A bit of heresy: networks for matrices used in Cladistics studies

[This is Part 1 of a two-part topic – this one is Historical matrices from the 1980s]

When I first came into contact with phylogenetics (usually based on morphological data sets, back then) and after reading Hennig's book (the original German version, published in 1950), I dreamed about publishing in Cladistics, the journal of the Willi Hennig Society (WHS). I never did. In this post, I show why.

Later on, in 2016, Cladistics achieved renewed fame due to an editorial that triggered a twitter uproar under the hashtag #parsimonygate. A lot of people were shocked to read in the editorial that the journal (still) prefers and requires parsimony-based inferences (in fact, parsimony-based trees). Some people, like Joe Felsenstein, were not at all surprised. I wasn't either, because Cladistics is the journal of the Willi Hennig Society (WHS), which has always been dedicated to parsimony: "Ockham told Popper told Hennig to use parsimony" (see the historical summary by Felsenstein in Systematic Biology, 2001; free access).

Historical buttons that you (allegedly) could get at meetings of the WHS. Left: Joe Felsenstein; right: L for Likelihood. Just a gag, of course! Nothing serious behind it.

In the good old days, when the "Phylogenetic Wars" were still on (in the 1980s, petering out in the 90s), they would invite a probability-ist to their conference to tear him down. My first phylogenetic paper (2002) got a negative review (ie. rejection, invitation to resubmit) by a WHS member solely because it did not include a parsimony tree, which he described as "standard these days". More recently, they ensured free access to TNT, the current main software for doing parsimony analysis and an essential tool for many palaeontologists.

I stopped using parsimony trees very early in my career, but I'm still a great fan of the family of methods based on median networks, which operate under the same parsimony criterion (Clades, Cladograms, ...; Using Median networks ...). Fate exposed me early to the Neighbor-nets, which can be used as a quick check of how tree-like the signal is in data matrices, to start with.

The thing that bugged me most concerning many journals, including Cladistics, is not a focus on parsimony, but the lack of data documentation and easy data access. To me, it seems natural to use a service like TreeBASE, when my main dedication is to tree-inference. TreeBASE allows you to provide your data and inferred trees to the general public in the common NEXUS format, so that other people can make use of it.

Luckily, some authors of Cladistics upload their data (about one study per 1–3 years). So, here are some data-display networks showing the strengths and weaknesses of the parsimony trees in the original publications, which have been randomly selected from among the oldest ones and the newest ones (I found) in TreeBASE. I won't discuss the actual results, as Cladistics is pay-walled, so just enjoy the graphs.

The oldest one (in my list), Dahlgren & Bremer 1985, TreeBASE submission number S231

The submission (a binary matrix, including some missing data; published in the first volume of Cladistics) comes with three angiosperm trees: one composite order-level tree, plus two empirical trees labelled as "Fig. 2" and "Fig. 3" using the family-level OTUs in the matrix. The latter two look like this:

Connected cladograms of "Fig. 2" and "Fig. 3", the result of two parsimony analyses. Jumping taxa/clades highlighted with colours.

That the matrix is not only highly homoplasious (CI = 0.28) but has a severe signal problem, becomes obvious when inferring a NJ tree, providing a third topology.

A NJ tree (fulfilling least-squares optimality criterion for phylogenetic trees) from the same matrix: blue, branches incongruent among the original trees and the NJ tree. Color coding: light blue, branch congruent to "Fig. 2" tree (different in "Fig. 3" tree); green, branch found in all three trees; red, branch incongruent to consistent placement in both original trees.

Not surprisingly, the Neighbor-net inferred from simple (mean) Hamming distances is a spider-web, as the matrix' signal is not tree-like at all — all non-green branches above, or their conflicting alternatives, receive low to very low bootstrap support, independent of the optimality criterion used.

The Neighbor-net inferred from Dahlgren & Bremer's matrix.

Despite its spider-web structure, we do learn quite a lot from the Neighbor-net regarding what is behind the clades in the original trees. For example, we can overlay a Dahlgrenogram representing the top-most subtree of the "Fig. 2" tree.

Blue, red and yellow fields denote (sub)clades in Dahlgren & Bremer's "Fig. 2" tree that compose the top clade (grey).

The same could be done for all the other clades.

TreeBASE submission S329, worms (Oligochaeta) by Jamieson et al. (1987)

The more perfect is a character matrix regarding tree-inference (ie. with tree-compatible characters), the more similar the NJ and the parsimony-tree will be (or any other tree, under any other optimality criterion), as we can see in this second example published in the third volume of Cladistics.

