Should we bother about character independence?

The comments of David Marjanović to one my last posts (Please stop using cladograms!), kept me musing about an old question of mine: Why should we be concerned about whether characters in a matrix are independent or not?

When I started to get into phylogenetics (I taught myself by reading and just doing it and never had a course in phylogenetics at university), I learned that the most important thing for a phylogenetic matrix is:

All characters are independent of each other.

In other words: the mutation (change) in one character doesn't affect the mutation (change) in any other character.

I could never wrap my head around this. After all, the characters are all part of the same organism and must therefore function together, so how can they possibly be biologically independent? Even the fact that everything is part of the same universe means that everything is functionally dependent to one extent or another — when a butterfly sneezes the polar bears tremble, as they poetically say.

However, what is meant is that characters must be independent enough for practical mathematical purposes. This is a fundamental assumption of most mathematical analyses, in order to make them tractable. Trying to account for the dependencies is far too difficult, mathematically.

However, it is still worthwhile thinking about whether these "practical purposes" are likely to be realistic for phylogenetics. Consider this:

1. Traditional phylogenetics mostly uses morphological traits, some of which must have been evolutionary beneficial and evolved as consequence of the same reason (adaptive process).
2. Working at the tips of the tree of life, our data were from the nuclear-encoded 35S rDNA, the cistron encoding for 18S rRNA (small subunit), 5.8 S rRNA, and 25 rRNA (large subunit, erroneously called 26S in some of the phylogenetic literature), which is known for compensatory mutations (eg. strands of the 5.8S rRNA have to fit to the 5' end of the 25S rRNA; here's a link for those interested in RNA structure).

To investigate point 1, let's look at a dolphin (image source) and a bat (image source).

Without sequencing their entire genomes and establishing the function of each gene (and kicking out one or another gene during development), we cannot assess how independent (genetically) the traits are that make a dolphin a near-perfect swimmer, and a bat the only actively flying mammal. But obviously, a lot of their traits are adapted to this single function of movement. The practical consequence is that instead of a plethora of distinguishing characters, we only can score two fully independent ones: "can swim" versus "can fly".
(And then eliminate these two, because another rule in phylogenetics is that we should only include characters that are not under positive selection. The commonly implemented models all assume that evolution is neutral. This is why Charles Darwin has two parts to The Origin, one discussing historical dependence of characters and one discussing natural selection.)

As for point 2, everyone who worked with ITS, the internal transcribed spacers of the 35S rDNA, can easily see that some mutational patterns always come in pairs or some other series. Although rarely done, we can correct for linked mutations during inference by using the assumed secondary structures as a functional corrective. This is rarely done, because even without this correction you still get trees (or networks) that make sense.

Linked mutations and evolutionary trends within the LP3 of the 5' ITS2 in species of Acer section Acer (see my Ph.D. thesis, open access; figure from Grimm et al., Plant Syst. Evol., 2007). This (non-coding) length-polymorphic region (found in all angiosperms in various modifications) comprises an upstream CT- and partly linked (complementary) downstream GA-motif.

A very simple example

Let's take a group of very simple, made-up organisms differing in two trait complexes (note that it may be a collection of genes that trigger the difference): form and colour.

In total, "evolution" came up with 15 different combinations ("species"), five of which are extinct, two of which are primitive in the sense that they still occur today, but have also been found as fossils.

We all know that morphologies have a high level of homoplasy. Homoplastic traits mean that groups will not accurately reflect the true tree. Having as many forms (9) as colors (9), we have no clue as to which trait is more conservative, and hence could better reflect the true tree.

The 15 species form nine potentially monophyletic genera.

The alternative nine potentially monophyletic genera.

The promise of phylogenetics is that we can infer the true tree based on the scored characters. We could follow the strict independence rule, and score them as two multi-state characters, leading us to the following "tree" — this has been parsimony-optimized and unweighted, as in most studies using morphological data, with the sample of MPTs summarized using a strict consensus cladogram.

The strict consensus tree of 355602 equally parsimonious trees with 17 steps, a CI of 0.94 and RI of 0.88: a pitchfork (an extreme case, but pitchfork-like subtrees are very common in palaeontological phylogenetic literature).

Alternatively, we could score the features as a series of binary characters such as:

• Is the center depressed?
• Is it horizontally or vertically elongated?
• Is it round or pointed?
• Do we have few (<= 6) or many tips (>= 8; "?" for all round species)?
• Is it reddish? Or greenish? Or bluish? (Example: purple doughnut would be 1 - 0 - 0, the turquoise five-star 0 - 1 - 1)
• Has it a dark or light shade (relatively speaking: green taken as darker than turquoise)?

