Stacking networks based on sign language manual alphabets

This post is the first of a mini-series on sign language manual alphabets. While the evolution of spoken languages has been studied intensively using phylogenetic methods, sign languages have not, as yet.

In this post we will first introduce our readers to a set of stacked networks, and how it assists in establishing ancestor-descendant relationships in a pretty straightforward (but not trivial) case: the evolution of manual alphabets in sign languages. In the next post, I will demonstrate the use of networks for character mapping and putting forward hypothesis about ancestor-descendant relationships.

In 2004, Spencer et al. (Two papers you may want to read...) showed that Neighbor-nets outperform tree inferences when it comes to explicit ancestor-descendant relationships. The data set they used was quite particular: copies of written text. Here, scribes copy a text, and then other scribes, some of them ignorant of the language of the text they are copying, copy the copies. In the paper, the sequence of copies was recorded (the 'true tree'), and then the various texts were transferred into phylogenetic matrices, in order to infer trees and networks, and then this result was compared to the 'true tree'. The best fit of the data to the truth was the Neighbor-net.

This is a compelling conclusion, because, as a planar network and in contrast to median networks, Neighbor-nets don't explicitly place taxa in ancestor-descendant relationships. However, we have shown for many cases here at the Genealogical World of Phylogenetic Networks how ancestors are often placed with respect to their descendants: they are often closer to the center of the graph, or the root when known, and thus they bridge the center or sister lineages and their descendants. We can thus see why Neighbor-nets might be useful in practice.

In this context, the evolution of sign language manual alphabets, ie. the hand-shapes used to represent letters of a written alphabet, should be relatively easy to reconstruct. Once an alphabet is established in a sign language school / community, the ancestor, it will be passed on to other "generations" within the community and other schools / communities, the descendants. However, this is not necessarily a dichotomous process, as depicted in the first figure.

A scheme depicting how manual alphabets may evolve and disperse.

There are a few complications here: for example, hand-shapes may change in course of being used (the hand-shape evolves); contact may lead to exchange or appropriation of hand-shapes (called "borrowing" in linguistics); and, in some cases, entire alphabets will need to be adapted to a particular use. The latter case occurs when changing from one script (Latin, say) to another (Cyrillic or Arabic) — the first formal school for the deaf was established in Paris, for example. As a teacher, I need to decide: Do I take a hand-shape from the morphologically similar letter, or the phonetically similar one? As a scientist, I need to assess the homologies among such hand-shapes without inflicting systematic bias.

Standardization will wipe out local customs and replace them with a multinational standard. For instance, Country 2 in the scheme above, drops its original B-type manual alphabet (red) for an A-type (blue); and in Country 7 both traditions are fused. Over time, originally distinct sign languages may converge due to geographic proximity, or even just feasibility.

The evolution of spoken languages has been studied intensively using phylogenetic methods, and in particular networks are much more commonly found in the linguistic literature than in the biological one. For sign languages we have made a first step in a recently published pre-print:

Justin M. Power, Guido W. Grimm, and Johann-Mattis List (2019) Evolutionary dynamics in the dispersal of sign languages. Humanities Commons. http://dx.doi.org/10.17613/0smt-j414

What excites me about our study is that it combines historical manual alphabets (going back to 1593), which are potential ancestors, with a set of modern-day alphabets, which are their likely descendants. The data set is thus an evolutionary paleontologist's dream (and, possibly, a cladist's nightmare, if we expect a simple tree-like set of relationships rather than a network). As a scientist, I simple love to boldly go where no-one has gone before.

The next figure shows the all-inclusive network from our paper, but focusing on the age of the manual alphabets.