The tree (the abstract notes a single most-parsimonious tree) was inferred from a multistate matrix with up to seven states, possibly including some characters that should be treated as ordered, but such specifics are not included in the original NEXUS file, so we will treat them as unordered.

Aside from grades becoming clades (and vice versa), the published tree (unordered: 102 steps, high CI = 0.81, RC = 0.53) and the NJ tree are quite similar, even regarding their relative branch-lengths.

Two phylograms: left, the original MPT, right, a NJ tree, shared branches in green, (partly) conflicting ones in orange. Cladists address the left tree as "phylogenetic", the right one as "phenetic", but both are equally valid solutions using different optimality criteria.

Moreover, the Neighbor-net is much less complex than in the previous examples, with individual edges corresponding to branches in both trees — Neighbor-nets are truly meta-phylogenetic graphs.

Splits found in the original MPT in green, when corresponding with edges in the Neighbour-net, and orange, when there is no corresponding edge (according to the abstract, the authors discuss alternatives to certain branches in their tree). Edges found in the NJ tree (providing an alternative topology/phylogenetic hypothesis) in blue.

Submission S349, an amniote phylogeny by Gaulthier et al. (1988)

This is a matrix much to my liking, as it includes extinct taxa, with quite impressive dimensions (computers back in 1988 were awfully slow): 316 characters with up to four states for 31 taxa. Naturally, it includes a lot of missing data, as do all fossil-including matrices.

Missing data is potentially a bigger problem for distance-based approaches than for character-based ones like parsimony, maximum likelihood or Bayesian inference — when there is little character overlap between the fossil taxa, their pairwise distances will be distorted. Missing data can be an equal problem for tree-inference — depending which characters are missing, many different topologies are equally optimal, or nearly so. In Gaulthier et al.'s matrix 10% of the characters are parsimony-uninformative.

Similar to the angiosperm matrix, Gaulthier et al.'s tree has a relatively low CI (0.45) and RC (0.33), i.e. there is homoplasy adding to the missing data as a source of incompatible, tree-unlike signals.

Just by comparing the NJ tree to the parsimony tree, we can see that distance distortion because of missing data is no big deal for this matrix.

The trees are largely congruent, with three striking exceptions: the birds (Aves), the crocodiles (Crocodylia) and turtles (Testudines) are not placed as sisters to the lineage leading to modern-day mammals (tree provided by Gaulthier et al.), but fall in the "dinosaur"-only clade in the NJ tree (compare with the current Tree of Life: Archosauria). This makes sense (data-wise), because in Gaulthier's matrix the taxon pairs Aves + Ornithosuchia and Crocodylia + Pseudosuchia are identical in their shared defined characters (ie. zero-distance pairs). Obviously, the parsimony tree comes with some implicit assumptions: the unweighted/unordered single most-parsimonious tree PAUP* infers for the matrix using the branch-and-bound algorithm has only 510 steps, a higher CI (0.66) and RC (0.59), and is largely congruent with the NJ tree; except that Captorhinidae and Testudines are sisters and Casea, Ophiacodon and Edaphosaurus form a grade not a clade.

As in the other cases so far, the Neighbor-net well captures the actual data situation.

Blue edge bundles refer to splits shared with both the NJ tree and the (inferred, not provided) MPT. Note that some splits in the NJ tree and or the MPT have no counterpart in the Neighbour-net. One split found in the MPT but not in the NJ tree has a corresponding edge in the Neighbour-net (light blue).

The thin "upper trunk" in the Neighbor-net further shows that the matrix provides a strong signal for an increase of shared derived ('mammalian') and decrease of shared ancestral ('reptilian') traits, which is a bias. Although the MPT and NJ tree agree well, the matrix provides clear tree-like signal only for terminal relationships in the other main, inferred clade. The thinning trunk may also indicate a taxon sampling issue. Well-sampled phylogenetic data sets usually result in more star-like networks (see eg. graphs in this post on fossil and extant walnuts, dinosaurs, spermatophytes, or the above ones and the next one) in contrast to non-phylogenetic data sets (see eg. the posts on breast sizes, airlines, or moons)


Take-home message in the middle of the film

Even though they are arbitrary choices, the three matrices above show what phylogeneticists had to work with in the 1980s morphological datasets:

