Ockham's Razor applied, but not used: can we do DNA-scaffolding with seven characters?

One of the most interesting research areas in organismal science is the cross-road between palaeontology and neontology, which puts together a picture marrying the fossil record with molecular-based phylogenies. Unfortunately, when it comes to plant (palaeo-)phylogenetics, some people adhere to outdated analysis frameworks (sometimes with little data).

How to place a fossil?

The fossil record is crucial for neontology as it can provide age constraints (minimum ages when doing node dating) and inform us about the past distribution of a lineage. This, especially in the case of plants that can't run away from unfortunate habitat changes, can be much different than today.

The main question in this context is whether a fossil represents the stem, ie. a precursor or extinct ancient sister lineage, or the crown group, ie. a modern-day taxon (primarily modern-day genus). For instance, the oldest crown fossil gives the best-possible minimum age for the stem (root) age of a modern lineage, whereas a stem fossil can give (at best) only a rough estimate for the crown age of the next-larger taxon/clade when doing the common node dating of molecular trees (note that fossilized birth-death dating can make use of both).

There are two commonly accepted criteria to identify a crown-group fossil:

1. Apomorphy-based argues that if a fossil shows a uniquely derived character (ie. a aut- or synapomorphy sensu Hennig) or character suite diagnostic for a modern-day genus, it represents a crown-group fossil.
2. Phylogeny-based aims to place the fossil in a phylogenetic framework, the position of the fossil in the genus- or species-level tree (most commonly done) or network (rarely done but producing much less biased or flawed results) then informs what it is.

(We will focus on members of modern-day genera, since it becomes more trickier for higher-level taxa, see eg. my posts thinking about What is an angiosperm? [part1][part2][why I pondered about it].)

There a three basic options to place a fossil using a phylogenetic tree.

1. Putting up a morphological matrix, then inferring the tree. A classic but due to the nature of most morphological data sets leading to a partly wrong tree as we demonstrated in some posts here on the Genealogical World of Phylogenetic Networks (hence, such analysis should always be done in a network-based exploratory data analysis framework).
2. Putting up a mixed molecular-morphological matrix, then inferring a "total evidence" tree. This includes sophisticated approaches that use the molecular data to implement weights on the morphological traits and/or consider the age of the fossils (so-called total evidence dating approaches). Works not that bad with animal-data, provided the matrix includes a lot of morphological traits reflecting aspects of the (molecular-based) phylogeny. Doesn't work too well for plants because we usually have much fewer scorable traits, most of which are evolved convergently or in parallel. Non-trivial plant fossils love to act as rogues during phylogenetic inference.
3. Optimise the position of a fossil in a molecular-based tree, eg. using so-called "DNA scaffold approach" (usually using parsimony as optimality criterion) or the evolutionary placement algorithm implemented in RAxML (using maximum likelihood). A special form of this approach is to first map the traits on a (dated) molecular tree, and then find the position where a fossil would fit best.

Why (standard) phylogenetic tree-based approaches are tricky

Below a simple example, including three fossils of different age (and often, place) with different character suites.

Even though none of the derived traits (blue and red "1") is a synapomorphy (fide Hennig), we can assign the youngest fossil X to the lineage of genus 1A just based just based on its unique derived ('apomorphic') character suite. Its likely a crown-group fossil of clade 1, and may inform a minimum age for the most-recent common ancestor (MRCA) of the two modern-day genera of Clade 1.
Apomorphy-wise, fossils Y and Z cannot be unambiguously placed. The red trait appears to be independently obtained in both clades, and the blue trait may have been

• a synapomorphy of the whole ingroup (Clade 1+2) till some point in time, lost in the genus 2B-2C lineage, ie. a symplesiomorphy sensu Hennig, or
• a parallelism / homoiology (see also Has homoiology been neglected in phylogenetics?)

To discern between the options, we'd be well-advised to do character mapping in a probabilistic framework which require a tree with independently defined branch-lengths.

Just by using parsimony-based DNA-scaffolding, fossil X would be confirmed as crown-group fossil and member of genus 1A (being identical and different from all others) and fossil Z would end up as a stem-group fossil. Fossil Y, however, would be placed as sister to genus 2C (again, identical to each other and different from all others). Using Y in node dating, would then lead to a much too old divergence age for the crown-group age of Clade 2. In reality, what researchers do with such a seemingly too old fossil is not to use it by the book, as MRCA of Genus 2B and 2C, but to inform the MRCA of eg. genera 2A, 2B, and 2C assuming that the fossil's age and trait set indicate the 2C morphology is primitive within the clade or Y is an extinct sister lineage and the shared derived trait a convergence (parallelism).

Four characters, three homoplastic and one invariant, are surely not enough for DNA-scaffolding, but adding more and more characters has a catch. Easy to do for the modern-day taxa, for which we also have molecular data, the preservation of fossils limits adding many more traits; any trait not preserved in the fossil is effectively useless when placing it (including not-preserved traits in total evidence approach may, nonetheless, help the analysis). Which brings us to the real-world example just published in Science:

Wilf P, Nixon KC, Gandolfo MA, Cúneo RA (2019). Eocene Fagaceae from Patagonia and Gondwanan legacy in Asian rainforests. Science 364, 972. Full-text article at Science website.

Why one should not place a fossil using DNA-scaffolding with seven characters

Wilf et al. show (another) spectacularly preserved fossil from the Eocene of Patagonia. Personally, I think that just publishing and shortly describing such a beautiful fossil should be enough to get into the leading biological journals.

But Wilf et al. wanted (needed?) more and came up with the following "phylogenetic analysis" to argue that their fossil is a crown-group Castanoideae, a representative of the modern-day firmly Southeast Asian tropical-subtropical genus Castanopsis, and evidence for a "southern route to Asia hypothesis" (via Antarctica and Australia, both well-studied but devoid so far of any Fagaceae presence; despite the fact that the modern-day climate allows cultivating them as eg. source for commercially used wood).

Wilf et al's Fig. 3 and Table 1 suggest to me that the paper was not critically reviewed by anyone familiar with the molecular genetics of Fagaceae or phylogenetic methods in general — perhaps this is not needed, since the first author is well-merited and the second author a world-leading expert of botanical palaeo-cladistics. However, parsimony-based DNA-scaffolding can be tricky, even with a larger set of characters (see eg. the post on Juglandaceae using a well-done matrix), and using seven is therefore quite bold. Notably, of the seven characters, one is parsimony-uninformative and four are variable within at least one of the included OTUs.

