Monday, October 28, 2019

Typology of sound change (Open problems in computational diversity linguistics 9)

We are getting closer to the end of my list of open problems in computational diversity linguistics. After this post, there is only one left, for November, followed by an outlook and a wrap-up in December.

In last month's post, devoted to the Typology of semantic change, I discussed the general aspects of a typology in linguistics, or — to be more precise — how I think that linguists use the term. One of the necessary conditions for a typology to be meaningful is that the phenomenon under questions shows enough similarities across the languages of the world, so that patterns or tendencies can be identified regardless of the historical relations between human languages.

Sound change in this context refers to a very peculiar phenomenon observed in the change of spoken languages, by which certain sounds in the inventory of a given language change their pronunciation over time. This often occurs across all of the words in which these sounds recur, or across only those sounds which appear to occur in specific phonetic contexts.

As I have discussed this phenomenon in quite a few past blog posts, I will not discuss it any more here, but I will rather simply refer to the specific task, that this problem entails:
Assuming (if needed) a given time frame, in which the change occurs, establish a general typology that informs about the universal tendencies by which sounds occurring in specific phonetic environments are subject to change.
Note that my view of "phonetic environment" in this context includes an environment that would capture all possible contexts. When confronted with a sound change that seems to affect a sound in all phonetic contexts, in which the sound occurs in the same way, linguists often speak of "unconditioned sound change", as they do not find any apparent condition for this change to happen. For a formal treatment, however, this is unsatisfying, since the lack of a phonetic environment is also a specific condition of sound change.

Why it is hard to establish a typology of sound change

As is also true for semantic change, discussed as Problem 8 last month, there are three major reasons why it is hard to establish a typology of sound change. As a first problem, we find, again, the issue of acquiring the data needed to establish the typology. As a second problem, it is also not clear how to handle the data appropriately in order to allow us to study sound change across different language families and different times. As a third problem, it is also very difficult to interpret sound change data when trying to identify cross-linguistic tendencies.

Problem 1

The problem of acquiring data about sound change processes in sufficient size is very similar to the problem of semantic change: most of what we know about sound change has been inferred by comparing languages, and we do not know how confident we can be with respect to those inferences. While semantic change is considered to be notoriously difficult to handle (Fox 1995: 111), scholars generally have more confidence in sound change and the power of linguistic reconstruction. The question remains, however, as to how confident we can really be, which divides the field into the so-called "realists" and the so-called "abstractionalists" (see Lass 2017 for a recent discussion of the debate).

As a typical representative of abstractionalism in linguistic reconstruction, consider the famous linguist Ferdinand de Saussure, who emphasized that the real sound values which scholars reconstructed for proposed ancient words in unattested languages like, for example, Indo-European, could as well be simply replaced by numbers or other characters, serving as identifiers (Saussure 1916: 303). The fundamental idea here, when reconstructing a word for a given proto-language, is that a reconstruction does not need to inform us about the likely pronunciation of a word, but rather about the structure of the word in contrast to other words.

This aspect of historical linguistics is often difficult to discuss with colleagues from other disciplines, since it seems to be very peculiar, but it is very important in order to understand the basic methodology. The general idea of structure versus substance is that, once we accept that the words in a languages are built by drawing letters from an alphabet, the letters themselves do not have a substantial value, but have only a value in contrast to other letters. This means that a sequence, such as "ABBA" can be seen as being structurally identical with "CDDC", or "OTTO". The similarity should be obvious: we have the same letter in the beginning and the end of each word, and the same letter being repeated in the middle of each word (see List 2014: 58f for a closer discussion of this type of similarity).

Since sequence similarity is usually not discussed in pure structural terms, the abstract view of correspondences, as it is maintained by many historical linguists, is often difficult to discuss across disciplines. The reason why linguists tend to maintain it is that languages tend to change not only their words by mutating individual sounds, but that whole sound systems change, and new sounds can be gained during language evolution, or lost (see my blogpost from March 2018 for a closer elaboration of the problem of sound change).