• ... trapped in homoplasy (Dahlgren & Bremer, 1985) — datasets in which phylogenetic relationships were obscured behind highly ambiguous, non-treelike signal;
• ... asking for a model (Jamieson et al., 1987) — datasets with partly consistent signal, but not consistent enough to result in the same tree independent of the optimality criterion;
• ... encoding a tree (Gaulthier et al., 1988) — datasets tweaked to promote a certain evolutionary hypothesis, including (superficially) simple series of gradual evolution and ancestor-descendant pairs (see Trivial data, not so trivial graphs). Such data will result in a single optimal tree (method independent!) dominanted by staircase-like subtrees. This may be fine for a cladist, but nothing a phylogeneticist / evolutionary biologist could really be content with (not in the 1980s, or before 1950).

Top, two phylogenetic tress sketched by Darwin; bottom, Hilgendorf's (1866) phylogenetic tree. There are quite a few before 1950 (eg. Pojárkova, 1933, Acta Institute of Botany, Academy of Sciences of the USSR, ser. 1, 1: 225–374; unfortunately have no copy/scan)

The curious case(s) of tree-like matrices with no synapomorphies

(This is a joint post by Guido Grimm and David Morrison)

Phylogenetic data matrices can have odd patterns in them, which presumably represent phylogenetic signals of some sort. This seems to apply particularly to morphological matrices. In this post, we will show examples of matrices that are packed with homoplasious characters, and thus lead to trees with a low Consistency Index (CI), but which nevertheless have high tree-likeness, as measured by a high Retention Index (RI) and a low matrix Delta Value (mDV). We will also try to explore the reasons for this apparently contradictory situation.

Background

A colleague of ours was recently asked, when trying to publish a paper, to explain why there were low CI but high RI values in his study. This reminded Guido of a set of analyses he started about a decade ago, using an arbitrary selection of plant morphological matrices he had access to.

The idea of that study was to advocate the use of networks for phylogenetic studies using morphological matrices, based on the two dozen data sets that he had at hand. The datasets were each used to infer trees and quantify branch support, under three different optimality criteria: least-squares (via neighbour-joining, NJ), maximum likelihood, and maximum parsimony. This study was was never wrapped up for a formal paper, for several reasons (one being that 10 years ago Guido had absolutely no idea which journal could possibly consider to publish such a paper, another that he struggled to find many suitable published matrices).

The signals detected in the collected matrices were quite different from each other. The set included matrices with very high matrix Delta Values (mDV), nontree-like signals, and astonishingly low mDVs, for a morphological matrix. Equally divergent were the CI and RI of the inferred equally most-parsimonious trees (MPT) and the NJ tree. The data for the MPTs and the primary matrices are shown in the first graph, as a series of scatterplots, where each axis covers the values 0-1. (Note: in most cases the NJ topologies are as optimal as the MPTs, and have similar CI and RI values.)

As you can see, the CI values (parsimony-uninformative characters not considered) are not correlated with either the RI or mDV values, whereas the latter two are highly correlated, with one exception.

The most tree-like matrix (mDV = 0.184, which is a value typically found for molecular matrices allowing for inference of unambiguous trees) was the one of Hufford & McMahon (2004) on Besseya and Synthyris. The number of MPTs was undetermined —using a ChuckScore of 39 steps (the best value found in test runs), PAUP* found more than 80,000 MPTs with a CI of 0.39 (third-lowest of all of the datasets), but an RI of 0.9 (highest value found).

A strict consensus network of the 80,003 equally parsimonious solutions, the network equivalent to the commonly seen strict consensus tree cladograms. Trivial splits are collapsed. Colours solely added for orientation (see next graph).

Oddly, the NJ tree had the same number of steps (under parsimony), but a much higher CI (0.69). The proportion of branches with a boostrap support of > 50% was twice as large in a distance-based framework than using parsimony.

Bootstrap consensus networks based on 10,000 pseudoreplicates each. Left, distance-based and inferred using the Neighbour-Joining algorithm; right, using a branch-and-bound search under parsimony as optimality criterion (one tree saved per replicate). Edge-lengths reflect branch support of sole or competing alternatives; alternatives found in less than 20% of the replicates not shown; trivial splits are collapsed. Same colour scheme than above for orientation.

The Neighbour-net based on this matrix has quite an interesting structure. Tree-like portions are clearly visible (hence, the low mDV) but the branches are not twigs but well developed trunks. The large number of MPTs is mainly due to the relative indistinctness of many OTUs from each other.