These characters are not particularly independent. Certain evolutionary steps make it impossible to go back or evolve something in parallel / convergently. For example, the Roundish group never evolved pointed tips, and the Pointish organisms can vary their outline, but not smooth it. The characters are also not overly compatible (e.g. shading splits each basic coloring into two subsets), so we wouldn't expect a very resolved tree or one that matches the true tree exactly:

Adams consensus tree of 80 MPTs with 19 steps, CI = 0.57, RI = 0.79, naming follows the principles of cladistic classification (only subtrees in a rooted tree may be named; not to be confused with phylogenetic classification fide Hennig)

However, it doesn't look like a very bad evolutionary hypothesis. In fact, the inferred clades only miss one monophyletic group (I can tell, because I invented this group to illustrate that 'cladistics' is a subset of 'phylogenetics'): Fivestar reflects the morph of the common ancestor of all stars, resolved as part of a monophyletic grade "basal" to the (reciprocally monophyletic) polygons:

Evolution as it happened. Note, each dichotomy is accompanied by one or two exclusive subsequent mutations (synapomorphies at the time). Unknown ancestors (not found in the fossil records) are dimmed. Green: valid names following Hennig's phylogenetic classification; orange: only valid for the most recent time frame (Purpleoval is indistinguishable from the ancestor of all non-olive Roundish, Fivestar from the ancestor of all stars, and the ancestor of all polygons was a blue pentagon).

Of course, I would always show all of the topological alternatives in the optimized tree sample. Here is the strict consensus network of all of the MPTs:

Strict consensus network of all 80 MPTs, the network analogue to the commonly seen strict consensus cladograms.

In contrast to the consensus trees, we see the equally optimal alternatives, and can even make a call as to which trait to give a higher weight (evolution-wise). For instance, although only 12 MPTs have a Pentagon clade, 40 have an Octagon clade, which would fit with the hypothesis of reciprocal monophyly. The shading-based alternative seen in other MPTs (light vs. dark polygons) can be argued to be less likely, noting how scattered this feature is across the entire graph (this is what TNT's iterative weighting does, except that it starts from one of the alternative trees)

And here's the distance network, probably (like with real-world data) the least-biased depiction of the differentiation pattern:

All labelled taxa are monophyletic (as defined by the true tree). Note how some neighborhoods reflect monophyly while others would result in paraphyletic groups.

Take-home message

Now, you could rightfully point out that this is totally hypothetical and, having generated the group, I made sure that the analysis works out — actually, I didn't, and I was quite surprised at how well the binary matrix, which just scores everything that differs between the species, resolves aspects of the true tree. However, just compare the above graphs with trees published in (paleo)phylogenetic studies, and the real-world data we dealt with here on the Genealogical World of Phylogenetic Networks.

You might also point out that this is just like using stepmatrices — forcing a topology by suitably coding complex characters. Likewise, this thought must be discouraged (but see Joe Felsenstein 2004 book, Inferring Phylogenies). I would respond that scoring complex traits filtered by evolution as a single multi-state character severely underestimates the information content. An example from my own research: in the King Ferns (Osmundaceae), the subsequent modification of the sclerenchyma ring along the leaf traces is fully compatible with the molecular tree, so why should I be forced to reduce the surely interdependent (and traceable in the fossil record) aspects of this evolutionary filtered trait complex to a single, multi-state (and unweighted) character?

Coding of a single complex trait (Bomfleur et al., PeerJ, 2017, fig. 7), the structure of the sclerenchym ring in Osmundaceae leaf traces, as five binary characters that reflect the ontogenetic sequence seen in Osmundaceae rhizomes (arrows), a case where ontogeny mirrors phylogeny (Bomfleur et al., BMC Evol. Biol., 2015; cf. Additional file 1, fig. S1-1).

If we have character complexes that we can score, then we should not bother ourselves with drawing a (often very subjective) line between biologically dependent and independent characters. We should just score as much as we can see, and then explore the signal in the resulting matrix (see our many blog posts on the latter topic).

Exploratory data analysis benefits from few-state characters. This is because characters with many states (nine in the above example, which is something also found in the actual literature) that do not inform any taxon bipartitions, lead only to quite useless pitchfork-trees.