It is important to emphasize, however, that despite prominent abstractionalists such as Ferdinand de Saussure (1857-1913), and in part also Antoine Meillet (1866-1936), the majority of linguists think more realistically about their reconstructions. The reason is that the composition of words based on sounds in the spoken languages of the world usually follows specific rules, so-called phonotactic rules. These may vary to quite some degree among languages, but are also restricted by some natural laws of pronunciability. Thus, although languages may show impressively long chains of one consonant following another, there is a certain limit to the number of consonants that can follow each other without a vowel. Sound change is thus believed to originate roughly in either production (speakers want to pronounce things in a simpler, more convenient way) or perception (listeners misunderstand words and store erroneous variants, see Ohala 1989 for details). Therefore, a reconstruction of a given sound system based on the comparison of multiple languages gains power from a realistic interpretation of sound values.

The problem with the abstractionalist-realist debate, however, is that linguists usually conduct some kind of a mixture between the two extremes. That means that they may reconstruct very concrete sound values for certain words, where they have very good evidence, but at the same time, they may come up with abstract values that serve as place holders in lack of better evidence. The most famous example are the Indo-European "laryngeals", whose existence is beyond doubt for most historical linguistics, but whose sound values cannot be reconstructed with high reliability. As a result, linguists tend to spell them with subscript numbers as *h₁, *h₂, and *h₃. Any attempt to assemble data about sound change processes in the languages of the world needs to find a way to cope with the different degrees of evidence we find in linguistic analyses.

Problem 2

This leads us directly to our second problem in handling sound change data appropriately in order to study sound change processes. Given that many linguists propose changes in the typical A > B / C (A becomes B in context C) notation, a possible way of thinking about establishing a first database of sound changes would consist of typing these changes from the literature and making a catalog out of it. Apart from the interpretation of the data in abstractionalist-realist terms, however, such a way of collecting the data would have a couple of serious shortcomings.

First, it would mean that the analysis of the linguist who proposed the sound change is taken as final, although we often find many debates about the specific triggers of sound change, and it is not clear whether there would be alternative sound change rules that could apply just as well (see Problem 3 on the task of automatic sound law induction for details). Second, as linguists tend to report only what changes, while disregarding what does not change, we would face the same problem as in the traditional study of semantic change: the database would suffer from a sampling bias, as we could not learn anything about the stability of sounds. Third, since sound change depends not only on production and perception, but also on the system of the language in which sounds are produced, listing sounds deprived of examples in real words would most likely make it impossible to take these systemic aspects of sound change into account.

Problem 3

This last point now leads us to the third general difficulty, the question of how to interpret sound change data, assuming that one has had the chance to acquire enough of it from a reasonably large sample of spoken languages. If we look at the general patterns of sound change observed for the languages of the world, we can distinguish two basic conditions of sound change, phonetic conditions and systemic conditions. Phonetic conditions can be further subdivided into articulatory (= production) and acoustic (= perception) conditions. When trying to explain why certain sound changes can be observed more frequently across different languages of the world, many linguists tend to invoke phonetic factors. If the sound p, for example, turns into an f, this is not necessarily surprising given the strong similarity of the sounds.

But similarity can be measured in two ways: one can compare the similarity with respect to the production of a sound by a speaker, and with respect to the perception of the sound by a listener. While production of sounds is traditionally seen as the more important factor contributing to sound change (Hock 1991: 11), there are clear examples for sound change due to misperception and re-interpretation by the listeners (Ohala 1989: 182). Some authors go as far as to claim that production-driven changes reflect regular internal language change (which happens gradually during acquisition, or (depending on the theory) also in later stages (Bybee 2002), while perception-based changes rather reflect change happening in second language acquisition and language contact (Mowrey and Pagliuca 1995: 48).

While the interaction of production and perception has been discussed in some detail in the linguistic literature, the influence of systemic factors has so far been only rarely regarded. What I mean by this factor is the idea that certain changes in language evolution may be explained exclusively as resulting from systemic constellations. As a straightforward example, consider the difference in design space for the production of consonants, vowels, and tones. In order to maintain pronunciability and comprehensiblity, it is useful for the sound system of a given language to fill in those spots in the design space that are maximally different from each other. The larger the design space and the smaller the inventory, the easier it is to guarantee its functionality. Since design spaces for vowels and tones are much smaller than for consonants, however, these sub-systems are more easily disturbed, which could be used to explain the presence of chain shifts of vowels, or flip- flop in tone systems (Wang 1967: 102). Systemic considerations play an increasingly important role in evolutionary theory, and, as shown in List et al. (2016), also be used as explanations for phenomena as strange as the phenomenon of Sapir's drift (Sapir 1921).