Neighbour-net based on simple mean (Hamming) morphological distances. Same colour scheme as above.

This distance-based 2-dimensional graph captures all main aspects of the tree inferences and bootstrap analyses, with one notable exception: B. alpina which is clearly part of the red clade in the tree-based analyses. We can see that the orange group, B. wyomingensis and close relatives, is (morphology-wise) less derived than the red species group. Although B. alpina is usually placed in a red clade, it would represent a morphotype much more similar to the orange cluster as it lacks most of the derived character suite that defines the rest of the red clade. In trees, B. alpina is accordingly connected to the short red root branch as first diverging "sister" with a very short to zero-long terminal branch, but in the network it is placed intermediate between the poorly differentiated but morphologically inhomogenous oranges and the strongly derived reds — being a slightly reddish orange. This reddishness may reflect a shared common origin of B. alpina and the other reds, in which case the tree-based inferences show us the true tree. Or just a parallel derivation in a member of the B. wyoming species aggregate, in which case the unambiguous clade would be a pseudo-monophylum (see also our recent posts on Clades, cladistics, and why networks are inevitable and Let's distinguish between Hennig and cladistics).

Interpretation, what does low CI but high RI stand for?

The distinction between the Consistency Index and the Retention index has been of long-standing practical importance in phylogenetics. For a detailed discussion, you can consult the paper by Gavin Naylor and Fred Kraus (The Relationship between s and m and the Retention Index. Systematic Biology 44: 559-562. 1995).

For each character, the consistency index is the fraction of changes in a character that are implied to be unique on any given tree (ie. one change for each character state): m / s, where m = the minimum possible number if character-state changes on the tree, and s = the observed number if character-state changes on the tree. The sum of these values across all characters is the ensemble consistency index for the dataset (CI).

The retention index (also called the homoplasy excess ratio) for each character quantifies the apparent synapomorphy in the character that is retained as synapomorphy on the tree: (g - s) / (g - m), where g = the greatest amount of change that the character may require on the tree. Once again, the sum of these values across all characters is the ensemble retention index for the dataset (RI).

Both CI and RI are comparative measures of homoplasy — that is, the degree to which the data fit the given tree. However, CI is negatively correlated with both the number of taxa and the number of characters, and it is inflated by the inclusion of parsimony-uninformative characters. RI is less sensitive to these characteristics. However, RI is inflated by the presence of unique states in multi-state characters that have some other states shared among taxa and, therefore, are potentially synapomorphic.

It is these different responses to character-state distributions (among the taxa) that apparently create the situation noted above for morphological data. Neither CI nor RI directly measures tree-likeness, but instead they are related to homoplasy. So, it is the relative character-state distributions among the taxa that matter in determining their values, not just the tree itself.

For example, increasing the number of states per character will, in general, increase CI faster than RI. Increasing the number of states that per character that occur in only one taxon will, in general, increase RI faster than CI.

Take-home message

This is just another example demonstrating that morphological data sets should not be used to infer (parsimony) trees alone, but analysed using a combination of Neighbour-nets and support Consensus Networks. No matter which optimality criterion is preferred by the researcher, the signal in such matrices is typically not trivial. It calls for exploratory data analysis, and inference methods that are able to capture more than a trivial sequence of dichotomies.

[Update 10/9/2018] Related data files can now be found in my Collection of morphological matrices (some including extinct taxa) and related phylogenetic inferences (Version 2) on figshare. 

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.

Should we try to infer trees on tree-unlikely matrices?

Spermatophyte morphological matrices that combine extinct and extant taxa notoriously have low branch support, as traditionally established using non-parametric bootstrapping under parsimony as optimality criterion. Coiro, Chomicki & Doyle (2017) recently published a pre-print to show that this can be overcome to some degree by changing to Bayesian-inferred posterior probabilities. They also highlight the use of support consensus networks for investigating potential conflict in the data. This is a good start for a scientific community that so far has put more of their trust in either (i) direct visual comparison of fossils with extant taxa or (ii) collections of most parsimonious trees inferred based on matrices with high level of probably homoplasious characters and low compatibility. But do those matrices really require or support a tree? Here, I try to answer this question.