For more linguistic details see the pre-print.
* Historical version(s) of these lineages are not included in our data set

Obviously, there has been quite a lot of evolutionary changes, as well as standardization, going on, although some parts, like the Swedish SL (sign language), have stuck to its unique original. Historical and contemporary Spanish / Catalan are still most similar to the oldest manual alphabets that Justin dug out for our study. On the other hand, the contemporary Norwegian SL is placed far apart from his historical counterparts, and lacks any obvious affinity. Austrian, Danish, and German look back on a long and diverse history, the green "Austrian-origin Group", but the contemporaries have been homogenized by standardization (note the closeness to the International Sign manual alphabet). If we use an analogy with common biological and biogeographical processes (such as range expansion, competition, extinction, etc), then the Austrian-origin Group only survived in a remote island population, where we still find a sort of living fossil, the Icelandic SL.

In contrast to biological data, the old, putatively ancestral, manual alphabets are not closer to the graph's center, or the oldest manual alphabets in our data set. The reason for this seems to lie in the data itself and how manual alphabets evolve, and this will be the topic of the next post(s).

Still, we can isolate some evolutionary pathways, especially when we make time-wise taxon-filtered networks and stack them (see this introduction to stacking and this application using Osmundaceae, a data set including an even larger ratio of fossil taxa to modern taxa).

Fig. 4 from Power et al. Coloring same as above: pink – Spanish; turquoise – French-origin; green – Austrian-origin; orange – Polish; red – Russian; light blue – Swedish Group. The English-origin and Afghan-Jordanian groups are not included, since not represented by historical manual alphabets in our data set

Each of the three networks includes manual alphabets from a certain time period, starting with pre-1840 at the bottom, historical 19th-/20th-century manual alphabets in the middle, and post-1950 manual alphabets in the top network. The dotted links between the networks connect manual alphabets that are included in two of the networks.

Even from these graphs alone, we can say a lot about how ancestors (original manual alphabets in a country) relate to descendants (later and contemporary manual alphabets) and their evolutionary pathways. Here are some examples.

Shortly after the time when the first schools for the deaf were established in continental Europe (late 18th, early 19th centuries), manual alphabets showed quite a diversity, and were very different from their potential Spanish sources, such as Yebra 1593 and Bonet 1620, with the French and Austrian teachers and communities going different ways. The oldest Cyrillic alphabet, Russian 1835, is more closely related to (ancient) Austrian than it is to (ancient) French.

The Swedish manual alphabet of 1866 is a fresh invention. Some hand-shapes may have been borrowed from one or another alphabet in use on the continent, but, as we will see in the next post of the series, includes genuinely new forms.

The French tradition was dispersed into the new World (American SL appears to be a direct derivation from the French, while the Brazilian SL is an adaptation) but remained a relatively homogeneous group. On the other hand, the Austrian-origin languages diversified, in particular within the Danish influence zone. Politically, the Danish king ceded Norway to Sweden in the Treaty of Kiel 1814 (note the distance between Norwegian and Danish languages in the late 19th century), while Iceland was a Danish dependency until 1918, when the Danish-Icelandic Act of Union was signed. Furthermore, the German manual alphabets subsequently diverged from the Austrian source.

The Polish manual alphabet, originally an adaptation of the Austrian-Danish manual alphabets (see the graph in the middle), became closer to the Russian group, with the Latvian sign language taking up an intermediate position. The Cyrillic alphabets evolved further away, too (top graph).

In the following post(s) of this miniseries, we will explain what we learned from simple character mapping on the time-taxon-filtered networks, and how to score manual alphabets in the first place.


Follow-up posts in this miniseries

• Character cliques and networks: mapping haplotypes of manual alphabets – how we explored the principal signals in our matrix

Stacking neighbour-nets: a real-world example

In my last post, I outlined two ideas about how stacking neighbour-nets can assist in tracing evolutionary change over time, using a theoretical example. In this post, I will show how this could work using a (tricky) real-world example: a morphological matrix including a high proportion of fossil taxa and a good deal of (strongly) homoplasious characters (Bomfleur, Grimm & McLoughlin 2017).

Stacking can be valuable when both fossil and extant taxa are included in the study. The idea of stacking is to construct networks for each time slice, rather than creating one giant network that tries to encompass everything. Adjacent time-slice networks can then be directly compared, which should reveal the evolutionary changes that occurred between those two times. The final phylogeny can then be constructed from this information, including all of the extant taxa and fossils together.