However, the crucial question, when trying to establish a typology of sound change, is how these different effects could be measured. I think it is obvious that collections of individual sound changes proposed in the literature are not enough. But what data would be sufficient or needed to address the problem is not entirely clear to me either.

Traditional approaches

As the first traditional approach to the typology of sound change, one should mention the intuition inside the heads of the numerous historical linguists who study particular language families. Scholars trained in historical linguistics usually start to develop some kind of intuition about likely and unlikely tendencies in sound change, and in most parts they also agree on this. The problem with this intuition, however, is that it is not explicit, and it seems even that it was never the intention of the majority of historical linguists to make their knowledge explicit. The reasons for this reluctance with respect to formalization and transparency are two-fold. First, given that every individual has invested quite some time in order to grow their intuition, it is possible that the idea of having a resource that distributes this intuition in a rigorously data-driven and explicit manner yields the typical feeling of envy in quite a few people who may then think: «I had to invest so much time in order to learn all this by heart. Why should young scholars now get all this knowledge for free?» Second, given the problems outlined in the previous section, many scholars also strongly believe that it is impossible to formalize the problem of sound change tendencies.

The by far largest traditional study of the typology of sound change is Kümmel's (2008) book Konsonantenwandel (Consonant Change), in which the author surveys sound change processes discussed in the literature on Indo-European and Semitic languages. As the title of the book suggests, it concentrates on the change of consonants, which are (probably due to the larger design space) also the class of sounds that shows stronger cross-linguistic tendencies. The book is based on a thorough inspection of the literature on consonant change in Indo-European and Semitic linguistics. The procedure by which this collection was carried out can be seen as the gold standard, which any future attempt of enlarging the given collection should be carried out.

What is specifically important, and also very difficult to achieve, is the harmonization of the evidence, which is nicely reflected in Kümmel's introduction, where he mentions that one of the main problems was to determine what the scholars actually meant with respect to phonetics and phonology, when describing certain sound changes (Kümmel 2008: 35). The major drawback of the collection is that it is not (yet) available in digital form. Given the systematicity with which the data was collected, it should be generally possible to turn the collection into a database; and it is beyond doubt that this collection could offer interesting insights into certain tendencies of sound change.

Another collection of sound changes collected from the literature is the mysterious Index Diachronica, a collection of sound changes collected from various language families by a person who wishes to remain anonymous. Up to now, this collection even has a Searchable Index that allows scholars to click on a given sound and to see in which languages this sound is involved in some kind of sound change. What is a pity about the resource is that it is difficult to use, given that one does not really know where it actually comes from, and how the information was extracted from the sources. If the anonymous author would only decide to put it (albeit anonymously, or under a pseudonym) on a public preprint server, such as, for example, Humanities Commons, this would be excellent, as it would allow those who are interested in pursuing the idea of collecting sound changes from the literature an excellent starting point to check the sources, and to further digitize the resource.

Right now, this resource seems to be mostly used by conlangers, ie., people who create artificial languages as a hobby (or profession). Conlangers are often refreshingly pragmatic, and may come up with very interesting and creative ideas about how to address certain data problems in linguistics, which "normal" linguists would refuse to do. There is a certain tendency in our field to ignore certain questions, either because scholars think it would be too tedious to collect the data to address that problem, or they consider it impossible to be done "correctly" from the start.

As a last and fascinating example, I have to mention the study by Yang and Xu (2019), in which the authors review studies of concrete examples of tone change in South-East Asian languages, trying to identify cross-linguistic tendencies. Before I read this study, I was not aware that tone change had at all been studied concretely, since most linguists consider the evidence for any kind of tendency far too shaky, and reconstruct tone exclusively as an abstract entity. The survey by Yang and Xu, however, shows clearly that there seem to be at least some tendencies, and that they can be identified by invoking a careful degree of abstraction when comparing tone change across different languages.