Background

Coiro et al. mainly rely on a recent matrix by Rothwell & Stockey (2016), which marks the current endpoint of a long history of putting up and re-scoring morphology-based matrices (Coiro et al.’s fig. 1b). All of these matrices provide, to various degrees, ambiguous signal. This is not overly surprising, as these matrices include a relatively high number of fossil taxa with many data gaps (due to preservation and scoring problems), and combine taxa that perished a hundred or more millions years ago with highly derived, possibly distant-related modern counterparts.

Rothwell & Stockey state (p. 929) "As is characteristic for the results from the analysis of matrices with low character state/taxon ratios, results of the bootstrap analysis (1000 replicates) yielded a much less fully resolved tree (not figured)." Coiro et al.’s consensus trees and network based on 10,000 parsimony bootstrap replicates nicely depicts this issue, and may explain why Rothwell & Stockey decided against showing those results. When studying an earlier version of their matrix (Rothwell, Crepet & Stockey 2009), they did not provide any support values, citing a paper published in 2006, where the authors state (Rothwell & Nixon 2006, p. 739): “… support values, whether low or high for particular groups, would only mislead the reader into believing we are presenting a proposed phylogeny for the groups in question. Differences among most-parsimonious trees are sufficient to illuminate the points we wish to make here, and support values only provide what we consider to be a false sense of accuracy in these assessments”.

Do the data support a tree?

The problem is not just low support. In fact, the tree showed by Rothwell & Stockey with its “pectinate arrangement” conflicts in parts with the best-supported topology, a problem that also applied to its 2009 predecessor. This general “pectinate” arrangement of a large, low or unsupported grade is not uncommon for strict consensus trees based on morphological matrices that include fossils and extant taxa (see e.g. the more proximal parts of the Tree of Life, e.g. birds and their dinosaur ancestors).

The support patterns indicate that some of the characters are compatible with the tree, but many others are not. Of the 34 internodes (branches) in the shown tree (their fig. 28 shows a strict consensus tree based on a collection of equally parsimonious trees), 12 have lower bootstrap support under parsimony than their competing alternatives (Fig. 1). Support may be generally low for any alternative, but the ones in the tree can be among the worst.

The main problem is that the matrix simply does not provide enough tree-like signal to infer a tree. Delta Values (Holland et al. 2002) can be used as a quick estimate for the treelikeliness of signal in a matrix. In the case of large all-spermatophyte matrices (Hilton & Bateman 2006; Friis et al. 2007; Rothwell, Crepet & Stockey 2009; Crepet & Stevenson 2010), the matrix Delta Values (mDV) are ≥ 0.3. For comparison, molecular matrices resulting in more or less resolved trees have mDV of ≤ 0.15. The individual Delta Values (iDV), which can be an indicator of how well a taxon behaves during tree inference, go down to 0.25 for extant angiosperms – very distinct from all other taxa in the all-spermatophyte matrices with low proportions of missing data/gaps – and reach values of 0.35 for fossil taxa with long-debated affinities.

The newest 2016 matrix is no exception with a mDV of 0.322 (the highest of all mentioned matrices), and iDVs range between 0.26 (monocots and other extant angiosperms) and 0.39 for Doylea mongolica (a fossil with very few scored characters). In the original tree, Doylea (represented by two taxa) is part of the large grade and indicated as the sister to Gnetidae (or Gnetales) + angiosperms (molecular trees associate the Gnetidae with conifers and Ginkgo). According to the bootstrap analysis, Doylea is closest to the extant Pinales, the modern conifers. Coiro et al. found the same using Bayesian inference. Their posterior probability (PP) of a Doylea-Podocarpus-Pinus clade is 0.54, and Rothwell & Stockey’s Doylea-Ginkgo-angiosperm clade conflicts with a series of splits with PPs up to 0.95.

Figure 1. Parsimony bootstrap network based on 10,000 pseudoreplicate trees
inferred from the matrix of Rothwell & Stockey.
Edges not found in the authors’ tree in red, edges also found in the tree in green.
Extant taxa in blue bold font. The edge length is proportional to the frequency of the
according split (taxon bipartition, branch in a possible tree) in the pseudoreplicate
tree sample. The network includes all edges of the authors’ tree except for
Doylea + Gnetidae + Petriellales + angiosperms vs. all other gymnosperms and
extinct seed plant groups. Such a split has also no bootstrap support (BS < 10)
using least-square and maximum likelihood optimum criteria.

Do the data require a tree?