Scoring what we see as detailed as possible may, of course, get some things wrong. We may face one or another paraphyletic (or even polyphyletic) clade and monophyletic grade — inferring trees/networks and establishing branch-support with more than a single optimality criterion is advisable as is character mapping. At least it gets us a data-based hypothesis to discuss and to investigate further; or several hypotheses, when using consensus networks or distance-based splits graphs instead of consensus trees.

How languages lose body parts: once more about structural data in historical linguistics

This is a joint post by Guido Grimm and Johann-Mattis List.

Mattis’ last two blog posts dealt with problems of what linguists call "structural data". Here we discuss what this means for the inference of relationships between languages.

A closer look at structural data: the questionnaire issue

As pointed out before, what is called structural data in comparative linguistics is a very diverse mix of data solely unified by the idea of having some kind of questionnaire that a linguist may use when going into the field and trying to describe a certain language. These questionnaires are a bit different from the traditional concept lists usually used for the purpose of historical language comparison (see the collection of different lists in the Concepticon project by List et al. 2016). The main difference is that they are based on an imaginative question that a field worker asks an informant (which could as well be a written grammar of the language under question). Since questions can be asked in many different ways, while concepts in historical language comparison are usually restricted to the so-called "basic vocabulary", the diversity of structural datasets is much greater than the diversity we encounter when comparing questionnaires based on concept lists.

When analyzing these data, we deal with characters of very different nature, and likely different evolutionary pathways or histories. A biological analogy would probably be (true) total evidence data sets that combine genetic data from: genes/genomes with different inheritance pathways (paternally, maternally, biparentally; basic information level), morphological-anatomical data (visible form, phenotypic), palaeontological data (historical evidence), ontogenetic (life-history stages, developmental features), and biochemical data (expression level). The only difference is probably that the linguistic characters’ histories may be more complex. [Side-remark: ‘total evidence’ datasets found in the biological literature are typically just combination of genetic and morphological data, allowing for the inclusion of extinct/fossil taxa.]

To give a specific example, let's have a look at a the Chinese dataset by Szeto et al. (2018), mentioned in Mattis' blogpost from September. This dataset is now accessible as a GitHub repository (https://github.com/cldf-datasets/szetosinitic). Mattis added some information regarding the different features of the questionnaire. We list these features in slightly abbreviated form in the table below, adding rough categorizations by Mattis in the Comment column.

ID	Description	Comment
p-1	5 or more tone categories	phonological / diachronic
p-2	Retroflex fricative initials	phonological / diachronic
p-3	Bilabial nasal coda	phonological / diachronic
p-4	Stop codas	phonological / diachronic
p-5	Monosyllabic word for 'snake'	lexical
p-6	Differentiation between 'hand' and 'arm'	lexical / semantic
p-7	Differentiation between 'defecate' and 'urinate'	lexical / semantic
p-8	Differentiation between 'eat' and 'drink'	lexical / semantic
p-9	Semantically void suffix in 'table'	lexical
p-10	Different classifiers for humans and pigs	lexical / semantic
p-11	[CLF N] constructions in subject position with definite reference	syntactic
p-12	Reduplicated monosyllabic nouns	morphological
p-13	Post-verbal modal auxiliary developed from 'ge/acquire'	syntactic / diachronic
p-14	Modified-modifier order in animal gender marking	morphological / syntactic
p-15	Post-verbal adverb meaning 'first'	lexical / syntactic
p-16	[V DO IO] order in double object dative constructions	syntactic
p-17	'Give' as a disposal marker	syntactic / diachronic
p-18	'Give' as a passive marker	syntactic / diachronic
p-19	'Go' as a post-VP associated motion marker	syntactic / diachronic
p-20	Marker-Standard-Adjective order in comparatives	syntactic
p-21	case system	morphological / syntactic

Mattis has tried to characterize the features, i.e. matrix’ characters, by generalizing linguistic categories: "phonological", pointing roughly to questions about pronunciation (the biological equivalent would be phenotypic traits in morphology or anatomy); "lexical", pointing to the words in the lexicon (this would be the DNA of a language); "morphological", pointing to the ways in which words are constructed; and "syntactic", pointing to the ways in which words are combined to form sentences. In combination, “morphological” and “syntactic” are equal to ‘meta-level’ biological traits, such as development-related features, ontogenetic evidence, and biochemical composition — the ways in which the genetic code is expressed or used in a living organism in adaption to the environment.