Side note: The tree used as a backbone is outdated and not comprehensive. Plastid and nuclear-molecular data indicate that the castanoids Lithocarpus (mostly tropical SE Asia) and Chrysolepis (temperate N. America) may be sisters. However, the morphologically quite similar Notholithocarpus is not related to either of these, but is instead a close relative of the ubiquitous oaks, genus Quercus (not included in Wilf et al.'s backbone tree), especially subgenus Quercus. Furthermore, the (today Eurasian) castanoid sisterpair Castanea (temperate)-Castanopsis (tropical-subtropical) have stronger affinities to the (today and in the past) Eurasian oaks of subgenus Cerris. The Fagaceae also include three distinct monotypic relict genera, the "trigonobalanoids" Formanodendron and Trigonobalanus, SE Asia, and Colombobalanus from Columbia, South America. Using a more up-to-date instead of a 2-decade-old molecular hypothesis would have been a fair request during review, as would compiling a new molecular matrix to infer a tree used as backbone (currently gene banks include > 238,000 nucleotide DNA accessions including complete plastomes). This would have also enabled the authors to map their traits using a probabilistic framework, which can protect to some degree against homoplastic bias but requires a backbone tree with defined branch-lengths.

There are many more problems with the paper and its conclusions, but this critique would be content- not network-related. Let's just look at the data and see why Wilf et al. would have better off not showing any phylogenetic analysis at all (and the impact-driven editors and positive-meaning reviewers should have advised against it). Or a network.

Clades with little character support

The scaffolding placed the Eocene fossil in a clade with both representatives of Castanopsis, from which it differs by 0–2 and 1–4 traits, respectively. Phylogeny-based, the fossil is a stem- or crown-Castanopsis.

However, the fossil has a character suite that differs in just a single trait (#6: valve deshiscence) from the (genetically very distant) sister taxon of all other Fagaceae, Fagus (the beech), used here as the outgroup to root the Castanoideae subtree. As far as apomorphies are concerned, the data are inconclusive as to whether the fossil represents a stem-Castanoideae (or extinct Fagaceae lineage) or a Castanopsis — this critical, potentially diagnostic derived trait, partial valve dehiscence, is only shared by the fossil and some but not all modern-day Castanopsis. This particular trait is not mentioned elsewhere in the text, although it is the reason the fossil is placed next to Castanopsis and not the outgroup Fagus in the "phylogenetic analysis".

In the following figure, I have mapped (with parsimony) the putative character mutations on the tree used by Wilf et al.

Black font: shared by Fagus (outgroup) and "Castanoideae". Green font: potential uniquely derived traits. Blue font: traits reconstructed as having evolved in parallel/convergently. Red branches, clades in the used backbone tree that are at odds with currently available molecular data (the N. American relict Notholithocarpus should be sister to the Eurasian Castanea-Castanopsis).

This hardly presents a strong case of crown-group assignation. Except for partial dehiscence, even the modern-day Castanopsis have little discriminating derived traits — they are living fossils with a primitive ('plesiomorphic') character suite. Intriguingly, they are also genetically less derived than other Castanoideae and the oaks (see eg. the ITS tree in Denk & Grimm 2010).

The actual differentiation pattern

The best way to depict what the character set provides as information for placing the fossil is, of course, the Neighbor-net, as shown next.

Neighbor-net based on Wilf et al.'s seven scored morphological traits used to place the fossil. Green: the current molecular-based phylogenetic synopsis — based mostly on Oh & Manos 2008; Manos et al. 2008; Denk & Grimm 2010. I had the opportunity to get familiar with all of the then-available genetic data when harvesting all Fagaceae data from gene banks in 2012 for a talk in Bordeaux. One complication in getting an all-Fagaceae-tree is that plastids, geographically constrained, and nuclear regions tell partly different stories.

Castanopsis, including the fossil, is morphologically a paraphyletic (see also our other posts dealing with paraphyla represented as clades in trees). Note also the long edge-bundle separating the temperate Chrysolepis and chestnuts (Castanea), from their respective cold-intolerant sister genera (Lithocarpus viz Castanopsis) — derived traits have been accumulated in parallel within the "Castanoideae". The scored aspects of Fagaceae morphology are very flexible and ~50 million years is a long time, possibly leading to partial valve indehiscence (or losing it) without being part of the same generic lineage. The puzzling differentiation, and the profoundly primitive appearance of the fossil (shared with modern-day Castanopsis), may in fact be the reason the authors didn't: (i) optimize / discuss very similar, co-eval fossils from the Northern Hemisphere interpreted (and cited) as extinct genera (eg. Crepet & Nixon 1989), (ii) left out the two Fagaceae genera today occurring in South America, (iii) opted for classic parsimony and a partly outdated molecular hypothesis, and (iv) just showed a naked cladogram without branch support values as the result of their "phylogenetic analysis" (Please stop using cladograms!)

Based on the scored characters, the position of the fossil in the graph, and on the background of a more up-to-date molecular-based phylogenetic synopsis (the green tree in the figure above), the most parsimonious interpretation (and probably, the most likely) is that the fossil may indeed be a stem-Castanoideae, a representative of the lineage from which the Laurasian oaks evolved at least 55 million yrs ago (oldest Quercus fossil was found in SE Asia), or even represent a morphologically primitive, extinct (South) American lineage of the Fagaceae. Regarding the "southern route", Ockham's Razor would favor that they are just a South American extension of the widespread Eocene Laurasian Fagaceae / Castanoideae, since very similar fossils and castaneoid pollen is found in equally old and older sites in North America, Greenland (papers cited by Wilf et al.) and Eurasia but not Australia, New Zealand or Antarctica.

A final note: when you have so few characters to compare, you should use OTUs that are not completely ambiguous in every potentially discriminating character, as scored for the "C. fissa group" — the "Castanopsis group" has a single unambiguously defined, potentially derived trait. Using artificial bulk taxa is generally a bad idea when mapping trait evolution onto a molecular backbone tree. Instead, you should compile a representative placeholder taxa set, with as many taxa as you need (or are feasible) to represent all character combinations seen in the modern species/genera.

Other cited references, with comments

Crepet WL, Nixon KC (1989) Earliest megafossil evidence of Fagaceae: phylogenetic and biogeographic implications. American Journal of Botany 76: 842–855. – introducing a Castanopsis-like infructescence interpreted to represent an extinct genus but very similar to the new Patagonian fossil in its preserved features; and co-occuring with castaneoid pollen (not reported so far for Patagonia) and foliage.
 