As David made a point in an earlier post, neighbour-nets are not really “phylogenetic networks” in the evolutionary sense. Being unrooted and 2-dimensional, they don’t depict a phylogeny, which has to be a sort of (rooted) tree, a one-dimensional graph with time as the only axis (this includes reticulation networks where nodes can be the crossing point of two internodes rather than their divergence point). The neighbour-net algorithm is an extension into two dimensions of the neighbour-joining algorithm, the latter infers a phylogenetic tree serving a distance criterion such as minimum evolution or least-squares (Felsenstein 2004). Essentially, the neighbour-net is a ‘meta-phylogenetic’ graph inferring and depicting the best and second-best alternative for each relationship. Thus, neighbour-nets can help to establish whether the signal from a matrix, treelike or not as it is the cases here, supports potential and phylogenetic relationships, and explore the alternatives much more comprehensively than would be possible with a strict-consensus or other tree (Fig. 2).

Figure 2. Neighbour-net based on a mean distance matrix inferred
from the matrix of Rothwell & Stockey.
The distance to the "progymnosperms", a potential ancestral group of the
seed plants, can be taken as a measurement for the derivedness of each
major group. The primitive seed ferns are placed between progymnosperms
 and the gymnosperms connected by partly compatible edge bundles; the
putatively derived "higher seed ferns" isolated between the progymnosperms
and the long-edged angiosperms. Shared edge-bundles and 'neighbourness'
reflect quite well potential phylogenetic relationships and eventual ambiguities,
as in the case of Gnetidae. Colouring as in Figure 1; some taxon names
are abbreviated.

In addition, neighbour-nets usually are better backgrounds to map patterns of conflicting or partly conflicting support seen in a bootstrap, jackknife or Bayesian-inferred tree sample. In Fig. 3, I have mapped the bootstrap support for alternative taxon bipartitions (branches in a tree) on the background of the neighbour-net in Fig. 2.

Obvious and less-obvious relationships are simultaneously revealed, and their competing support patterns depicted. Based on the graph, we can see (edge lengths of the neighbour-net) that there is a relatively weak primary but substantial bootstrap support for the Petriellales (a recently described taxon new to the matrix) as sister to the angiosperms. Several taxa, or groups of closely related taxa, are characterised by long terminal edges/edge bundles, rooting in the boxy central part of the graph. Any alternative relationship of these taxa/taxon groups receives equally low support, but there are notable differences in the actual values.

There is little signal to place most of the fossil “seed ferns” (extinct seed plants) in relation to the modern groups, and a very ambiguous signal regarding the relationship of the Gnetidae (or Gnetales) with the two main groups of extant seed plants, the conifers (Pinidae; see C. Earle’s gymnosperm database) and angiosperms (for a list and trees, see P. Stevens’ Angiosperm Phylogeny Website).

The Gnetidae is a strongly distinct (also genetically) group of three surviving genera, being a persistent source of headaches for plant phylogeneticists. Placed as sister to the Pinaceae (‘Gnepine’ hypothesis) in early molecular trees (long-branch attraction artefact), the currently favoured hypothesis (‘Gnetifer’) places the Gnetidae as sister to all conifers (Pinatidae) in an all-gymnosperm clade (including Gingko and possibly the cycads).

As favoured by the branch support analyses, and contrasting with the preferred 2016 tree, the two Doyleas are placed closest to the conifers, nested within a commonly found group including the modern and ancient conifers and their long-extinct relatives (Cordaitales), and possibly Ginkgo (Ginkgoidae). In the original parsimony strict consensus tree, they are placed in the distal part as sister to a Gnetidae and Petriellales + angiosperms (possibly long-branch attraction). The grade including the ‘primitive seed ferns’ (Elkinsia through Callistophyton), seen also in Rothwell and Stockey’s 2016 tree, may be poorly supported under maximum parsimony (the criterion used to generate the tree), but receives quite high support when using a probabilistic approach such as maximum likelihood bootstrapping or Bayesian inference to some degree (Fig. 3; Coiro, Chomicki & Doyle 2017).

Figure 3. Neighbour-net from above used to map alternative support patterns.
Numbers refer to non-parametric bootstrap (BS) support for alternative phylogenetic
splits under three optimality criteria: maximum likelihood (ML) as implemented in
RAxML (using MK+G model), maximum parsimony (MP), and least-squares
(via neighbour-joining, NJ; using PAUP*); and Bayesian posterior probabilties
(using MrBayes 3.2; see Denk & Grimm 2009, for analysis set-up). The circular
arrangement of the taxa allows tracking most edges in the authors’ tree and their,
sometimes better supported, alternatives. The edge lengths provide direct
information about the distinctness of the included taxa to each other; the structure
of the graph informs about the how tree-like the signal is regarding possible
phylogenetic relationships or their alternatives. Colouring as in Figure 1;
some taxon names are abbreviated.