I regard our work as quite innovative for a palaeobotanical/-phylogenetic systematic study, as it generated a taxon-dense dataset down to species (sometimes individual specimens) as ‘operational taxonomic units’ (OTUs). Our goal was to provide a unifying classification for extant and fossil Osmundales (royal ferns) rhizomes. The primary purpose is hence not to infer a phylogenetic tree but to assist in describing and placing new-found rhizome fossils in the phylogeny. The placement workflow (see this tutorial) combines a polytomous key (using conserved, lineage-diagnostic traits) with neighbour-nets that use different taxon sets. We discussed odd placements in the splits graphs, and matrix signal quality (robustness) from differential branch support, as estimated by non-parametric bootstrapping (least-squares, maximum likelihood, maximum parsimony).

Sources of incompatible data patterns in real-world data

The main problem with real-world data when it comes to inferring phylogenetic relationships, i.e. estimating the true phylogeny, are incompatible data patterns. For molecular matrices, the two main sources of signals that will be incompatible with the true phylogeny are back-mutations and model-bias. For instance, there is usually a higher probability for transitions than for transversions; and for coding gene regions, the 3rd codon position can become over-saturated and thus stochastically distributed, providing little phylogenetic signal. By adapting the model in a probabilistic environment, we can (try to) counter such biases during inference

In the case of morphological (or other non-molecular) traits, incompatible signals arise from:

1. homoplasious characters – traits that evolve convergently or in parallel, which are frequently included in such matrices;
2. epigenetic effects – morphological traits not, or not fully, controlled by the genetic composition of the organism; and
3. pseudo-homologies – traits that are seemingly the same but are the endpoint of different evolutionary pathways.

Inferring a tree reflecting the true phylogeny from such a matrix may be very difficult or even impossible. For a perfect probabilistic approach, we would need to establish character-wise probabilities for change, which requires that a lineage has a modern-day diversity fairly matching that in the past.

Fossils add further sources of signals incompatible with the true phylogeny, such as: preservation artefacts and misinterpretations (false homologies); uncertainty linked to heterochrony; and, last but not least, ‘temporal’ convergences, i.e. the parallel or convergent evolution of the same (or similar) trait in an ancient sister or unrelated lineage of a modern (or much younger) lineage.

For all of these aspects, the royal fern rhizomes provide a nice example (i.e. a bad-case scenario). Only a few of the 45 scored traits that can be observed in fossil material are conserved within the modern lineages and their extant representatives, and hence are of high diagnostic value for assigning fossils to one of these lineages. Many other rhizome features are variable within extant members of the now six genera (some even within a species), and increasingly so looking back into the past.

The royal ferns became arborescent several times, as reflected by convergent adaptations in rhizome anatomy — highly complex stele architectures are found from the Permian onwards in (morpho)species that differ in all relatively stable, lineage-diagnostic traits. The most complex modern-day rhizomes have anatomies that appear to be less derived than those of some of their ancient counterparts. Nonetheless, the rhizomes, scored for 129/130 OTUs (fossil species, partly referring to individual specimens) in our matrix (click here for an annotated version for use with Mesquite), reflect a substantial past diversity and cover more than 250 million years of evolution.

Basic data situation

The all-inclusive neighbour-net (Fig. 1; see here for a fully annotated version) captures aspects of similarity patterns related to phylogenetic relationships, but does not clearly resolve the known (modern) or putative (extinct) genera within the core group Osmundoideae, for example. Overall branch-support is generally low for any alternative (details can be found here), independent of the optimality criterion used. [For our systematic treatment, we used data subsets to generate a series of networks including only members of the same (putative) lineage, which were increasingly proficient to sort the OTUs.]