Denk T, Grimm GW (2010) The oaks of western Eurasia: traditional classifications and evidence from two nuclear markers. Taxon 59: 351–366. — includes an all-"Quercaceae" ITS-tree (fig. 3) and -network (fig. 4) using data of ~ 1000 ITS accessions; the nuclear-encoded ITS is so far the only comprehensively sampled gene region that gets the genera and main intra-generic lineages apart (recently confirmed and refined by NGS phylogenomic data), something wide-sampled plastid barcodes struggle with. Analysed with up-to-date methods and avoiding long-branch interference by excluding the only partially alignable Fagus, Castanopsis dissolves into a grade in the all-accessions tree and Quercus is deeply nested within the Castanoideae (as already seen in the 2001 tree used by Wilf et al. as backbone). The species-level PBC neighbor-net prefers a ciruclar arrangement in which Notholithocarpus remains a putative sister of substantially divergent and diversified Quercus, followed by Castanea-Castanopsis, and Lithocarpus, while Chrysolepis is recognized as unique.

Oh S-H, Manos PS (2008) Molecular phylogenetics and cupule evolution in Fagaceae as inferred from nuclear CRABS CLAW sequences. Taxon 57: 434–451. – Probably still the best Fagaceae tree, and surely not a bad basis for probabilistic mapping of morphological traits in the family.

Manos PS, Cannon CH, Oh S-H (2008) Phylogenetic relationships and taxonomic status of the paleoendemic Fagaceae of Western North America: recognition of a new genus, Notholithocarpus. Madroño 55: 181–190. – the tree failed to resolve the monophyly of the largest genus, the oaks, but depicts well the data reality when combining ITS with plastid data and, hence, provides a good trade-off guide tree.

Has homoiology been neglected in phylogenetics?

In a recently published pre-print on PaleorXiv, Roland Sookias makes a point for distinguishing between parallelism, ie. shared inherited traits that can be found in some but not all of the offspring of a common ancestor, and convergences in a strict sense, involving similar traits that are not homologous. The former is also known as homoiology, a term Sookias attributes to Ludwig Plate.

As a geneticist working mostly at the tips of the Tree of Plant Life, I'm quite familiar with the (pre-Hennigian) concept: we much more often than not lack Hennig's 'synapomorphies', ie. shared, derived traits exclusive to an evolutionary lineage. But we have many highly diagnostic characters suites including 'shared apomorphies' (I think that the angiosperm phylogeneticist Jim Doyle coined the term) that collect the same species or higher taxa, eg. groups of taxa that also form highly supported clades in molecular trees, but are not exclusive. In every plant group you can additionally observe that certain traits are exclusive to some members of one lineage, because the lineage has the genetic-physiological prerequisites to express these traits, while their sister lineages or distant relatives lack this potential. Epigenetics deals with tendencies to express a trait in response to the environment without even changing the genetic code.

If you look close enough, you can find such patterns even at the molecular level.

Molecular evolution of the 5' half of the ITS1 in beeches. Each sequence motif is assigned a state (Ax, Bx etc; x = 0 represents the ancestral state, x > 0 are derived states) and evolution involves usually the gain ("+") or loss ("-") of sequence motifs including some potential genetic homoiologies (see here for context and references).

However, it has apparently been ignored by my fellow paleontologists: Sookias' wants to discuss "the neglected concept of homoiology ... in the context of palaeontological phylogenetic methods". Paleontological phylogenetic methods are, of course, tree inferences, and the idea is that recognition of homoiologies can be a means of establishing node support or to "help to choose between equally parsimonious or likely trees". He provides an R function "to calculate two measures for a given tree and matrix: (a) the potential support for clades based on potential homoiologies; and (b) the fit of the tree to all states given the concept of homoiology".

Sookias provides a nice and conscise introduction to the problem with some examples, and makes the connection to linguistics (see also Mattis' and my post on the Chinese dialects continuum: How languages lose body parts); so, give the short paper a read. Like all paleontological literature it is strongly influenced by cladistic views, such as that life is monophyletic, and it revolves around the central theme how to get better supported trees.

My inner geneticist has a principal problem with such a goal, because there has (to my knowledge) not been a single morphology-based tree that was fully congruent to a molecular tree with sufficient taxon and gene sampling, which applies also to the real-world data example that Sookias chose (as we will see).

My inner paleontologists also knows that there are highly diagnostic morphs in the fossil record, but diagnostic character suites and morphs reflect as many paraphyla as monophyla. He also knows that the fossil record, provided you find the right fossil from the right time, may alter your perspective on ancestral and derived character states.

An inferred tree (see this post). Given the inferred tree (quasi-dated tree), we would assume that star shapes are primitive (a symplesiomorphy) within the Pointish lineage, and possibly 10-tipped stars; and conclude that the Tenstars are paraphyletic. Greenish is clearly ancestral (a Pointish symplesiomorphy), and bluish derived (a Polygonia synapomorphy).

If we have the full picture, we can confirm star shapes are symplesiomorphic within the Pointish (the first common ancestor being a five-pointed colorless star). However, all greenish stars form a monophylum not a paraphylum.
Having ten tips is a synapomorphy of the monophyletic Tenstars.

So, why should we aim to get more resolved, better supported, morphology-based trees? Any such tree will inevitably include wrong branches!

I argue that, instead, we should just explore the signal in our data matrices using networks. Any potential tree is included in a network. But networks are more comprehensive because they provide not only a single tree but alternative, competing trees. By visualizing the alternatives, we can discern between mere convergence (random similarity), homoiology (parallelism, convergence related to descent), symplesiomorphy (shared, lineage-consistent primitive traits) and synapomorphy (lineage-unique and consistent shared derived traits), which can be very tricky with just a tree. Thus, we can try to evaluate which evolutionary scenario best explains all our data.

Compatibility

The basic problem when using morphological and such-like data sets to infer phylogenies is that most of the scored characters are, to some degree, incompatible with the true tree, ie. the actual evolutionary pathways.

Let's take a hypothetical evolution (no reticulations), in which the x-axis represents the morphological diversification and the y-axis time.

As in real-world data, sister taxa (eg. Species A and B) may have different levels of morphological derivation compared to their common ancestor(s). This leads us to this unrooted true tree in which the branch lengths are proportional to the real (above) amount of change.

Unrooted representation of the above evolution.
All commonly used tree inferences infer unrooted trees.

The only characters providing a taxon bipartition that is fully compatible with the true tree are Hennig's 'synapomorphies':

Clade A–D shares a unique, derived trait.
The character split is fully compatible with the true tree.

Next come Hennig's 'symplesiomorphies' (Sookias' R-script discards them):

Blue is the ancestral state within the ingroup, lost/modified in Species A.
The character split is compatible with the true tree except for A.
In phylogenetic inference, symplesiomorphies will usually stabilize the topology
as there will be enough other characters supporting A as sister of B and Clade A–D(–F).