Numerous morphological matrices provide non-treelike signals. A tree can be inferred, but its topology may be only one of many possible trees. In the framework of total evidence, this may be not such a big problem, because the molecular partitions will predefine a tree, and fossils will simply be placed in that tree based on their character suites. Without such data, any tree may be biased and a poor reflection of the differentiation patterns.

By not forcing the data in a series of dichotomies, neighbour-nets provide a quick, simple alternative. Unambiguous, well-supported branches in a tree will usually result in tree-like portions of the neighbour net. Boxy portions in the neighbour-net pinpoint the ambiguous or even problematic signals from the matrix. Based on the graph, one can extract the alternatives worth testing or exploring. Support for the alternatives can be established using traditional branch support measures. Since any morphological matrix will combine those characters that are in line with the phylogeny as well as those that are at odds with it (convergences, character misinterpretations), the focus cannot be to infer a tree, but to establish the alternative scenarios and the support for them in the data matrix.

References

Coiro M, Chomicki G, Doyle JA. 2017. Experimental signal dissection and method sensitivity analyses reaffirm the potential of fossils and morphology in the resolution of seed plant phylogeny. bioRxiv DOI:10.1101/134262

Crepet WL, Stevenson DM. 2010. The Bennettitales (Cycadeoidales): a preliminary perspective of this arguably enigmatic group. In: Gee CT, ed. Plants in Mesozoic Time: Morphological Innovations, Phylogeny, Ecosystems. Bloomington: Indiana University Press, pp. 215-244.

Denk T, Grimm GW. 2009. The biogeographic history of beech trees. Review of Palaeobotany and Palynology 158: 83-100.

Felsenstein J. 2004. Inferring Phylogenies. Sunderland, MA, U.S.A.: Sinauer Associates Inc.

Friis EM, Crane PR, Pedersen KR, Bengtson S, Donoghue PCJ, Grimm GW, Stampanoni M. 2007. Phase-contrast X-ray microtomography links Cretaceous seeds with Gnetales and Bennettitales. Nature 450: 549-552 [all important information needed for this post is in the supplement to the paper; a figure showing the actual full analysis results can be found at figshare]

Hilton J, Bateman RM. 2006. Pteridosperms are the backbone of seed-plant phylogeny. Journal of the Torrey Botanical Society 133: 119-168.

Holland BR, Huber KT, Dress A, Moulton V. 2002. Delta Plots: A tool for analyzing phylogenetic distance data. Molecular Biology and Evolution 19: 2051-2059.

Rothwell GW, Crepet WL, Stockey RA. 2009. Is the anthophyte hypothesis alive and well? New evidence from the reproductive structures of Bennettitales. American Journal of Botany 96: 296–322.

Rothwell GW, Nixon K. 2006. How does the inclusion of fossil data change our conclusions about the phylogenetic history of the euphyllophytes? International Journal of Plant Sciences 167: 737–749.

Rothwell GW, Stockey RA. 2016. Phylogenetic diversification of Early Cretaceous seed plants: The compound seed cone of Doylea tetrahedrasperma. American Journal of Botany 103: 923–937.

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.

Models and processes in phylogenetic reconstruction

Since I started interdisciplinary work (linguistics and phylogenetics), I have repeatedly heard the expression "model-based". This expression often occurrs in the context of parsimony vs. maximum likelihood and Bayesian inference, and it is usually embedded in statements like "the advantage of ML is that it is model-based", or "but parsimony is not model-based". By now I assume that I get the gist of these sentences, but I am afraid that I often still do not get their point. The problem is the ambiguity of the word "model" in biology but also in linguistics.

What is a model? For me, a model is usually a formal way to describe a process that we deal with in our respective sciences, nothing more. If we talk about the phenomenon of lexical borrowing, for example, there are many distinct processes by which borrowing can happen.