For the detailed reasons outlined in the previous paragraph, I do not think that a collection of sound change examples from the literature addresses the problem of establishing a typology of sound change. Specifically, the fact that sound change collections usually do not provide any tangible examples or frequencies of a given sound change within the language where it occurred, but also the fact that they do not offer any tendencies of sounds to resist change, is a major drawback, and a major loss of evidence during data collection. However, I consider these efforts as valuable and important contributions to our field. Given that they allow us to learn a lot about some very general and well-confirmed tendencies of sound change, they are also an invaluable source of inspiration when it comes to working on alternative approaches.

Computational approaches

To my knowledge, there are no real computational approaches to the study of sound change so far. What one should mention, however, are initial attempts to measure certain aspects of sound change automatically. Thus, Brown et al. (2013) measure sound correspondences across the world's languages, based on a collection of 40-item wordlists for a very large sample of languages. The limitations of this study can be found in the restricted alphabet being used (all languages are represented by a reduced transcription system of some 40 letters, called the ASJP code. While the code originally allowed representing more that just 40 sounds, since the graphemes can be combined, the collection was carried out inconsistently for different languages, which has now led to the situation that the majority of computational approaches treat each letter as a single sound, or consider only the first element of complex grapheme combinations.

While sound change is a directional process, sound correspondences reflect the correspondence of sounds in different languages as a result of sound change, and it is not trivial to extract directional information from sound correspondence data alone. Thus, while the study of Brown et al. is a very interesting contribution, also providing a very straightforward methodology, it does not address the actual problem of sound change.

The study also has other limitations. First, the approach only measures those cases where sounds differ in two languages, and thus we have the same problem that we cannot tell how likely it is that two identical sounds correspond. Second, the study ignores phonetic environment (or context), which is an important factor in sound change tendencies (some sound changes, for example, tend to occur only in word endings, etc.). Third, the study considers only sound correspondences across language pairs, while it is clear that one can often find stronger evidence for sound correspondences when looking at multiple languages (List 2019).

Initial ideas for improvement

What we need in order to address the problem of establishing a true typology of sound change processes, are, in my opinion:
  1. a standardized transcription system for the representation of sounds across linguistic resources,
  2. increased amounts of readily coded data that adhere to the standard transcription system and list cognate sets of ancestral and descendant languages,
  3. good, dated phylogenies that allow to measure how often sound changes appear in a certain time frame,
  4. methods to infer the sound change rules (Problem 3), and
  5. improved methods for ancestral state reconstruction that would allow us to identify sound change processes not only for the root and the descendant nodes, but also for intermediate stages.
It is possible that even these five points are not enough yet, as I am still trying to think about how one should best address the problem. But what I can say for sure is that one needs to address the problem step by step, starting with the issue of standardization — and that the only way to account for the problems mentioned above is to collect the pure empirical evidence on sound change, not the summarized results discussed in the literature. Thus, instead of saying that some source quotes that in German, the t became a ts at some point, I want to see a dataset that provides this in the form of concrete examples that are large enough to show the regularity of the findings and ideally also list the exceptions.

The advantage of this procedure is that the collection is independent of the typical errors that usually occur when data are collected from the literature (usually also by employing armies of students who do the "dirty" work for the scientists). It would also be independent of individual scholars' interpretations. Furthermore, it would be exhaustive — that is, one could measure not only the frequency of a given change, but also the regularity, the conditioning context, or the systemic properties

The disadvantage is, of course, the need to acquire standardized data in a large-enough size for a critical number of languages and language families. But, then again, if there were no challenges involved in this endeavor, I would not present it as an open problem of computational diversity linguistics.


With the newly published database of Cross-Linguist Transcription Systems (CLTS, Anderson et al. 2018), the first step towards a rigorous standardization of transcription systems has already been made. With our efforts towards a standardization of wordlists that can also be applied in the form of a retro-standardization to existing data (Forkel et al. 2018), we have proposed a further step of how lexical data can be collected efficiently for a large sample of the worlds' spoken languages (see also List et al. 2018). Work on automated cognate detection and workflows for computer-assisted language comparison has also drastically increased the efficiency of historical language comparison.