Homoiologies / parallelisms can be partly compatible:

Blue is a homoiology found in 50% of the species composing Clade A–F.
The character split supports the sister relationship of A and B (compatible aspect)
but joins them with F (incompatible aspect).
A, B and F belong to the same monophylum/clade (semi-compatible aspect).
As long as homoiologies are confined to otherwise
coherent (or flat) subtrees, they will contribute to the overall decision capacity of the data.

Note that without a molecular backbone tree, it may be impossible to distinguish homoiologies from symplesiomorphies – whether a trait will be resolved as either the one or the other in a tree depends solely on its frequency and distribution across the subtree, and the situation in outgroups.

Purple is the plesiomorphy of the ingroup, blue the homoiology
found in members of Clade A–F, evolved twice

Considering the phylogenetic root-tip distances in the true tree, it makes sense that blue is the plesiomorphy of the ingroup retained in the shorter branching members, and purple a homoiology found in the most derived sublineages (again, evolved twice).

Both scenarios require three steps, but probabilistic character mapping methods would prefer the second scenario as they assume the longer the internal branches, the higher the likelihood for a change. To dismiss symplesiomorphies, Sookias' script infers the ancestral state of the MRCA of a clade and only considers states as homoiologies that differ from the inferred ancestral state (the cut-off value can be modified to "less stringently exclude potential symplesiomorphies as homoiologies").
 
Doyle's 'shared apomorphies' are locally compatible:

Blue is a shared apomorphy of the GH lineage, convergently evolved in the
outgroup (see original tree above: the GH lineage is a strongly derived
ingroup lineage evolving into the direction of the outgroup
in contrast to the remainder of the ingroup).

The example above also illustrates how shared apomorphies may trigger branching artifacts such as ingroup-outgroup long-branch attraction. Imagine that GH is not the first diverging branch of the ingroup but instead a strongly derived sublineage nested within Clade A–F, and that we lack the short-branching sister-group but have a large outgroup sample. Any ingroup-outgroup shared apomorphies will then draw GH towards the outgroup-defined ingroup's root and detrimental for inferring the true tree.

Convergence in a strict sense, ie. superficial or random similarity, is incompatible with the true tree:

Blue is a randomly distributed derived state found in all longer-branched taxa.

A tree-incompatible signal is, naturally, best handled using a network and not by forcing it into a single tree. Unless, of course, we have a sensible molecular tree and can go for total evidence approaches assuming the molecular tree reflects the true tree.

PS: Also, in molecular data the true tree incompatible characters may outnumber the compatible ones, but there we have many more characters and (usually but not always) a lot that are not filtered by negative or positive selection. Our stochastic molecular models are for sure never accurate enough to model molecular evolution for our sequences, but apparently precise enough for most applications. Even before next generation sequencing and big data, molecular phylogenies outshined morphological phylogenies, something that paleontologists cannot afford to ignore any more — not because the data are much better (to infer evolution) but because the patterns and processes are much less complex.

Sookias' data example, crocodiles and relatives

The supplement of Sookias' paper includes a morphological character matrix for crocodilians and the resulting molecular tree for the group. Here's Sookias' fig. 3 ,using these data to make his point for how to select the better-fitting tree using homoiology recognition:

Now, the unsolved problem is: if we don't have a molecular tree, how can we possibly know 0 is a homoiology and not a symplesiomorphy, 1 not a reversal (scenario B) or likely convergence (scenario C), hence, B should be preferred over C (the legend has a little typo, cf. Sookias 2019, p. 3, l. 34)?

The matrix provided as the example is not the best one to make this point. Sookias' script, when stringently eliminating potential symplesiomorphies, identifies, using the molecular tree as input, one potential homoiology for the Crocodylinae, five for their larger clade (including Gavialis and Tomistoma), and one for the alligators' larger clade in a matrix with 117 characters. Less than 10% can hardly be a game-changer.

What the morpho-data shows

Furthermore, the morphological matrix will give us a single most-parsimonious tree (MPT, using PAUP*'s Branch-and-Bound algorithm), not two or more equally parsimonious alternatives that we need to weigh against each other.

The single most-parsimonious tree that can be inferred from the morpho-matrix (236 steps, CI = 0.64, RI = 0.84). Red branches are conflicting with the topology of the molecular (truer?) tree (green brackets).

Some of the red branches are supported by pseudo-synapmorphies, which, on the background of the molecular tree, are potential homoiologies for the comprising clade, however, interpreted as symplesiomorphies by Sookias' script (provided the molecular branch-lengths are sufficient, they might be recognized when using a probabilistic framework to infer the ancestral states).

Not a good example for Sookias goal, but the matrix shows the limitations of trees when it comes to morphological differentiation. Here's the distance-based, 2-dimensional network for the morphological data:

A Neigbor-net based on Sookias' morphological matrix.
The arrow indicates the position of the assumed root.

The signal from the morphological matrix is quite tree-like, and the structure of the left part of the network is synonymous to that of the single MPT (and the molecular tree). On the right-hand side, we find more complexity than we would expect from the single MPT. The data signal is not trivial regarding the position of the root as inferred by Bernissartia; and nor is the placement of Gavialis and Tomistoma (pink edge bundles), two genera producing a very prominent box-like structure. Called by cladists a "phenetic" approach, the distance-based network is nonetheless straightforward regarding the identification of monophyletic groups (green) and potential monophyletic groups (yellow) (the latter always include the particular alternative seen in the single MPT as well, in case of the pink box, also the molecular alternative). The light green monophylum is a necessary consequence of the prior knowledge about the position of the root, and the likely monophyly of Alligator and its relatives (the tree-like subgraph with long internal branches = lots of uniquely shared traits, including potential synapmorphies).

Potential synapomorphies that can be inferred from the morpho-matrix alone by mapping the states onto the network. Red, homoiologies reconstructed as synapomorphies ('pseudo-synapomorphies') and (except for one) excluded as potential symplesiomorphies by Sookias' test run of his script (strict and relaxed cut-off).