The main problems are: (i) the differentiation between less-derived rhizome anatomies of the Osmundoideae found in the likely paraphyletic extinct genus Millerocaulis (pink in Fig. 1) and the modern genus Claytosmunda (magenta, paraphyletic with one survivor); and (ii) the distinctness and superficial similarity of two arborescent lineages, the genus Osmundacaulis (red) and the extinct (Permian to Jurassic) family Guaireaceae (greenish). They differ in all stable, lineage-diagnostic characters but share highly dissected steles. Phylogenetic trees "resolve" this conflict by creating an artificial clade (e.g. the parsimony cladogram by Wang et al. 2014). The neighbour-net (Fig. 1) places Osmundacaulis between the Guaireaceae and the Osmundoideae, the subfamily of Osmundaceae including the surviving modern genera.

Fig. 1. Neighbour-net based on a morphological distance matrix of 122 OTUs representing Permian to extant Osmundales and their putative relatives, the Grammatopteridales (black).

Stacking procedure one: identifying closest relatives in subsequent time-slices

Signal ambiguity (from homoplastic characters and the related resolution issue) affects also the time-wise networks to some degree. Figures 2–4 show the network-per-time-slice stacks. Each neighbour-net includes only the OTUs from one stratigraphic period (Permian, Triassic, Jurassic, Cretaceous, Paleogene + Neogene) and the modern-day survivors. For simplicity, links are only established for the closest potential relative in the subsequent or preceding time-slice; and only shown when the mean morphological distance (MD) does not exceed 0.25. The colouring of the dots reflects the systematic affinity of the taxon as established by Bomfleur et al. and shown in Fig. 1.

A major taxonomic turnover characterises the transition from the (late) Permian to the Triassic (Fig. 2). The most primitive (rhizome-wise) Osmundales, the Thamnopterioideae (brown) become extinct, and are completely replaced by the Osmundoideae, their modern counterparts. The only representative of the Permian diversity remaining in the Triassic appears to be Millerocaulis (?Palaeosmunda) stipabonnetiorum, and this may provide a good taxon for rooting the Triassic phylogeny. However, it also one of the worst-preserved and most poorly described taxa — to some degree, its similarity with both lineages of Permian Osmundaceae (Thamnopterioideae and Palaeosmunda) may hint that the distances are under-estimated, since traits could not be scored that otherwise lead to increased distances.

Fig. 2. Taxon-reduced neighbour-nets, including only species from the same time-slice (as labelled). Inter-time-slice links indicate the morphologically closest match in the preceding or following time-slice for each species (in case of pairwise distances < 0.25)

The Jurassic graph (in Fig. 2) highlights a decrease in overall diversity, despite the much higher numbers of OTUs. The links can help to establish relationships between congeners of both time scales; but for Osmundastrum (today represented by a single, genetically and morphologically derived species) a more pronounced evolutionary shift is indicated: the Triassic putative member is linked to Jurassic Millerocaulis species (a paraphyletic Osmundoideae genus defined by the absence of a trait found in all extant genera), which are relatively close to the first unambiguous Osmundastrum. We also find that the three Jurassic newcomers have little relation to the Triassic basis (Fig. 2).

The linking of the Jurassic and Cretaceous time-slices highlights (Fig. 3) a general weakness of the approach using this matrix: poorer preserved, incompletely described fossils included in the matrix (Cretaceous Millerocaulis) attract most links from the Jurassic Osmundoideae — their distances are under-estimated.

Fig. 3. As above, but linking the Jurassic and subsequent Cretaceous neighbour-nets. Note the decreasing diversity but clear signals for Osmundacaulis (red) in contrast to the group of modern Osmundoideae (purplish). Plenasium (light blue) is a modern arborescent genus with complex and highly dissected steles and generally derived rhizomes.

The two Osmundastrum, which are probably part of the same evolutionary lineage, are not linked (see Bomfleur, Grimm & McLoughlin 2015 for the reasons). Two modern lineages with more or strongly derived rhizomes appear in the Cretaceous, the Todinae and Plenasium.