So, we are advancing towards a larger collection of high-quality and historically compared datasets; and it is quite possible that we will, in a couple of years from now, arrive at a point where the typology of sound change is no longer a dream by me and many colleagues, but something that may actually be feasible to extract from cross-linguistic data that has been historically annotated. But until then, many issues still remain unsolved; and in order to address these, it would be useful to work towards pilot studies, in order to see how well the ideas for improvement, outlined above, can actually be implemented.


Anderson, Cormac and Tresoldi, Tiago and Chacon, Thiago Costa and Fehn, Anne-Maria and Walworth, Mary and Forkel, Robert and List, Johann-Mattis (2018) A Cross-Linguistic Database of Phonetic Transcription Systems. Yearbook of the Poznań Linguistic Meeting 4.1: 21-53.

Brown, Cecil H. and Holman, Eric W. and Wichmann, Søren (2013) Sound correspondences in the worldś languages. Language 89.1: 4-29.

Bybee, Joan L. (2002) Word frequency and context of use in the lexical diffusion of phonetically conditioned sound change. Language Variation and Change 14: 261-290.

Forkel, Robert and List, Johann-Mattis and Greenhill, Simon J. and Rzymski, Christoph and Bank, Sebastian and Cysouw, Michael and Hammarström, Harald and Haspelmath, Martin and Kaiping, Gereon A. and Gray, Russell D. (2018) Cross-Linguistic Data Formats, advancing data sharing and re-use in comparative linguistics. Scientific Data 5.180205: 1-10.

Fox, Anthony (1995) Linguistic Reconstruction. An Introduction to Theory and Method. Oxford: Oxford University Press.

Hock, Hans Henrich (1991) Principles of Historical Linguistics. Berlin: Mouton de Gruyter.

Kümmel, Martin Joachim (2008): Konsonantenwandel [Consonant change]. Wiesbaden:Reichert.
Lass, Roger (2017): Reality in a soft science: the metaphonology of historical reconstruction. Papers in Historical Phonology 2.1: 152-163.

List, Johann-Mattis (2014) Sequence Comparison in Historical Linguistics. Düsseldorf: Düsseldorf University Press.

List, Johann-Mattis and Pathmanathan, Jananan Sylvestre and Lopez, Philippe and Bapteste, Eric (2016) Unity and disunity in evolutionary sciences: process-based analogies open common research avenues for biology and linguistics. Biology Direct 11.39: 1-17.

List, Johann-Mattis and Greenhill, Simon J. and Anderson, Cormac and Mayer, Thomas and Tresoldi, Tiago and Forkel, Robert (2018) CLICS². An improved database of cross-linguistic colexifications assembling lexical data with help of cross-linguistic data formats. Linguistic Typology 22.2: 277-306.

List, Johann-Mattis (2019): Automatic inference of sound correspondence patterns across multiple languages. Computational Linguistics 1.45: 137-161.

Mowrey, Richard and Pagliuca, William (1995) The reductive character of articulatory evolution. Rivista di Linguistica 7: 37–124.

Ohala, J. J. (1989) Sound change is drawn from a pool of synchronic variation. In: Breivik, L. E. and Jahr, E. H. (eds.) Language Change: Contributions to the Study of its Causes. Berlin: Mouton de Gruyter., pp.173-198.

Sapir, Edward (1921[1953]) Language. An Introduction to the Study of Speech.

de Saussure, Ferdinand (1916) Cours de linguistique générale. Lausanne: Payot.

William S-Y. Wang (1967) Phonological features of tone. International Journal of American Linguistics 33.2: 93-105.

Yang, Cathryn and Xu, Yi (2019) A review of tone change studies in East and Southeast Asia. Diachronica 36.3: 417-459.

Monday, October 21, 2019

Why the emperor has no clothes on – the mighty matK

In a recent paper published in PeerJ, Walker et al. (2019) take a close look at the complete plastome data of angiosperms. Although they don't find anything fundamentally new — well, at least not for those of us who have looked at the oligogene datasets we worked with — it's nice to see that somebody has been willing to do it in a very comprehensive way, and thereby published what some of us have long known:
  • A combined tree is not the sum of the genes that have been combined;
  • Single-gene trees can tell you very different stories.
Even if the overall branch support is pretty high, we always should be aware of internal data conflict.