The network provides more information than can be extracted from the MPT: one Crocodylus is significantly closer to the Osteolaemus (the neighborhood defined by the light blue edge bundle, see Sookias' fig. 3A). Crocodylus, however, is likely monophyletic, being generally very similar; and the third genus, Mecitops, is closely linked to (all of) them (neighbourhood defined by the dark blue edge). An inclusive common origin (including the third genus, Mecistops) is – just based on morphology and without using a "phylogenetic" tree inference – beyond question, even though we lack syn- or shared apomorphies (short corresponding edge bundle): Mecistops is obviously closely related to Crocodylus, and Osteolaemus is related to part of the latter, so it's not a bad hypothesis that all three are descendants of the same common ancestor, and that Tomistoma (and Gavialis) branched off the lineage before the Crocodylinae radiated. The only alternative explanation would be that the Crocodylinae show the primitive morphs of the entire lineage, and that the position of Tomistoma and Gavialis is affected by long-branch (-edge) attraction (however, if that is the case then we should have found a Tomistoma-Gavialis clade in the MPT — parsimony will always get it wrong in the Felsenstein zone)

The main flaw

But, any morphology-based alternative using this data matrix is not fully compatible with the molecular tree, which places Mecitops and Osteolaemus as sister to Crocodylus. Here's the consensus network based on 10,000 boostrap pseudoreplicate BioNJ trees inferred from the morpho-matrix, highlighting the support for splits compatible with the molecular tree (green) and their competing, partly incongruent (red edge bundles) alternatives (I do the information transfer manually, but those with R-scripting skills can use the functions in the phangorn library; Schliep et al., MEE, 2017; see also David's post):

NJ-Bootstrap (BS) consensus network based on 10,000 pseudoreplicates.
Edges/splits corresponding to clades in the molecular tree
(see Sookias' fig. 3 above) in green, those conflicting the molecular tree in red.
Edge values show BS support (edge-lengths are proportional to NJ-BS support),
while asterisks indicate the branches seen in the MPT.

Obviously, there is some signal in the morpho-matrix compatible with the molecular clades (this can be synaporphies, symplesiomorphies, homoiologies or shared apomorphies) clashing with the signal of pseudo-synapomorphies etc. supporting the topological alternatives seen in the morpho-based MPT.

Assuming the molecular tree is correct, the above reconstruction means that Osteolaemus is morphologically more derived, and hence placed as sister, while Mecitops and Crocodylus retain more primitive character states, and hence lacks discriminatiory derived traits — a sort of local ingroup-outgroup long-branch attraction (or 'short-branch culling').

What differentiates the Crocodylinae? Black, aut- or synapomorphies; blue, potential homoiologies (or symplesiomorphies); red, shared apomorphies (convergence). The Mecitops-Crocodylus pseudo-monophylum is mostly supported by traits shared between Osteolaemus and distant siblings (taxa of the larger alligator clade) and/or the outgroup.

We can also hypothesize that the initial radiation was fast, because the Mecitops-Osteolaemus ancestor did not accumulate a single, unique, discriminating character trait.

Excess of shared derived, pseudo-synapomorphic traits is the reason Tomistoma is not resolved as sister of Gavialis in the MPT — the molecular Gavialis-Tomistoma clade is represented by a morphological grade.

A 'splits rose' showing the basic splits. Black, aut- or synapomorphies; blue, potential homoiologies (or symplesiomorphies of the larger clade including Crocodylinae); pink, pseudo-synapomorphies (deep homoiologies or symplesiomorphies of the larger Crocodylinae clade); orange, shared ancestral (plesiomorph) or derived traits (convergent). 

And the homoiologies identified using the molecular tree as input cannot put things right. They are just partly compatible with unproblematic splits, ie. the larger clade including Alligator (character #7), the larger clade including Crocodylinae (#1, #18, #73, #74, #117) or exclusive to the Crocodylinae (#66)

Character mapping of the molecular-inferred homoiologies. The lush green splits represent the molecular splits.

However, if we are ignorant of the molecular tree, we would have to assume that Mecitops is the sister to Crocodylus, and that some of their shared traits not found in Osteolaemus are shared apomorphies (if occurring outside the clade and in the sister clade) or even synapomorphies (if exclusive for Mecitops + Crocodylus), while only those shared by Osteolaemus and C. porosus (#66) can be homoiologies. We also would have no reason to challenge the Gavialis-Tomistoma grade, until we infer networks.

Map of all potential synapomorphies (bold), symplesiomorphies (italics) and homoiologies (plain font) using the morphology-based Neighbor-net as basis. Red, pseudo-synapomorphies: split seen in the MPT and (with or without alternative in the Neighbor-net) but rejected by the molecular tree.

This is the main flaw of Sookias' idea. To identify homoiologies, we need the same prerequisite as for any of Hennig's concepts: we need to know the true tree. If we use the inferred tree based on the same data that we want to weight (here: use homoiologies for decision making or means of node support), then we propagate first-level errors; apply circular reasoning. Such as the red-marked pseudo-synapomorphies in the network above; vice versa, all actual (molecular-wise) synapomorphies supporting the molecular Gavialis-Tomistoma clade (dark purple split) would be reconstructed as homoiologies or symplesiomorphies based on the morpho-based single MPT (or morpho-based NJ tree, or probabilistic tree).

And if we have an independent molecular tree, it will make the decision on the fly: putative synapormorphies are the traits that are fully compatible, symplesiomorphies, homoiologies and shared apomorphies are decreasingly compatible, and random convergences are incompatible with the molecular tree.

It is not homoiology but tree-incompatible signal that is neglected in phylogenetics

Sookias points out: "In inference of phylogeny by parsimony, an occurrence of a character state in a part of a tree separated from it by another state is considered simply a homoplasy, and a tree where the occurrences are nearer or further from one another is not more or less parsimonious ... a tree where the 15 occurrences are nearer or further from one another is not more or less parsimonious". In principle, this is true, but has little consequence in application.

We, usually without realizing it, make frequent use of the discriminating power of potential homoiologies. See the example above, but also when, eg., placing fossils in a molecular framework or do post-inference character weighting. In these cases, homoiologies (and symplesiomorphies) will stabilize the inference and increase support. For better and worse:

• Better, because homoiologies will ensure that the fossil is placed in the right molecular-based subtree, and can compensate for the lack of synapomorphies. Imagine an extinct fossil sibling lineage showing only homoiologies shared by Osteolaemus and C. porosus. Using tree-based optimization (eg. RAxML's 'evolutionary placement algorithm'), it would be placed close to the Crocodylinae ancestor, likely next to Osteolaemus. Using a Neighbor-net, it would be placed between Osteolaemus and C. porosus. Either way, the homoiologies would ensure it is nested within the Crocodylinae.
• Post-inference character weighting, as implemented in eg. TNT, will downweight inferred convergences (ie. higher homoplasy, more stochastically distributed across the tree) more than putative homoiologies (ie. less homoplastic since confined to a single subtree). This can be better or worse. How do we avoid what happened for the crocodiles that homoiologies are not recognized as such but support (somewhat) misleading clades (act as synapomorphies)? Clades are commonly interpreted as a sufficient criterion to determine monophyly; however, they are not even a necessary one: taxa can be part of a monophyletic group despite not forming an inclusive subtree (ie. clade in a rooted tree) such as the genus Caiman or Gavialia-Tomistoma.