In the case of the Todinae the Jurassic links are partly ambiguous, with one Cretaceous OTU linked to Jurassic Claytosmunda (part of the Todinae’s sister clade according to molecular data), but the other with some relatively distinct Millerocaulis. The problem here is that the Todinae may have diverged earlier (Bomfleur, Grimm & McLoughlin 2015; Grimm et al. 2015), but their rhizome fossils have so far not been found (or lack the diagnostic characters of the lineage). Gaps in the fossil record can hinder establishing meaningful links. The links are, however, to a group of Millerocaulis that are closer to coeval Claytosmunda – which show a rhizome anatomy that may be closest to that of the common ancestor of all modern-day king ferns – than to their congeners. In the case of Plenasium, the genus with the most-derived rhizomes of all modern Osmundaceae, the closest older relative is part of the same subgroup of Millerocaulis. These potentially false links may reflect that some Millerocaulis show derived character suites, which are typically found also in one or another modern Osmundaceae genus (similarity due to convergence).

The closer we get to the modern-day situation, the more interpretable the links become (Fig. 4). Lineages with distinct and derived rhizome anatomies such as Osmundastrum and Plenasium are linked across time-slices. Cross-generic links from Cretaceous Millerocaulis to Paleogene-Neogene Osmunda to modern-day Claytosmunda relate directly to higher numbers of shared, possibly primitive characters in the connected taxa; these links can again be informative for rooting the graphs. Substantially weaker links (mean morphological distances > 0.1 between time-slices) are found for distantly related pairings (Cretaceous and extant Todinae with Paleogene-Neogene Osmundastrum and Claytosmunda).

Fig. 4. As above, but for Cretaceous to modern-day.

Stacking procedure two: graphs including taxa of two subsequent time-slices

Figures 5 and 6 show the two-adjacent-time-slices-per-graph stacks. Interpretation of these figures is more straightforward — one just compares the placement of the connecting taxa (Triassic and Jurassic in Fig. 5; Paleogene and Neogene in Fig. 6). The resolution issue regarding the relationship between Millerocaulis and genera representing the modern lineage (Claytosmunda, Osmundastrum, Plenasium, Leptopteris, Todea) is obvious — the Triassic Millerocaulis are clustered in the Permo-Triassic graph, but are placed apart within the spider-web-like portion in the Triassic-Jurassic graph (Fig. 5). This could mean that several lineages of Millerocaulis diversified in the Jurassic, all of which have their roots in the Triassic. Some of the emerging Millerocaulis groups remain coherent in the Jurassic-Cretaceous graph (and can include Cretaceous species), put their position relative to each other can change. In contrast, for Osmundacaulis the Cretaceous newcomers simply fit into the existing organisation.

Fig. 5. Stack of neighbour-nets comprising species of two subsequent time-slices, covering the time from the Permian to the Cretaceous. Connections relate to Triassic (lower half) or Jurassic (upper half) species that are included in two subsequent splits graphs.

The transition from the Cretaceous to the modern-day situation (Fig. 6) fairly reflects what could be inferred by mapping morphological characters onto the molecular tree. The placement of Osmunda species in the graphs reflect evolutionary change towards the modern-day species, whereas stasis can be assumed for Osmundastrum, and a loss of diversity for Claytosmunda. According to the structures of the graphs, the modern-day Plenasium (subgenus Plenasium) replaced the more diverse (and partly more derived) Cretaceous-Paleogene Plenasium (subgenus Aurealcaulis); but the genus is absent from the Neogene, so there are no connections between the ‘65–5 Ma’ and ‘last 25 Ma’ graphs.

Fig. 6. As above, but covering the time from the Cretaceous to now. Connections refer to Paleogene (lower half) and Neogene (upper half) species.

Now that it’s done, what can be said?

Establishing similarity links across time-slices can be tedious or even misleading, especially with increasing numbers of taxa and increasing complexity of the signals in the matrix (Figs 2–3). The process is more time-consuming and the result (Figs 2–4) is graphically more challenging than the alternative stacking procedure (Figs 5–6).

With most real-world data, it may be difficult to get a set of links between time slices that reflect the true phylogeny, like it did in my earlier theoretical example. Nonetheless, the procedure can help to identify potential relatives (ancestors, descendants, sister lineages) of groups that are restricted to a single time slice, or highlight the lack of potential or favourable candidates.