When looked at closely, the emperor, in this case the Angiosperm Phylogeny Group (APG) complete plastome tree, maybe not be entirely naked, but is clothed in very few of the many garments at his disposal. Effectively the branches in the plastome reference tree draw their support from very few of the 79 genes/gene regions in the plastome.As Walker et al. note:
"Of the most commonly used markers, matK, greatly outperforms rbcL; however, the rarely used gene rpoC2 is the top-performing gene in every analysis. We find that rpoC2 reconstructs angiosperm phylogeny as well as the entire concatenated set of protein-coding chloroplast genes."

Fig. 1 from Walker et al. showing the (lack of) individual gene support for the angiosperm reference phylogeny.

However, there is one aspect of the paper that calls for a network-based blog post:
"Following the typical assumptions of chloroplast inheritance [i.e. that the entire plastome shares a common history being passed on solely by the mother in angiosperms], we would expect all genes in the plastomes to share the same evolutionary history. We would also expect all plastid genes to show similar patterns of conflict when compared to non-plastid inferred phylogenies ... Our results, however, discussed below, frequently conflict with these common assumptions about chloroplast inheritance and evolutionary history."
Getting incongruent branches in the single-gene trees, including a few highly supported ones, is taken as evidence for different histories potentially mixed within the plastome. Walker et al. give references for (potential) recombination and reticulation in plastomes.

I asked a question about whether this logic isn't a bit naive about tree inference. In their response, they pointed to the paper by Sullivan et al. (Mol. Biol. Evol. 2017) — these authors made test for recombination in Picea (spruce) plastomes, then split the complete plastomes into three structural units, and found two embedded conflicting phylogenies, as shown in the next figure.

Fig. 4 from Sullivan et al. (2017). F1 and F2 are structural regions comprising most of the large single-copy unit, the F3 the two (duplicate) inverted-repeat regions and the small single-copy unit of the Picea plastomes.

This seems to be a compelling case (but note the BS < 100 for conflicting critical branches). It is also quite possible, since gymnosperm plastomes, in contrast to angiosperms, may be paternally or bipartentally inherited. But, is it a valid assumption that each single-gene tree (or, in Sullivan et al.'s case, trees based on multigene regions) reflects the true tree of that gene or gene complex? That is, even if I assume that all of the genes in my matrix share the same history, must they support the same inferred tree?

Since I have worked a lot at low taxonomic levels, and often with other people's (plastid) data (during my entire career, I remained faithful to the nuclear-encoded ribosomal DNA spacers), my spontaneous answer would be: Absolutely not! Topological conflict may hint towards decoupled gene histories — it is a neccessary criterion but not a sufficient criterion.

There are quite a lot evolutionary scenarios that will lead to data inevitably supporting wrong branches, or false positives (see also Walker et al.'s discussion). Even if evolution is a strictly dichotomous process (which it clearly isn't):
  • low divergence may result in primitive (underived) sequences ('genetic symplesiomorphies') being shared by distant taxa
  • high divergence may result in saturation, which ultimately triggers branching artifacts
  • long isolation coupled with small active population sizes, repeated bottleneck / massive extinction events and/or lack of radiations will lead to sequences that are different from anything else in our data (in angiosperms, this phenomenon has a name: Ceratophyllum).
In fact, the very argument for angiosperm molecular phylogeneticists to move away from using single-gene phylogenies was that these first single-gene trees had branches that made little sense, especially when based on plastid data.

Single-gene trees will get things wrong. The more signal we add, usually by adding additional gene regions, the more we will reduce these errors (this is best-case scenario, but see Delsuc et al., Nature Rev. Genet. 2005). Thus, if some gene-trees conflict more with the combined tree than do others, it can be for two possible reasons:
  1. The conflicting genes had indeed different evolutionary histories. However, this would have to involve intra-plastome recombination and heteroplasmy, which so far have been very rarely documented in angiosperms.
  2. All genes had the same evolutionary history, but some of the data get more aspects of this true tree right than do others (and, of course, some are wrong that others get right).

And the matK said: "I'm your lord, follow my lead"

Walker et al. (all their scripts and results files can be found on github) find that it's only a few of the genes that essentially make up the combined tree. One of them is an old reliable pal of angiosperm phylogeneticists, the chloroplast matK gene. The literature is full of "multigene" trees that are effectively matK gene-trees using enlarged matrices. The matK determines a topology, and by adding genes that cannot compete with it (being too conserved, too variable or just inconsistently different), we re-enforce this topology. Only branches unresolved by matK will be further optimized using the added data.