Hence, we should disencourage any form of data-self-dependent or post-analysis weighting and instead just explore the signal in our data — using networks.

One thing is also obvious from the crocodile example: if we have enough signal in the morphological data, then we may get one or another thing wrong and, in some cases, may not be able to decide between one or another alternative. However, overall, the morphological differentiation pretty well captures what the genes provide us as the best approximation of the true tree. Even when the matrix includes very few potential synapomorphies and clear homoiologies but a lot of shared apomorphies, most of which were convergently evolved in parts of both major clades.

At least, this will be so when we analyze the data using networks and not just trees (compare the single MPT to the networks).

Using the alternative evolutionary scenarios provided by the networks, we can then look back into our data (see the maps above), to see what may be a homoiology, a symplesiomorphy (very useful for deciding between evolutionary scenarios, as well) or a synapomorphy. The phangorn library (used for Sookias' script) has now network functionality and allows transferring information between trees and networks. An R-affine person may be able to extract lists of potential (partly competing) synapomorphies, symplesiomorphies, and homoiologies directly from the network showing all possible or the most likely trees.

And then use this information to eg. place fossils in a phylogenetic context, or reconstruct evolutionary trends in extinct groups of organisms — reconstruction of evolutionary trends in extant organisms should always rely on morphological data analyzed in a molecular-phylogenetic framework.

Data

A NEXUS-version of Sookias' test matrix (slightly annotated for Mesquite, simple version for PAUP*), tree- and distance matrix files have been added to my figshare collection of morphological matrices.  

Clades, cladograms, cladistics, and why networks are inevitable

During the work for another post, I stumbled on a kind of gap-in-knowledge that has nagged me for quite some time. This gap exists because researchers like to stay within chosen philosophical viewpoints, rather than reassessing their stance.

This gap involves the use of cladistic methodology in a manner that obscures information about evolutionary history, rather than revealing it. A clade, a subtree in a rooted tree that fulfills the parsimony criterion (or, indeed, any other criterion), may or may not reflect monophyly in a Hennigian sense, i.e. inclusive common origin. This is especially true for studies of extinct lineages.

I will explore this idea here in some detail.

Assumptions when studying fossils

Phylogenetic papers dealing with the evolution of extinct groups of organisms frequently use strict consensus trees (typically cladograms) of a sample of equally parsimonious trees (MPT) as the sole or main basis for their conclusions. They do this under two important implicit assumptions:

• The morphological differentiation patterns encoded in a character matrix provide a generally treelike signal. In other words, the data patterns in the morphological matrix can be explained by a single, dichotomous, 1-dimensional graph. This assumption is also the basis for posterior filtering or down-weighting of characters that support splits (taxon bipartitions) conflicting with the branches in the inferred tree(s).
• Morphological evolution is generally parsimonious. Although this may apply for characters that evolved only once or only evolve under very rare conditions, total evidence and DNA-constrained analysis demonstrate that this is not generally the case: the tree inferred by total-evidence or molecular constraints is typically longer than the tree(s) with the fewest character changes inferred on the morphological partition alone.

Another implicit assumption seems to be that all fossil specimens must represent extinct sister clades, and that no fossil specimen is ancestral to any other (or to an extant species) — hence, all taxa can be treated as terminals (not ancestors). Rooting typically relies on outgroups, under the assumption that ingroup-outgroup branching artefacts (such as long-branch attraction) play no role for parsimony inference when using morphological data sets.

In many of these morphology-phylogenetic papers (using parsimony or other methods) the authors state that they have conduct a “cladistic” study (I also made this error in my masters thesis; Grimm 1999). Cladistics is a classification system established by Hennig (1950) that relies on synapomorphies, exclusively shared, derived traits, that are linked with groups of inclusive common origin, the so-called monophyla.

Over 90 years earlier, Haeckel (1866) used the German word monophyletisch to refer to “natural” groups defined by a shared evolutionary history (a common origin). The latter could also include what Hennig identified as paraphyla: groups that have a common origin, but are not inclusive. To avoid confusion between Haeckelian and Hennigian monophyletic groups, Ashlock (1971) suggested the term holophyletic for the latter. This can be useful when a classification should recognise evolutionary relationships but needs to classify potentially or definitely paraphyletic groups for reasons of practicality (see e.g. Bomfleur, Grimm & McLoughlin 2017). Here, I will stick to Hennig’s terminology, as it is much more commonly used (although not necessarily correctly applied).
 
Hennig’s monophyla are from a theoretical (and computational) point of view a brilliant concept, as they can be inferred using a rooted tree. The test for monophyly is simple: Do A and B have a common ancestor? If yes, identify all taxa that are part of the same subtree as A and B. Unfortunately, we often find more than one possible tree, and roots can be misleading.

Strict consensus trees poorly represent the alternative topologies in a MPT sample

All consensus-tree approaches are limited to depicting the topological alternatives in a tree sample, but strict consensus trees are probably the worst (see e.g. Felsenstein 2004, chapter 30). They also have become obsolete with the development of consensus networks (Holland & Moulton 2003), and their subsequent implementation in freely accessible software packages such as SplitsTree (Huson 1998; Huson & Bryant 2006) and, more recently, the PHANGORN library for R (Schliep 2011; Schliep et al. 2017).

Figure 1 illustrates this difference for two extreme cases of binary matrices and their MPT collections. The two datasets in Fig. 1 reflect a substantially different data situation. The data in one matrix are perfectly tree-unlike (completely “confused about relationships”): any possible non-trivial bipartition of the 5-taxon set is supported by one (parsimony-informative) character. The data in the other matrix reflect two incongruent trees: each character is compatible with either one of the trees (parsimony-informative characters) or both trees (unique characters). The non-treelike matrix allows for many more MPTs than does the tree-like matrix, which results in two MPTs perfectly matching the two conflicting true trees. But both consensus analyses result in the same, unresolved (polytomous) strict consensus tree. In contrast, the two consensus networks highlight the difference in the quality between the data sets and the MPT sample.

Fig. 1 Non-treelike and treelike data, and the representation of their most-parsimonious tree collections as strict consensus trees and networks

Another example is shown in Figure 2, which shows four trees that differ only in the placement of one taxon (T8). This is a common phenomenom, particularly when dealing with extinct groups of organisms. The three main reasons for such topological ambiguity are:

1. Indicisive data regarding the exact position of T8 with respect to the members of the red (T1–T4) and green clades (T5–T7).
2. Conflicting data, T8 shows a combination of traits that are otherwise restricted to (parts of) the green or red clade.
3. T8 is an ancestor or primitive member of the green or red clade, or both. 