However, in general, joining the taxa from two subsequent time-slices in one graph, and connecting these graphs by the shared taxa, seems to be a more feasible and straightforward approach. Once a matrix is compiled, the distance calculation and splits-graph inference is a matter of minutes, and it takes less than half-an-hour to produce a first graphical output using the graphical functions in SplitsTree and software to graphically stack the exported SVG or EPS files (further beautification may take a day). Taxa with odd signals (with ambiguous affinity) will be placed accordingly in the nets and eventually move around in the two containing graphs (Fig. 5) and the amount of evolutionary change across time may be directly visible (Fig. 6).

Additional links for readers interested in details

— Figure illustrating the history of taxonomic systems for Osmundales.
— An archive including all analysis files generated in the course of the original study is hosted at the Dryad Digital Repository.
— Further annotated versions of the figures shown in this post and the used analysis files have been published under a CC-BY licence: Grimm G. (2017) Osmundales diverstity through time: stacking networks. figshare. https://doi.org/10.6084/m9.figshare.5255014.v1.

References

Bomfleur B, Grimm GW, McLoughlin S (2015) Osmunda pulchella sp. nov. from the Jurassic of Sweden—reconciling molecular and fossil evidence in the phylogeny of modern royal ferns (Osmundaceae). BMC Evolutionary Biology 15: 126.

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

Grimm GW, Kapli P, Bomfleur B, McLoughlin S, Renner SS (2015) Using more than the oldest fossils: Dating Osmundaceae with the fossilized birth-death process. Systematic Biology 64: 396-405.

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

Maddison WP, Maddison DR (2001 onwards) Mesquite: a modular system for evolutionary analysis.

Wang S-J, Hilton J, He X-Y, Seyfullah LJ, Shao L (2014) The anatomically preserved Zhongmingella gen. nov. from the Upper Permian of China: evaluating the early evolution and phylogeny of the Osmundales. Journal of Systematic Palaeontology 1: 1-22.

Stacking neighbour-nets: ancestors and descendants

Although they are not phylogenetic networks in an evolutionary sense, neighbour-nets are amazingly efficient when it comes to depicting actual ancestor-descendant relationships. Spencer et al. (2004), for example, applied various methods of phylogenetic inference to reconstruct a known phylogeny of scripts, text copies made by scribes based on an original text, or copies of that text. They found that the neighbour-net algorithm produced a graph that best depicts the actual ancestor (original text) to descendant (text copy made by a scribe) relationships. The reason is relatively simple: neighbour-nets are well-suited to extract and reflect differentiation patterns from a distance matrix.

In this post I will explore this idea in some detail, because I think that it has important practical implications (which I will further elaborate in future posts). If data are available for time slices of the evolutionary history, then it is possible to stack a series of networks that describe each time slice, thus providing a much more comprehensively inferred genealogy.

Neighbor-nets

If a distance matrix reflects exactly the phylogeny (i.e. if the signal from the matrix is trivial), then the neighbour-net looks like a tree, with the ancestors placed seemingly at the internal nodes (medians) of the subtree(s) containing their descendants — that is, the neighbour-net looks like a median network (Figure 1). In fact, this is just mimicry. The ancestors are not actually placed on the internal nodes (medians) but are connected by zero-length edge bundles to the centre of the graph (the roots of their descendants).

Figure 1. Neighbour-net inferred from a perfect distance matrix (from Denk & Grimm 2009)

In reality, distance matrices will not be exact reflections of the phylogeny (the ‘true’ tree) but distorted; and this will be reflected also in the neighbour-net (Fig. 2).

Figure 2. Neighbour-net inferred from an imperfect distance matrix (cf. Denk & Grimm 2009, fig. 1)

I superimposed a potentially inferred tree on Figure 2 to highlight some distorting effects. Note that this could be a tree optimised using a distance criterion such as minimum evolution or least-squares, or a tree optimised under maximum likelihood or maximum parsimony (one of the alternative topologies found in the sample of equally parsimonious trees).