Let's look at an example.

For the purpose of this post (and the follow-up), I'll use an old angiosperm matrix on stock (I know the quirks of this matrix). For analysis, I eliminated all of the OTUs with missing gene partitions, mainly to make sure that all of the trees and bootstrap (BS) pseudoreplicate trees have the same set of leaves, so I can summarize the tree samples using consensus networks.

Here's the my combined tree, unpartitioned.

Gray – current APG IV classification, "gold tree" (primary relationships within Mesangiospermae still a matter of debate)
And here is the fully partitioned one (over-parametrized; with each gene/codon position treated as data partition).

Essentially the same tree (some branches elongated, others shortened), eudicot clade and the Ceratophyllum-monocot clade swapped positions. Both trees have the same scale.

Even though my matrix includes only relatively few genes (just 21,550 sites), the tree gets the main aspects of the APG IV standard tree. The support for most of the branches is nearly unambiguous (irrespective of data partition), with the exception of some deep-down relationships within the Mesangiospermae (a long-standing issue, called the "dirty dozen"). The fact that the unpartioned and partitioned analysis agree for most part, indicates the signal in my matrix has no model-related issues (at least, none we could fix by using "better" models).

And the matK tree mirrors the fully partitioned tree, as shown here.

A tanglegram of the matK and the combined trees. Shown is the matK BS support for shared and conflicting edges. Orange asterisks, the monocot subtrees have the same structure but when using only matK, the conifer outgroup Podocarpus is nested deep within.

The similarity is indeed striking, in particular since the gene sample in the matrix comprises data from:
  • two of the nuclear-encoded ribosomal RNA genes (18S, 25S; biparentally inherited) that did follow partly different evolutionary trajectories, as e.g. well-studied in the case of Fagales (being a derived eudicot, not included in my matrix)
  • six chloroplast genes/gene regions (maternally inherited including the classics rbcL and matK but also the rpoC2, the most informative gene identified by Walker et al.)
  • three mitochondrial genes (also maternally inherited, but most mutations are, amino-acid-wise, synonymous, being concentrated at the third codon position).
The main things that matK get's wrong* in contrast to the combined tree are deep divergences represented by (very) short branches, in the part of the graph following the (very rapid) split of the mesangiosperm common ancestor (known as "Darwin's abominable mystery").

Also, it nests Podocarpus, the conifer in the outgroup, with unambiguous support in the monocots — which clearly is wrong, a false positive. Looking into the alignment, we can see that the reason for this is a mix of moderate-LBA (long-branch attraction) with missing-data-culling. To minimize LBA artifacts in the matrix originally used, I blanked out parts of the matK in the outgroup (which included a more derived conifer, Pinus, but also the extremely divergent gnetophytes); parts that were not straightforwardly alignable with the angiosperm matK.

The best way to illustrate internal signal conflict is, however, to directly show the BS Consensus network, not mapping support on two alternative topologies as seen in the tanglegram.

BS Consensus network based on 150 matK BS pseudoreplicates (numbers of necessary BS replicates determined by Pattengale et al.'s extended majority rule bootstop criterion implemented in RAxML)

When looking at BS << 100 and the boxes of competing splits in BS-support networks, it is important to keep in mind that low support can have two reasons:
  • Lack of decisive signal, because the BS pseudoreplicates will have (semi-)random or biased branching patterns; in the tree this surfaces usually as low (when random) to moderately high (when biased) support associated with (very) short branches.
  • Conflicting signals, ie. signals incompatible with a single tree; depending which site is eliminated or duplicated during resampling, the BS pseudoreplicate will show one or another topology; strong, deep conflict can surface in a tree by low support associated with (normally) long internal branches but also relatively high support for one alternative topology, the other only manifesting in very long terminal branches.
Regarding Walker et al.'s results, we now need to ask:
  1. Are the non-conflicted branches in the combined tree (major clades equal to the gold tree) the result of shared history of all of the included genes, or just that of the matK?
  2. Is the conflict with the combined tree and locally ambiguous signals due to a different history of the matK, located in the large single-copy unit, and the other genes, or just matK's inability to get certain things right?
In this case, all relatively high-supported conflicting matK splits are associated either with: (i) very short internal branches in the tree, the non-discriminative product of a fast ancient radiation, or (ii) are the result of an obvious data/branching artifact, ie. the misplaced Podocarpus.