Mattis also flagged some characters as "diachronic", to mark whether the respective feature was selected by the authors due to their independent knowledge about the history of the Chinese dialects. This is something rarely possible in biology, but imagine that we could go back in time to literally observe the evolution of a lineage over a given time-period, and code this observed evolution as traits. Note that this is not entirely science-fiction — there are two examples where we can observe directly pathways of biological evolution: mutation patterns in viruses, and horizontal modification of marine morphs in high-resolution sediment cores.

While one can discuss to what degree a certain feature should belong to this category, it is rather obvious that all phonological features are diachronic, because they name distinctions that reflect well-known processes of sound change, which happened in a couple of Chinese dialects and have been proposed in the past by dialectologists in order to classify the Chinese dialects historically.

For example, consider feature p-3 of the questionnaire: Does a given dialect have a syllable that ends in [-m]? From the history of the Chinese dialects we know that the [-m] was present in Middle Chinese, but later merged with [-n] and [-ŋ] in many varieties. Given that we know that this happened, and that we know that people have used this to mark a split, especially between the "innovative" dialects in the North and the South, it is clear that this feature bears explicit historical information. The same holds for all phonological features that we find in the data: p-1, the number of different tones in the dialects is again roughly reflecting the differences between languages in the North and in the South (the North having lost many tones); p-2 reflects the retention or specific development of retroflex sounds (similar to sh in English as opposed to s) mostly in the North; and p-4 reflects if a variety has syllables that can end in [-p, -t, -k], again a feature characteristic for the more "conservative" varieties in the South of China.

Figure 1: Overlap of features in Szeto et al.'s (2018) structural feature collection of Chinese dialects

Four lexical features have further been flagged as "semantic"; we query here existing or missing distinctions of concepts. People who learned, for example, Russian or certain German dialects know that it is rather common to have a single word for what other languages call "arm" and "hand" (see the respective entry in the CLICS database) or "foot" and "leg".

This diverse feature collection is coded as binary characters, reflected by presence/absence, or a yes/no answer to the question in the questionnaire. The choice of features is very selective. A biological analogy would be a matrix collecting incompatible splits of paternal (molecular) genealogies, along with a few prominent phenotypical traits (reflecting major evolutionary steps), and some traits that we expect to be primarily triggered not by genetics (inheritance) but by expression or adaptation to the environment. Biologists would not phylogenetically analyze such diverse and complex, potentially selection-biased data (although it could be very interesting), but linguists do.

In this context, it is remarkable, but also typical for these kind of data, that the 21-character feature collection by Szeto et al. (2018) has no feature in common with the collection by Norman (2003), a 15-character-matrix, which we also converted to our Cross-Linguistic Data Formats (see Forkel et al. 2018) in order to increase the data comparability.

Figure 2: A Neighbor-net splits graph of the structural data by Szeto et al. (2018).

The typification, coded as binary matrix to infer the Neighbor-net splits graph in Figure 2, demonstrates some basic characteristics of such 2-dimensional graphs. Note four of the 'characters' (typification categories) correlate with an edge(-bundle) in the network, separating the 'taxa' (the queried features). All "semantic" taxa are also "lexical", but "lexical" is more comprehensive, hence, "semantic" is placed as 'descendant' of "lexical" (Neighbor-nets can visualize ancestor-descendant relationships to some degree). "Morphological" taxa are either just "morphological" or also "syntactic", hence the pronounced box.

For "diachronic" and "syntactic", we have no corresponding edge(-bundle), because one taxon is also "lexical", but the others are "diachronic" and "syntactic" — this is a conflict that cannot be resolved with two dimensions. To visualize all the resultant 'taxon' splits, called also taxon bipartitions, we would need a third dimension. Lacking a third dimension, the Neighbor-net prioritizes keeping most "syntactic" together, because the "diachronic-syntactic" are closer to "syntactic" (max. 1 'character' difference) than to "diachronic-phonological" (2 character difference). The "syntactic-lexical" has to be placed apart because it is equally close to "lexical" and "syntactic" 'taxa', but differs much from "morphological-syntactic" or "diachronic-syntactic", the closest two relatives of "syntactic"-only 'taxa'. It is resolved closer to the centre of the graph, because it is more closely related to the other "syntactic" taxa than to the rest of the "lexical" taxa. This is also the reason why the "syntactic"-only taxa have to be placed farther out: "Diachronic-phonological" and "syntactic-lexical" are closer to the other endpoints, and the distance of "syntactic"-only to "diachronic-phonological", "lexical" and "morphological" should be as large as possible.