The following distorting effects may apply during tree-inference: (i) a misplaced outgroup-inferred ingroup root (due to convergences shared by the outgroup and members of lineage B), (ii) lineage B is dissolved into a grade, although it should be a clade (convergences shared by members of lineages A and B), and (iii) the all-ingroup ancestor is resolved as the sister to lineage A, but not B. The neighbour-net illustrates the uncertainties of placing several taxa (the box-like parts of the graph), while keeping the ancestors equally close to their descendants. This provides information lost (or overlooked) when just inferring a tree (but not by exploratory data analysis of e.g. the bootstrap support patterns).

The basics — why stack networks?

Figure 3 shows a hypothetical evolution of a phylogenetic lineage in a two-dimensional morpho-space. The common ancestor (black dot) gives rise to two, morphologically somewhat distinct lineages (bluish vs. reddish coloured). The lineages evolve over time and diverge again. The overall differentiation within the group increases, but eventually the potential niche/morphospace is filled. When looking only at the final situation (i.e. the modern-day situation), we may be tempted to infer wrong relationships based on the morphological distinctness. Each one of the blue and red daughter lineages evolved into similar niches and obtained somewhat similar morphological character suites substantially distinct from the one of their respective sister taxa. Translating this situation into a distance matrix (or a character matrix) to infer a tree, will provide a wrong topology, when long-branch attraction steps in, that recognises one or two blue-red sister pair(s).

Figure 3. Evolution (vertically) and diversification of a lineage in a two-dimensional morphospace (horizontally)

Adding all of the ancestors can help to escape long-branch attraction (Figure 4; see also Wiens 2005). We don’t find red111 as sister to blu11, but still resolve the wrong sister relationship between the overall too-similar endpoints of the converging red and blue sub-lineages (red222 and blu22). The remainder of the red lineage is erroneously dissolved into (A) an ancient sister lineage (red0); (B) a real clade (red1, red11, red111), the red sub-lineage most distinct from the blu lineage; and (C) a grade (red2, red22), “basal” (wrong terminology, but often used) to the blue lineage, collecting the older members of the red sub-lineage evolving towards the morphospace of the blue lineage.

Figure 4. Neighbour-joining tree inferred on a distance matrix exactly reflecting the pairwise distances along both axes in the 2-dimensional morphospace

Only a few, (data-wise) trivial branches of the true tree (broadened green edges) are found in the inferred tree. An obvious defect of this tree is that the phylogenetic distance, the sum of branch lengths between two tips, does not reflect the pairwise distances encoded in the matrix. For instance, the all-ancestor should be equally distant from both of the ancestors of the red and blue lineages (red0, blu0).

The neighbour-net shows something rather different (Figure 5). A large box can be seen, referring to the highly incompatible signal induced by the ancestors and their direct and subsequent descendants.

Figure 5. Neighbour-net splits graph inferred on the same distance matrix

Red222 and blu22, the false sisters, are placed next to each other and share an edge bundle. They are most similar to each other and increasingly distinct from all other taxa included in the analysis. However, their nearest relatives are their actual ancestors (red22 and blu2), which are already quite distinct from each other, and show affinities to further members to their clade but not to the other clade (the topology of the tree from Figure 4 is shown in yellow in Figure 5).

The network includes the true tree in addition to edge bundles referring to wrong alternatives (induced by imperfect data; in this case, convergence due to evolution into a similar morphospace). The phylogenetic distances between two tips (via alternative pathways) reflect much better the pairwise distances (almost exactly). Thus, the neighbour-net is a much more comprehensive display of the actual signals in the imperfect matrix than a tree could ever be (independent of the optimisation criterion used).

The fossils included in our example represent a time sequence, an actual change in time. With that information as background, we can much more easily access the neighbour-net’s structure (Figure 6).

