference criterion one uses, one always gets the true tree. In such a case, the taxon sampling should be irrelevant; and it is. Any 5-taxon sub-tree correctly shows only splits found in the 6-taxon true tree — shown below are the actual most parsimonious trees (MPT) of each inference using the branch-and-bound algorithm.

Six most-parsimonious trees showing the topology of the true tree; trees are midpoint-rooted and have the same scale.
Note: NJ/LS and ML would give the same result for this experiment.

Consequently, for the perfect case, the SuperNetwork of the six 5-taxon trees is the 6-taxon true tree.

Z-closure SuperNetwork (Huson et al. 2004) of the 5-taxon MPTs generated with SplitsTree (walkthrough at the end of the post) depicting the true tree.

Therefore, the simplest test to check for potential topological issues in any set of data is to sub-sample the taxa by sequentially pruning a single taxon, infer the resulting group of trees (which I will call minus-one trees), and then summarize this tree sample in the form of a SuperNetwork. If the data have no signal issues – and the inferred all-inclusive tree is unbiased – all minus-one trees will be congruent with the all-inclusive inferred tree. The resulting SuperNetwork will then be a tree matching the inferred all-inclusive tree.

On the other hand, if removing a single taxon has a significant effect on the inferred tree, then this either means you need this taxon to get the right tree or that this taxon is causing bias. We cannot assume that trees with many taxa are better than trees with fewer taxa. Only if a topology is independent of taxon sampling can we be sure that we are looking at a true tree (or one inevitable with the data at hand).

Taxon-sampling matters? Then the all-inclusive tree may be biased

Real data matrices are far from perfect. Paleophylogenetic matrices, for instance, not only include a lot of missing data limiting the decision capacity of any phylogenetic inference, but, being restricted to morphological traits, usually high levels of homoplasy — that is, similarity in conflict or only partial agreement with the phylogeny (here are some related posts: Has homoiology been neglected in phylogeny? Should we bother about character dependency? Please stop using cladograms! The curious case[s] of tree-like matrices with no synapomorphies and More non-treelike data forced into trees: a glimpse into the dinosaurs). While some OTUs are primitive in their character suites, others are highly derived. We often, without realizing it, are infering within or close to the Felsenstein Zone.

If we repeat the same minus-one experiment, but now use the Felsenstein Zone matrix, instead, we end up with something quite different. We get three most-parsimonious tree (MPT) solutions when eliminating the outgroup genus O or its fossil Z; and eliminating the genera A and B and their fossils C and D, respectively, each leads to a single MPT. This yields a total of 10 MPTs.

First row rooted with Z, all other trees mid-point rooted. All trees have the same scale.

By pruning the long-branching genera A or B, even parsimony analysis gets the correct tree because we have eliminated the source of the long-branch attraction. Adding fossils to break down long branches can be effective (classic paper: Wiens 2005), but dropping long-branching tip taxa works just as well. Changing between a close outgroup (fossil Z) and a distant outgroup (fossil O) has little benefit here.

In this case, the resulting SuperNetwork of our 10 MPTs is not a tree but a network including alternative clades, wrong ones (orange), ie. not monophyletic, and correct ones (green) — ie. branches (internodes, bipartitions) reflecting the monophyletic lineages of the true tree.

Comprehensive Z-closure SuperNetwork of the 10 minus-one MPT inferred based on the Felsenstein Zone matrix. The network includes all split patterns found in the MPT sample.

A real world example

To give an example of how sequentially dropping one taxon works with real-world data, we'll use the exhaustive 700 character matrix for bird-related dinosaurs provided by Hartman et al. (2019).

With its total of 501 taxa (OTUs), the apparent rationale behind the matrix is that, by including as many taxa as possible, one gets the best-possible (parsimony) trees, irrespective of the signal quality provided by individual OTUs. However, the full matrix cannot be forced into a single-optimal parsimony tree, due to missing data (72% of the matrix' cells are undefined or ambiguous, ie. 255969 cells) and a scarcity of synapomorphies (in a Hennigian sense) — this is discussed in Hartman et al.; see also the related Q&A.

Here, in light of the computational effort and to avoid heuristics when searching the MPTs, we'll use a pruned sub-matrix. For our first experiment, we take 15 out of the 19 best-covered OTUs. Thus, OTU pairs / triplets that are much more similar to each other than to any other OTU, are reduced to the best-covered representative.

The 19-taxon matrix that I used in a previous post (Large morphomatrices – trivial signal) had only one most-parsimonious tree solution, showing only clades in agreement with current opinion, which assumes a largely staircase-like evolution from dinosaurs to modern birds (Tree of Life). In contrast to the full matrix, the 19-taxon matrix provided high support for most clades (method-independent), reflecting the number of scored traits. The extant taxa, representatives of modern birds (duck, turkey and ostrich, all edible), have many derived cgaracters, with the extinct bird genus Lithornis being placed in-between ostrich and duck + turkey.

The optimal topologies for the 19 best-covered taxon matrix. Green, the single most-parsimonious tree. Clade names copied from Wikipedia/Tree of Life.

The ML and NJ/LS (except for one branch) trees were topologically identical; each branch is supported by about 100 inferred changes. The signal from the matrix should be straightforward.