Losing body parts: How data coding masks underlying processes

Most typologists collecting structural data are not per se interested in phylogenies. Yet, given that scholars deliberately collect historical (diachronic) features, this shows that even if they would not necessarily admit it, they have a genuine interest in uncovering the history of the languages under question; or at least, how closely related languages (or here: dialects) are. But this requires understanding the characters we analyze, the collected "structural data".

In evolutionary biology, the key question people (should) ask when trying to select characters is how their change can be modeled on a tree or a network. What processes could be expected that shaped the data? What is behind the diversity? Is similarity or dissimilarity instigated by:

• [A] inheritance, i.e. passed from an ancestor to all / some of its descendants,
• [B] random mutation and/or sorting, i.e. the product of a stochastic, evolutionary neutral process,
• [C] non-random mutation, i.e. processes that recur frequently, may be beneficial and positively (gain, or negatively: loss) selected for, or
• [D] secondary contact, mixing of lineages by hybridization (symmetric mixing) and introgression (asymmetric mixing)?

[A]–[C] are vertical processes following a tree, even if the tree does not necessarily need to be the same; [D] is (mostly) horizontal and can only be modeled using a network. For each of the above, we can find an analogy in the evolution of languages.

In addition, process [3], and to a lesser extent [4], can lead to what biologists call 'homoplasy', meaning that the same feature is observed in two unrelated or distantly related taxa. In the context of phylogenetic inferences, homoplasies inflict tree-incompatible signals, seemingly reticulate patterns originating from a tree-like evolution. Structural (or other) linguistic data and phenotypical biological data have a lot in common — complex processes are boiled down to mere absence or presence of features (or traits, as they are called in biology).

Figure 3: Basic evolutionary processes, we need to consider when looking at linguistic data. Or biological traits, when we replace simplification by adaptive evolution, positively selected traits.

If we check the features in our table above, and ask: to which degree can they be used to model these processes (see also David's last post on illogic in phylogenetics), e.g. simply distinguish between similarity by chance, relatedness, or secondary contact (mixing), we can easily see that they are by no means optimal for evolutionary investigations. This is not necessarily because of the processes they involve, but more importantly because of the data sampling, which makes modeling almost impossible, with each character needing its own model.

As an example, take the feature p-6 in our table. Whether or not a language makes a distinction between "arm" and "hand" does not seem to follow specific geographic or genealogical patterns. The following figure shows a plot from the CLICS database (List et al. 2018), visualizing the most frequently recurring polysemies (or colexifications) centering around the concept "arm". The full visualization in CLICS can be found here, and when hovering with the mouse over the link between "arm" and "hand" (marked in green below).

Figure 4: Colexification network in the CLICS database.

From eye-balling the data, it is hard to find a consistent geographic / language-family pattern, which suggests that the feature p-6 is likely to show a high degree of homoplasy in the languages of the world. Obviously, different people decided not to distinguish between "hand" or "arm". But, the example of the Sami languages in northern Scandinavia also demonstrate that some people using related, long-isolated languages, consistently don't make the distinction. Here, the homoplasy is inherited (lineage-conserved). A biological analogy would be the rarely applied difference between a 'convergence' (a trait is independently evolved in different lineages) and a 'parallelism' (a trait is expressed by different but not all members of the same lineage).

Figure 5: Geographic distribution of arm/hand colexifications in the CLICS database.

A specific analogy to the "hand-arm" colexification / differentiation pattern is leaf shedding in oaks and their relatives (Fagaceae, the beech family). Some oak lineages (section Cerris of oaks, beech trees, chestnuts) are essentially or strictly deciduous, others (sections Cylcobalanopsis, Ilex, the sister sections of Cerris; Castanopsis, the sister genus of chestnuts) are always evergreen, and the biggest group (number of species) of all Fagaceae, subgenus Quercus includes evergreen (1 section), mixed (the two by far largest sections), and deciduous (1 nearly extinct section) sublineages. To some extent this is linked to the climate in which the species thrive (high latitudes and/or per-humid = deciduous, low latitude and/or seasonally dry = evergreen), but consistently evergreen and deciduous lineages do co-exist.

Looking at the Chinese dialects, we see that p-6 represents a trivial split in the network.