A clearcut case is Chinese kāfēi 咖啡 "coffee". This word was obviously borrowed from some Western language not that long ago. I do not know the exact details (which would require a rather lengthy literature review and an inspection of older sources), but that the word is not too old in Chinese is obvious. The fact that the pronunciation comes close to the word for coffee in the largest European languages (French, English, German) is a further hint, since the longer a new word has survived after having been transplanted to another language, the more it resembles other words in that language regarding its phonological structure; and the syllable kā does not occur in other words in Chinese. We can depict the process with help of the following visualization:

Lexical borrowing: direct transfer

The visualization tells us a lot about a very rough and very basic idea as to how the borrowing of words proceeds in linguistics: Each word has a form and a function, and direct borrowing, as we could call this specific subprocess, proceeds by transferring both the form and the function from the donor language to the target language. This is a very specific type of borrowing, and many borrowing processes do not directly follow this pattern.

In the Chinese word xǐnǎo 洗脑 "brain-wash", for example, the form (the pronunciation) has not been transferred. But if we look at the morphological structure of xǐnǎo, being a compound consisting of the verb xǐ "to wash" and nǎo "the brain", it is clear that here Chinese borrowed only the meaning. We can visualize this as follows:

Lexical borrowing: meaning transfer

Unfortunately, I am already starting to simplify here. Chinese did not simply borrow the meaning, but it borrowed the expression, that is, the motivation to express this specific meaning in an analogous way to the expression in English. However, when borrowing meanings instead of full words, it is by no means straightforward to assume that the speakers will borrow exactly the same structure of expression they find in the donor language. The German equivalent of skyscraper, for example, is Wolkenkratzer, which literally translates as "cloudscraper".

There are many different ways to coin a good equivalent for "brain-wash" in any language of the world but which are not analogous to the English expression. One could, for example, also call it "head-wash", "empty-head", "turn-head", or "screw-mind"; and the only reason we call it "brain-wash" (instead of these others) is that this word was chosen at some time when people felt the need to express this specific meaning, and the expression turned out to be successful (for whatever reason).

Thus, instead of just distinguishing between "form transfer" and "meaning transfer", as my above visualizations suggest, we can easily find many more fine-grained ways to describe the processes of lexical borrowing in language evolution. Long ago, I took the time to visualize the different types of borrowing processes mentioned in the work of (Weinreich 1953[1974]) in the following graphic:

Lexical borrowing: hierarchy following Weinreich (1953[1974])

From my colleagues in biology, I know well that we find a similar situation in bacterial evolution with different types of lateral gene transfer (Nelson-Sathi et al. 2013). We are even not sure whether the account by Weinreich as displayed in the graphic is actually exhaustive; and the same holds for evolutionary biology and bacterial evolution.

But it may be time to get back to the models at this point, as I assume that some of you who have read this far have began to wonder why I am spending so many words and graphics on borrowing processes when I promised to talk about models. The reason is that in my usage of the term "model" in scientific contexts, I usually have in mind exactly what I have described above. For me (and I suppose not only for me, but for many linguists, biologists, and scientists in general), models are attempts to formalize processes by classifying and distinguishing them, and flow-charts, typologies, descriptions and the identification distinctions are an informal way to communicate them.

If we use the term "model" in this broad sense, and look back at the discussion about parsimony, maximum likelihood, and Bayesian inference, it becomes also clear that it does not make immediate sense to say that parsimony lacks a model, while the other approaches are model-based. I understand why one may want to make this strong distinction between parsimony and methods based on likelihood-thinking, but I do not understand why the term "model" needs to be employed in this context.

Nearly all recent phylogenetic analyses in linguistics use binary characters and describe their evolution with the help of simple birth-death processes. The only difference between parsimony and likelihood-based methods is how the birth-death processes are modelled stochastically. Unfortunately, we know very well that neither lexical borrowing nor "normal" lexical change can be realistically described as a birth-death process. We even know that these birth-death processes are essentially misleading (for details, see List 2016). Instead of investing our time to enhance and discuss the stochastic models driving birth-death processes in linguistics, doesn't it seem worthwhile to have a closer look at the real proceses we want to describe?

References

• List, J.-M. (2016) Beyond cognacy: Historical relations between words and their implication for phylogenetic reconstruction. Journal of Language Evolution 1.2. 119-136.
• Nelson-Sathi, S., O. Popa, J.-M. List, H. Geisler, W. Martin, and T. Dagan (2013) Reconstructing the lateral component of language history and genome evolution using network approaches. In: : Classification and evolution in biology, linguistics and the history of science. Concepts – methods – visualization. Franz Steiner Verlag: Stuttgart. 163-180.
• Weinreich, U. (1974) Languages in contact. With a preface by André Martinet. Mouton: The Hague and Paris.