Figure 6. The same neighbour-net with time-slices

Already in the second time-slice the lineage diverged into two distinct branches represented by red0 and blu0. Both evolved (blu0→blu00) and diverged (red1, red2) in the next time slice, and so on. The fact that the neighbour-net is not a phylogenetic graph (in an evolutionary sense) becomes a strength. In any tree, we would need to deduce, or be tempted to deduce, (inclusive) common origins (Hennig’s monophyly) from the clades exhibited in the rooted version of the tree. Here, using the most natural root to root the tree, the oldest representative of the lineage (ancestor), misplaces the two representatives of the second time-slice along with those involved in subsequent radiations.

Stacking networks

There are two simple ways to trace the change in differentiation patterns through time using stacked networks: (A) Generate a series of networks per time-slice and identify the closest relatives in the next (and/or preceding) time-slice, or (B) Generate networks that combine the taxa of two subsequent time-slices.

Figure 7. A sequence of neighbour-nets, with the taxa filtered by age. (These are actual reconstructions inferred by SplitsTree based on the taxon-filtered subsets of the all-inclusive distance matrix.)

My example only includes up to four co-eval taxa, and hence the neighbour-nets are trivial graphs for each time-slice (Figure 7). The connecting lines between the time-slices indicate the closest and next-closest possible descendants (as defined by the smallest and next-smallest distance) of each earlier taxon. The thickness of the connections reflects their absolute similarity — the thickest lines indicate a morphological pairwise distance of 0.13, and the thinnest are distances of > 0.33. The colour indicates whether the connection reflects a true (green) or false (yellow) relationship.

Analysed this way, the matrix’ signal appears quite perfect in relation to the true tree. One can trace the increasing diversity within the clade (all descendants of the all-ancestor), as well as the misleading decreasing distance between the blu2/blu22 and red22/red222 lineages. In this case, the same stacking procedure would also work with trees, as the neighbour-nets are trivial and very tree-like. With real world data, the differences may be more profound.

With more complex or less complete data, we have a higher risk that ancestor-descendant relationships will not be straightforwardly identified by highest-similarity pairs. Missing data, for instance, can result in distances that mask or over-estimate the actual phylogenetic distances between an older and a younger taxon. Using the stacking procedure illustrated in Figure 7, such problems can become visible in the form of related taxa from the same time-slice that are connected to unrelated or distantly related taxa in the preceding or following time-slices.

But how to identify more likely candidates? One possibility is to assess potential phylogenetic relationship by combining taxa of two subsequent time-slices. The connectives between the reconstructions are then straightforward: each taxon is always used in two different reconstructions (Figure 8). This procedure allows us to establish the phylogenetic affinities of a taxon with respect to co-eval and older taxa (potential siblings and ancestors) or co-eval and younger taxa (potential siblings and descendants).

Figure 8. A sequence of neighbour-nets, each one including the taxa of two subsequent time-slices

Stacking networks — what’s next?

The first thing, obviously, is to test the suggested procedures for real-world data, involving groups with a dense and well-studied fossil record. I will provide a real-world example in my next post using the matrix we put up for our systematic revision of Osmundaceae (King Ferns) rhizomes (Bomfleur, Grimm & McLoughlin 2017).

Simulations may help to identify misleads caused by missing data, and the resulting distorted distance matrices, and non-comprehensively sampled (time-wise) phylogenies. They may also be informative regarding whether consensus networks reflecting competing branch support can be used for similar approaches.

Programmers are needed, too. For my graphics, I established the inter-time-slice connectives by hand; but it would be handy to have a programme environment that can do this.

References

Bomfleur B, Grimm GW, McLoughlin S. 2017. The fossil Osmundales (Royal Ferns)—a phylogenetic network analysis, revised taxonomy, and evolutionary classification of anatomically preserved trunks and rhizomes. PeerJ 5: e3433. Open access: https://peerj.com/articles/3433/

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

Spencer M, Davidson EA, Barbrook AC, Howe CJ. 2004. Phylogenetics of artificial manuscripts. Journal of Theoretical Biology 227: 503-511.

Wiens JJ [, Soltis P ?]. 2005. Can incomplete taxa rescue phylogenetic analyses from long-branch attraction? Systematic Biology 54: 731-742. Open access: https://academic.oup.com/sysbio/article-lookup/doi/10.1080/10635150500234583