Figure 6: A Neighbor-net inferred from the Szeto et al. matrix. Dialects that distinguish "arm" and "hand" with filled dots ('1' for character 6 in the matrix), those that don't ('0') with empty dots. We can put a single line separating all don't- from do-taxa (dialects), i.e. a bipartition of the taxon set fitting the character partition seen in (p-)6.

But, given the general patterning of the feature on a global scale, does this really mean that it is inherited — that is, a good feature to reflect relatedness?

Whether a feature is likely to be homoplastic is just one part of the story. Linguists typically have more information about how things change than do biologists, putting a double-edged sword in their hands (that they hardly ever use). Asking whether "hand" and "arm" are expressed by distinctive concepts does not consider the underlying processes. Here, we can assume at least three different character states, namely:

1. "arm" and "hand" are expressed by the same word, which is the original word for "arm",
2. "arm" and "hand" are expressed by the same word, which is the original word for "hand", and
3. "arm" and "hand" are expressed by different word.

We could even have a forth state, in which "arm" and "hand", in the whole long history of the ancestral languages, was always used to express "arm or hand" (i.e., both body parts). No differentiation and no later generalization from either arm nor hand took place.

Figure 7: Left, current scoring; right, scoring taking into account the actual mutation process.

From Ancient Chinese, we know that "1" (Yes, I do differ between "arm" and "hand") was most likely the original state. We can further assume that once the distinction is dropped, it is less likely to come back again (although this can, of course, also happen). That is, our model involves two possible mutations (vertical process): we lose the word for "arm" due to its replacement by "hand", or we lose the word for "hand" due to its replacement by "arm", each with its own probability.

Figure 8: Probability distribution for transitions involving "hand" and "arm".

The probability, mutation or not, and which mutation, relates to four principal driving factors:

1. probability of random loss (mutation)
2. probability of random gain (mutation)
3. global linguistic tendencies
4. regional socially-enforced preference

Establishing p_-arm (loss "arm") and p_-hand (loss "hand") is not trivial, because they may be affected by what is the word for "arm" and "hand" (for simplicity we will assume that p_+arm and p_+hand are close to 0). We could expect a higher tendency to keep the word that is easier to pronounce or less easy to confuse with other words and, hence, is easier to understand. If two dialects with different states come into contact, this may also influence the decision to take over a state or not. In everyday language, a distinction between "arm" and "and" may be useless because of the clear context in which both words are used, so p_1-word > p_2-words. However, closeness to administration centers or areas with a higher percentage of educated people could decrease p_1-word, because it may be considered a sign of poor social standard to not make the difference between "arm" and "hand".

Figure 9: Vertical and horizontal processes involving transitions of "hand" and "arm".

Estimating p can only be left to phylogenetic algorithms (unless more detailed information is available). But we can (and should) design the questionnaire to capture as many of the processes as possible. In this case, to not only ask whether there is a distinction between "arm" and "hand", but also to find out whether the word "arm" or "hand" is used, e.g. by using two questions/binary characters:

• Do we use "hand"?
• Do we use "arm"?

Note that this question requires quite a deal of knowledge about the languages under investigation, since it may not be trivial to find out what was the "original" word for "arm" or "hand".

Therefore, a further step would be to replace the binary characters by a value measuring the similarity between the words used for "hand" and those used for "arm". One could again argue that adding this information would add historical information to the feature, but it is clear that the abstract nature of the question is hiding important phylogenetic (and also typological) information from us.

It seems therefore, that, instead of asking whether or not there is a distinction between "arm" and "hand", it would make much more sense to trace the cognacy (or homology) of the expressions for "arm" and "hand" across all taxa (languages, dialects), and think of ways how this could be scored and modeled by phylogenetic analyses. The structural data framework with its features based on simple yes-no questions therefore inevitably leads to a misinterpetation of processes when analyzing the data with phylogenetic software.

The need for exploratory data analysis

In reality, structural (or other) data sets in linguistics face problems similar to the ones palaeontologists face when trying to establish phylogenetic relationships between fossils (extinct organisms) — the probability for a mutation (visible change) is largely unknown, and differs not only from character to character but also within the same characters. A state 0, 1, 2 etc. may have a higher probability to manifest (or get lost) in one lineage than in another.