Fig. 2 A single rogue taxon (T8) with ambiguous affinities collapses the strict consensus tree. In contrast, the conensus network can simultaenously show all alternatives, and identifies T8 as the source of topological ambiguity.

The strict consensus tree shows only three clades (three pairs of sister taxa) and a large polytomy, but the strict consensus network shows simultaneously the topology of all four trees and the position of T8 in these trees. From the consensus network, it is clear that the members of the red and green clades share a common origin. T8 can easily be identified as the rogue taxon (lineage).

Cladograms are incomplete representations of evolutionary trees

Figure 3 shows one of the first phylogenetic trees ever produced, and how it would look in the results section of a cladistic study. The tree was produced 150 years ago by Franz Martin Hilgendorf — more than 100 years before Hennig’s ideas were introduced to the Anglo-Saxon world and became mainstream. Hilgendorf was a palaeontology Ph.D. student at the same institute (in Tübingen, Germany) that also promoted me. Quenstedt, his supervisor, forced a quick promotion to get him and his heretic Darwinian ideas out of his university; there are thus no figures in Hilgendorf's thesis, and he published a phylogenetic tree only after he left Tübingen. It shows the evolution of derived forms (terminals) from putative ancestral forms (placed at the nodes) of fossils snails from the Steinheimer Becken, and clearly distinguishes ancestors and sisters. At some point, Hilgendorf even considered including the reticulation of lineages to better explain some forms, but later dropped this idea, feeling it would violate Darwin’s principle (Rasser 2006; see The dilemma of evolutionary networks and Darwinian trees).

Fig. 3 Hilgendorf's phylogenetic tree of fossil snails and its representation in form of a cladogram. The coloured fields and boxes refer to a series of nested clades, which here equal monophyletic groups.

Translating Hilgendorf’s tree into a cladogram comes with a loss of information about the evolution of the snails. Some ancestors are placed as sisters to their descendants (e.g. 18 vs. 18a and 19) and others are collected in a polytomy together with their descendants/descending lineages (e.g. 15, the ancestor of the siblings 16, 17, and the 18+). The loss of information regarding assumed ancestor-descendant relationships is dramatic. But this is no problem for cladistic classification: all clades in the cladogram in Fig. 3 (boxes) refer to Hennigian monophyletic groups seen in the original phylogenetic tree (coloured backgrounds). The polytomies in the cladogram are hard polytomies and do not reflect uncertainty or ambiguity. This contrasts with most cladograms depicted in the phylogenetic (“cladistic”) literature, where polytomies can also reflect lack of support or topological ambiguity.

Accepting the possibility that some fossils (fossil forms) may be ancestral to others (or their modern counterparts), or at least represent an ancestral, underived form, we actually should not infer plain parsimony trees but median networks (Bandelt et al. 1995). Median networks and related inferences (reduced median networks: Bandelt et al. 1995; median joining networks: Bandelt, Forster & Röhl 1999) work under the same optimality criterion (evolution is parsimonious) but allow taxa to be placed at the nodes (the “median”) of the graph. In doing so, they depict ancestor-descendant relationships. That they have not been used for morphological data so far, nor in palaeophylogenetic studies (as far as I know), may have to do with their vulnerability to homoplasy and missing data. High levels of homoplasy are common in morphological matrices, and missing data can be a problem when working with extinct organisms.

An ideal matrix, in which each divergence is followed by the accumulation of synapomorphies (or “autapomorphies”, unique traits, close to the tips), results in a median network perfectly depicting the evolutionary tree (Figure 4). As soon as convergent evolution steps in, a median network can easily become chaotic, although less so for a median-joining network. Note that half of the characters are homoplasious, and yet the median-joining network is still largely treelike (Fig. 4), with only one 2-dimensional box. The true tree is included in the network; but an E-G clade evolving from D is indicated as alternative to the correct (and monophyletic) FGH clade, with G and H evolving from F. Another deviation from the true tree is that A, the ancestor of B and C, is not placed at the node, but is closer to the all-common ancestor X.

Fig. 4 Two datasets, one without (left) and one with homoplasy (right), and their median(-joining) networks. Green branches refer to exact fits with the true tree, red indicate deviation or conflict with the true tree.

Paraphyletic clades...

Figures 5A and B show the corresponding MPT for the ideal matrix and the strict consensus tree vs. strict consensus network for the matrix affected by homoplasy. As our ideal matrix includes actual ancestors, the MPT rooted with the most primitive taxon X (the common ancestor of A–H) cannot resolve the exact relationships, in contrast to the median network. It thus represents the true tree only partly. But it also does not show any clade that is not monophyletic.

In the case of the partly homoplasious data, the median-joining network reconstructs a synapomorphy of the clade BC, because A is not placed on the node. This is because one character in our matrix is a methodologically undetectable parallelism — the same trait evolved in the sister taxa B and C, but only after both evolved from A. Clade BC is non-inclusive (paraphyletic), since A is the direct ancestor of both B and C and the clade BC lacks a real synapomorphy (if we go back to Hennig's concept). The reconstructed A would, however, be a stem taxon and clade BC would be inclusive (monophyletic) with one (inferred) synapomorphy. But this is a purely semantic problem of cladistics. In the real world, we will hardly have the data to discern whether A represents: the last common ancestor of B and C, a stem taxon of the ABC-lineage (a’), a very early precursor of B or C (b/c), or an ancient sister lineage of A, B, and/or C (a*). For practicality, one would eventually include all fossil forms with A-ish appearance in a paraphyletic taxon A (Fig. 5C), in (silent) violation of cladistic classification, to name only monophyletic groups.

Fig. 5A The median network compared to the single most-parsimonious tree inferred based on the ideal matrix

Fig. 5B The median-joining network compared to the strict consensus tree and networks of five most-parsimonious trees inferred based on the matrix with homoplasy. Red edges indicate deviations from or conflicts with the true tree.

Fig. 5C Potential monophyla that could be inferred from the median-joining network (Clades XY), when rooted with the most ancient taxon X. Groups that are monophyletic according to the true tree in blue, groups that are not in orange.

The strict consensus tree of the five MPTs that can be inferred from the homoplasious matrix shows only the paraphyletic (pseudo-monophyletic) clade BC and two monophyletic clades (ABC and D–H); and it contains no further information about the actual topology of the five MPTs. Its lack of resolution is due to the ancestors, which have typically less derived traits (no autapomorphies and fewer synapomorphies), in combination with the homoplasy-induced topological ambiguity. In contrast, the strict consensus networks reveal that all five MPTs place D, the ancestor of the D–H lineage, as (zero branch length) sister to a technically paraphyletic E–H clade, thereby identifying D as the most primitive form of the monophyletic D–H clade. Furthermore, all MPTs recognise a paraphyletic FH clade (F again a zero-length branch). They disagree in the placement of G, which is either sister to F+H (monophyletic FGH clade) or sister to E (a wrong EG clade).