The tree-size weighted mean (default in SplitsTree) SuperNetwork, summarizing the result of an exhaustive branch-and-bound search using the 15-dropped-1-taxon matrices (each one resulting in a single optimal MPT) has a tree-like structure.

Allosaurus-rooted SuperNetwork of the 15 minus-one MPTs. Green – clades also found in the all-inclusive tree representing monophyla; orange – conflicting clades, blue – the all-inclusive tree doesn't resolve the assumed monophyly of modern birds, but places Lithornis as sister to Neognathae.

Conflicting clades are found in only two of the 15 inferred MPTs, being represented by short branches (their length in the other 14 trees is counted as zero).

Nonetheless, these conflicts received considerable character support. The frequency of a split in the minus-1 tree sample is irrelevant (see the A-B LBA problem discussed above — any tree including A and B showed the wrong clade). When summarizing our tree sample (especially when using MPTs), we should hence opt for a SuperNetwork, in which the edge lengths give the minimum branch lengths found in the MPT collection, ie. the edge length reflects the minimum length of the branch in all trees showing that branch.

Same SuperNetwork as above, but using the "Min" option instead of the default setting for computing edge lengths.

Without Dromiceiomimus – representing an earlier diverged lineage and step in bird evolution – the Dromaeosauridae clade, which is probably monophyletic (Wikipedia), flips and dissolves into a grade. By removing the intermediate step, we seem to create some ingroup-outgroup (long-branch) attraction.

Anas, the duck, forms the morphological link to Lithornis – with a mean morphological pairwise Hamming distance (MD) of 0.23, Anas is the most-similar OTU; and, hence, the MPT places Lithornis as sister to Anas + Meleagris (turkey; MD = 0.17). By eliminating Anas, the remaining contemporary birds form a clade — the modern birds (Neornithes) are assumed to be monophyletic but do not form a clade in the all-inclusive MPT (Struthio, the ostrich, is morphologically more distant from duck, turkey and Lithornis).

Conclusion

Even the most comprehensive, least gappy of paleophylogenetic matrices have substantial signal issues. If a tree inference is dependent on which OTUs are sampled, we cannot assume that we will automatically get better trees simply by including everything we have. Some OTUs (in our experiment: Dromiceiomimus) will stabilize correct aspects of a tree, while others will manifest bias or error (here: Anas). It's unlikely that a wrong, ie. not monophyletic, clade created by the attraction of two well-sampled taxa can be broken down by adding numerous taxa showing only a fraction of defined characters. SuperNetworks of minus-one trees can point you to the critical OTUs and unstable branching patterns of your (backbone) phylogeny.

PS. Personally, I would analyze a matrix with these properties, and a taxon sample spanning more than 150 myrs of evolution (from Allosaurus to modern birds), using ML not MP. I used MP in this post only because paleontologists are still very fond of it (not a few still discard anything else as unfit for their data). ML is less prone to long-branch attraction, results in a single tree (easier to compare when using larger taxon samples), and is speedy these days, allowing for more in-depth experiments towards the end of the exploratory data analysis. Both IQ-Tree (homepage; includes links to online servers) and RAxML-NG (open access paper providing essential links / github; implemented on various online servers) can quickly infer ML trees and establish branch support (including but not restricted to nonparametric bootstrapping) using binary and multistate data.

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Walk-through for computing Z-closure SuperNetworks (Huson et al. 2004) in SplitsTree (v. 4, since v. 5 is still not fully functional):

1. Make sure the tree sample for reading is in Newick format, including branch-length information. The trees can be in a single file or multiple files.
2. Start SplitsTree.
3. To read in the tree sample:
   • File > Open, if your trees are in one file;
   • File > Tools > Load multiple trees, if your files (eg. minus-1 MPTs) are in different files.
4. Go to Networks > SuperNetwork. Choose "Min" for "Edge Weight" in the pop-up analysis window for the first graph. You can also try out "Mean"/"Sum" (short, rare alternatives will be less prominent), "AverageRelative" (trade-off) or "None" (branch-lengths in the minus-one tree sample are ignored). When using simple tree samples (little topological variation, matrix with fairly stringent signals), a single run (default) suffices. Increasing the number (eg. to 100) ensures no branching pattern in the minus-one tree sample gets lost. For instance, for the Felsenstein Zone matrix, a single run will give you a SuperNetwork capturing the major conflicting aspects, while 100 runs will lead to a higher dimensional graph that includes the correct BD and AC clades as alternatives. If you like to view the overall best-fitting tree instead of a network, tick "SuperTree".

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Cited papers

Hartman​ S, Mortimer M, Wahl WR, Lomax DR, Lippincott J, Lovelace DM (2019) A new paravian dinosaur from the Late Jurassic of North America supports a late acquisition of avian flight. PeerJ 7: e7247.

Huson DH, Dezulian T, Kloepper T, Steel MA (2004) Phylogenetic super-networks from partial trees. IEEE/ACM Transactions on Computational Biology and Bioinformatics 1: 151–158.


Wiens JJ (2005) Can incomplete taxa rescue phylogenetic analyses from long-branch attraction? Systematic Biology 54: 731–742.