In addition, the linguistic problems recur in a similar way to that of biologists working close to and below the species level (see also Guido's post on population dynamics and individual-based fossil phylogenies) — reticulation is rather the rule than the exception, as similarity is triggered by contact,  so that horizontal processes, not inheritance, may dominate evolutionary dynamics. Thus, the diversity pattern cannot be modeled by a tree alone. Establishing explicit probabilistic frameworks to deal with this may not only be difficult but even impossible (given the available data). Meanwhile, however, one can embrace exploratory data analysis as a heuristic tool.

So, let's look at the example. As in the original paper, we used the binary matrix of the 21 characters to infer a planar, 2-dimensional (meta-)phylogenetic network, a Neighbor-net splits graph. The resulting graph is a longitudinally inflated spider-web, with its endpoints defined by the southern Chinese dialects (e.g. Guangzhou, Nanning, Taishan) and the north-central (eg. Linxia and Xining) dialects. The latter are significantly closer (geographically and data-wise) to the Bejing version of Chinese.

Figure 10: The Neighbor-net based on simple mean (Hamming) pairwise binary character distances

The first thing to note is that the matrix includes dialects that are indistinct (green stars) for all 21 characters, and some that are geographically and data-wise very similar to each other, while being distinct from all others (green ovals). In biology, we call this (taxic, lineage-)coherence. In addition to Linxia and Xining, we have Nanchang and Lichuan characterized by elongated ('tree-like') terminal edge-bundles. These obviously represent closely related dialects sharing a long(er) common history.

Others have more than one possible closest relative. For instance, Liuzhou may share quite a few features with Guangzhou, but it is equally close to the Nanchang-Lichuan pair (yellow fields). Dongtai (orange star) is unique, but its 'neighborhood' (orange-ish brackets) as defined by shared edge-bundles that include Changsha (which again is most related to Jiujang) and Taiyuan plus Baotou, the latter two substantially closer to the Bejing (red star) group.

Similar to Dongtai, and also connected to the central part of the graph, are dialects with long-terminal branches (edges). Hefeng (blue star) is substantially different from Dongtai, and only has one further dialect in its neighborhood (blue bracket), Wangrong, a close relative of the Bejing group. The Wuhan, Chengdu, and Guiyang (gray field) dialects appear, on the other hand, to be completely isolated.

As explained above, there are different processes, vertical and horizontal ones, that may trigger similarity, and we want to get an idea as to which character may be influenced by which process. From the graph, several aspects are obvious:

• geographic closeness plays a major role,
• the signal provided by the data is not tree-like,
• the data is highly homoplastic, and includes internal conflict.

Not so obvious is whether this situation is due to random or evolutionary directed similarity, or reticulation. Since the graph is planar, and puts the Chinese dialects in a circular order, we can order the character matrix accordingly to see how the traits form groups (which could be called cliques in this context). In the next step, we can then map each character onto this network, to see how well they fit with the overall similarity pattern. We showed this above for p-6 (hand-arm-distinction, one split), and here we add a character with quite a poor fit, p-17 (syntactic-diachronic), "give" as a disposal marker.

Figure 11: Character mapping for p-17 (filled dots, "give" used as disposal marker; empty, not used), with the p-6 split indicated as well. Red, splits (taxon bipartitions defined by character cliques) that have no corresponding edge-bundle (neighborhood); blue, splits with neighborhood; green, unique, isolated change (deviation from the rule) within the neighborhood.

The number of inferred mutations in the map uses Ockham’s Razor, upon which parsimony (tree and network) inference relies as well. Using such a map, we can even provide an estimate for how likely (qualitatively spoken) a change is under the assumption that neighborhoods in the graph represent either exchange (homogenization) between closely related dialects or are inherited, reflecting both horizontal and vertical relatedness. Mapping characters on a 2-dimensional network allows finding a scenario beyond a single tree hypothesis.

For p-6, we need just one change (i.e. loss in all more south-bound dialects), but we don't find an edge bundle corresponding to this unique change. Given what we discussed above about p-6, we have more independent losses than the simple reconstructed one. Social preference or general contact for retaining the primitive state of having two words could explain why dialects closer to the Beijing dialect area have a "0", although not all are closely related in general.

For p-17, we need at least four (independent) changes from "0" → "1", two of which have a corresponding edge bundle (blue, Nanchang plus Lichuan, Changsha plus Dongtai), one isolated (green, Luoyang), and one without a corresponding edge bundle (Wuhan and Hefeng dialects). The (equally parsimonious) alternative for p-17 would be a series of gains and losses, with the same number of steps:

Figure 12: Alternative scenario for p-17.