... and monophyletic grades

Figure 6 shows a scenario in which paraphyletic groups are resolved as clades and monophyletic groups form grades, both because of outgroup-ingroup branching artefacts. The derived outgroup O is notably distinct from all ingroup taxa showing a character suite of convergently evolved traits that are randomly shared with parts of the ingroup. Within the ingroup, members of clade DEF are much more derived than are A and C.

Fig. 6 Ingroup-outgroup long-branch attraction can turn monophyla into grades and paraphyla into clades. The ingroup (A–F) consists of a sequence of nested monophyletic lineages (green shades) including two taxa (lowercase letters) that are ancestral to others. Each ingroup lineage evolved (convergent) traits also found in the outgroup O. The data allow inferring two MPTs that misplace O. The outgroup-misinformed root leads to a series of nested clades that a paraphyletic. Splits congruent with the actual monophyletic groups in green, those in conflict with the true tree in red.

Parsimony-tree inference finds two MPTs, which, rooted with the outgroup O, recognise a distinctly paraphyletic A–D+X clade. In both outgroup-rooted MPTs, the monophyletic DEF group is dissolved into a grade. By the way: using neighbour-joining (NJ) to find a tree fulfilling the least-squares (LS) criterion based on the corresponding pairwise mean distance matrix, the outgroup-inferred root is still misplaced with respect to the primitive taxa (X, A–C), but the DEF monophylum is correctly resolved as a clade. Call the Spanish Inquisition! A “phenetic” clustering algorithm finds a tree that is less wrong than the MPTs.

The most comprehensive display of the misleading signal in this matrix is nevertheless the neighbour-net (NNet; Figure 7), which includes both the parsimony and LS-solutions, and it can be used to map the competing support patterns surfacing in a bootstrap analysis of the data. In this network we can see that the signal is not compatible with a single tree, and that the signal from the distant outgroup O is too ambiguous for rooting the ingroup. Based on this graph, one can argue to delete the outgroup, thereby deleting all non-treelike signal — a NNet (or median network) excluding O matches exactly the true tree.

Fig. 7 Neighbour-net based on mean pairwise distances (same data in Fig. 6). The outgroup O provides a strongly ambiguous (non-treelike) signal, thus, triggering a series of splits (in red) conflicting the true tree (shown in grey). Edges compatible with the true tree shown in green. The numbers refer to non-parametric bootstrap support estimated under three optimality criteria: least-squares (LS; via neighbour-joinging), maximum likelihood (ML; using Lewis' 1-parameter Mk model), and maximum parsimony (MP) and 10,000 (pseudo)replicates each. Upper right: A splits-rose illustrating the competing support patterns for proximal splits involving O: green — split seen in the true tree, reddish — the competing splits seen in the two MPTs.

We need to accept that a clade, a subtree in a rooted tree (see e.g. Felsenstein 2004) fulfilling the parsimony criterion (or any other criterion), may or may not reflect monophyly in a Hennigian sense, i.e. inclusive common origin. Thus, it is imperative to distinguish between a classification concept that interprets trees (cladistics) and the method used to infer trees (typically parsimony, in the case of extinct lineages). This is especially so when one has to work with stand-alone data, such as morphological data of extinct groups of organisms.

Aside from the clades/grades ↔ monophyla / paraphyla / can't-say problem, the instability of clades in a parsimony or otherwise optimised rooted tree, or the alternative clades that can be inferred from the more data-comprehensive networks, make it difficult to enforce a strictly cladistic naming scheme. For the example shown in Fig. 2, we would be unable to name the red and green clades until the exact position of T8 is settled (see also Bomfleur, Grimm & McLoughlin 2017). In the end, the overall diversity patterns (studied using exploratory data analysis) may remain the most solid ground for classification.

It should also be obligatory in phylogenetic studies to use networks to display both competing topological alternatives and incompatible data patterns. There should also always be some information on edge-lengths. Consensus trees are insufficient, as they mask conflicting data patterns, and cladograms mask the amount of change.

References

Ashlock PD. (1971) Monophyly and associated terms. Systematic Zoology 20:63–69.

Bandelt H-J, Forster P, Röhl A. (1999) Median-joining networks for inferring intraspecific phylogenies. Molecular Biology and Evolution 16:37-48.

Bandelt H-J, Forster P, Sykes BC, Richards MB. (1995) Mitochondrial portraits of human populations using median networks. Genetics 141:743-753.

Bomfleur B, Grimm GW, McLoughlin S. (2017) Figure 8 of: The fossil Osmundales (Royal Ferns)—a phylogenetic network analysis, revised taxonomy, and evolutionary classification of anatomically preserved trunks and rhizomes. PeerJ 5:e3433.

Felsenstein J. (2004) Inferring phylogenies. Sunderland, MA, U.S.A.: Sinauer Associates Inc.

Grimm GW. (1999) Phylogenie der Cycadales. Diploma thesis. Eberhard Karls Universität. [in German]

Haeckel E. (1866) Generelle Morphologie der Organismen. Berlin: Georg Reiner.

Hennig W. (1950) Grundzüge einer Theorie der phylogenetischen Systematik. Berlin: Dt. Zentralverlag.

Holland B, Moulton V. (2003) Consensus networks: A method for visualising incompatibilities in collections of trees. In: Benson G, and Page R, eds. Algorithms in Bioinformatics: Third International Workshop, WABI, Budapest, Hungary Proceedings. Berlin, Heidelberg, Stuttgart: Springer Verlag, p. 165–176.

Huson DH. (1998) SplitsTree: analyzing and visualizing evolutionary data. Bioinformatics 14:68–73.

Huson DH, Bryant D. (2006) Application of phylogenetic networks in evolutionary studies. Molecular Biology and Evolution 23:254–267.

Rasser MW. (2006) 140 Jahre Steinheimer Schnecken-Stammbaum: der älteste fossile Stammbaum aus heutiger Sicht. Online version, originally published in Geologica et Palaeontologica, vol. 40.

Schliep K, Potts AJ, Morrison DA, Grimm GW. (2017) Intertwining phylogenetic trees and networks. Methods in Ecology and Evolution DOI:10.1111/2041-210X.12760.

Schliep KP. (2011) Phangorn: phylogenetic analysis in R. Bioinformatics 27:592–593.