This is where one needs to consider additional knowledge about the probability of getting or retaining a certain feature. The state shared by most dialects across the entire net is “0”, irrespective of overall similarity, which would make it a natural pick for the primitive state. Thus, assuming four (or more) changes from 0 → 1 (acquisition of the queried feature), rather than two independent acquisitions (starting with the Beijing group; note, the position of the root will not change the number of needed changes), then a loss (1 → 0) in many southbound dialects and a re-gain (0 → 1) in the Nanchang + Lichuan dialects.

The same assessment can be made for all of the characters, and we end up with something like this:

Figure 13: Fully annotated split network of the data. Changes relating to edge-bundles accordingly colored, arc indicate changes without a corresponding edge-bundle. Note, the prominent yellow split that defines a neighborhood of dialects most similar to the Beijing dialect, albeit there is no character supporting this edge. The rather poor fit of many character splits (cliques) with edge-bundles relate to the fact that we visualize a highly complex diversification (multi-dimensional processes) using a planar, 2-dimensional graph.

While this figure may be confusing at first sight, it comprehensively shows what the characters contribute to the overall graph. We can discriminate more-likely from less-likely mutations (how many changes are needed at least), but also the character assemblies shared by putatively closely related dialects.

• p-3 and p-11 are a typical feature of Guangzhou and allied dialects within the southern Chinese complex. p-3 is also present in Lichuan, and p-11 in Jixi (thus in not so distant dialects).
• Features p-6 to p-9, p-16, and p-19 form a diagnostic suite for the Guangzhou dialects and other dialects related to them in the one or other fashion and distinguish them from, e.g., the Beijing group
• The latter, the Beijing group, has fewer diagnostic character assemblies. One characteristic sequence could be p-1, p-2, p-12, p-14, but this includes three features with a minimum of 3+ changes. Similarity here is mostly the result of a lack of (potentially) derived features (hence, the character-unsupported yellow edge-bundle defining a Beijng-including neighborhood)

Outlook and summary

In this re-investigation, we have, once more, commented on the problems we see with the use of structural features for the purpose of historical language comparison and phylogonetic reconstruction. We see the major problems in the (often) unfortunate choice of question, resulting in elicitations of features that cannot be easily modeled with current software for phylogenetic analyses. It is important to keep in mind, in linguistics and phylogenetics, that we can infer trees or networks based on data of no matter what quality and information content. But before we present the result, we should have taken a look at the primary data.

• Does it fit with the resulting graph, or not?
• Where does it fit, and where not?

In the context of our critique of linguistic questionnaires, the mapping strategy discussed above opens a potential avenue to identify:

• stable / unstable features (geographically or evolution-wise) and
• coherent / incoherent features.

Based on this, we can then inquire as to which degree language (or dialect) groups influenced, stabilized or modified each other by geographic proximity.

Inference-wise, the natural next step would be to use the information about the minimum number of necessary changes to counter-weight characters. This would eventually allow to use median networks (and related) approaches on the data, which is currently the only way to explicitly identify ancestors using phylogenetic reconstructions. With the current matrices, the extreme homoplasy makes an unweighted application of median networks and related methods impossible.

References

Forkel, R., J.-M. List, S. Greenhill, C. Rzymski, S. Bank, M. Cysouw, H. Hammarström, M. Haspelmath, G. Kaiping, and R. Gray (2018) Cross-Linguistic Data Formats, advancing data sharing and re-use in comparative linguistics. Scientific Data 5.180205: 1-10.

List, J.-M., M. Cysouw, and R. Forkel (2016) Concepticon. A resource for the linking of concept lists. In: Proceedings of the Tenth International Conference on Language Resources and Evaluation, pp. 2393-2400.

List, J.-M., M. Walworth, S. Greenhill, T. Tresoldi, and R. Forkel (2018) Sequence comparison in computational historical linguistics. Journal of Language Evolution 3.2: 130–144.

Norman, J. (2003) The Chinese dialects. Phonology. In: Thurgood, G. and R. LaPolla (eds.): The Sino-Tibetan languages. Routledge: London and New York, pp. 72-83.

Szeto, P., U. Ansaldo, and S. Matthews (2018) Typological variation across Mandarin dialects: An areal perspective with a quantitative approach. Linguistic Typology 22.2: 233-275.

Supplementary data

The data we used to create the analyses and figures provided in this post are available at https://github.com/cldf-datasets/szetosinitic/tree/master/examples