So far, nothing challenges the assumption that the combined genes didn't follow the same history. Whether the other genes reveal something else, we'll see in my next post.

* or right: APG IV treats Ceratophyllum as the "probable sister of the eudicots" (see also Stevens' Angiosperm Phylogeny Website).

Monday, October 14, 2019

Some hitherto unkown genealogical trees of music

In last week's post, I discussed Petter Hellström's recent doctoral thesis: Trees of Knowledge: Science and the Shape of Genealogy. In this thesis he discusses three "genealogical tees" in detail. Augustin Augier’s tree of plant families and Félix Gallet’s family tree of languages have already been covered in this blog (you can look them up using the Search box, to the right), but Henri Montan Berton’s family tree of chords has not.

Indeed, the historical literature at large has pretty much ignored the idea of a genealogical tree being associated with music. Nevertheless, the tree itself is explicitly labeled a Genealogical Tree of Chords. This tree, and its predecessor by François Guillaume Vial, thus deserve examination.

Henri Montan Berton (1767–1844) is well known within the history of music; and his tree was published as an independent broadsheet as two (almost identical) editions in c. 1807 and 1815. It seems to have been produced as a teaching tool, as indeed were also the trees of Augier and Gallet. As Petter Hellström notes, for these authors "genealogy did not necessarily involve chronology or change ... the introduction of family trees into secular knowledge production had more to do with the needs of information management, visualisation and communication".

Berton himself states (translated from the French):
In composing the Genealogical Tree, one has has had the intention to present to the eye, at a single glance, the reunion of the great family of Chords, and to demonstrate to the eye that there is only one Primordial [Chord], and that it is the source of all Harmonies.
At the base of the tree is a fundamental bass note along with its 12th and 17th major — this was the harmonic series in 18th century music theory. From here the tree produces 8 branches above, each labeled (at the bottom) with a musical chord, and with another 20 chords labeled further up the branches (all highlighted by arrows at the left). The main trunk (denoted A) is labeled Perfect or Constant Chord. The eight branches are intended to show the relationships between "8 fundamental chords [bottom arrow] and 20 inverted chords [the upper arrows]".

The tree thus displays the harmonic relationships among the chords, rather than any sort of chronological development. It was devised as an aid to learning the fundamentals of music composition.

Berton was not the first to use this idea within music theory. Four decades earlier, in 1766, François Guillaume Vial (1725–?) had produced another broadsheet, this time labeled Genealogical Tree of Harmony.

Like Berton's tree, this is not about chronology, but is about "family relationships" in a different sense. Moreover, in this instance the branching aspect of the tree is abandoned, and the tree foliage is simply festooned with medallions, labeled with chords — it is the different sections of the tree's crown that show relationships, not different branches.

The objective here was to illustrate "the most natural order of harmonic modulation", once again devised as a teaching tool. The two compass roses at the bottom left and right show the circle of fifths (left), guiding horizontal modulation among the chords, and the circle of thirds (right), guiding vertical modulation among the chords.

Vial himself states (translated from the French):
This Genealogical Tree simplifies and allows those who are capable of intonation [to practice] the art of preluding not only on a leading note, but even to change between the most desired modulations of any instrument.
Hellström traces these uses of the "family tree" metaphor in music back to Jean-Philippe Rameau (1683–1764), an influential music theorist. Thus, he concludes that we should:
read the trees of Vial and Berton as graphical codifications of an already established metaphor and manner of thinking about harmony, especially as both authors were informed by Rameau in their understanding of harmony in the first place.
In constructing their respective tree diagrams, Berton and Vial both seized upon an already existing metaphor and made it visible on paper. Their trees are not 'genealogical' in the sense that they charted family history or cross-generational relationships, they are 'genealogical' in the sense that they depict presumably natural, organic relationships, in which every part has its place in the whole, and where every part can be referred back to a common source or root.
These trees do not, therefore, fit into the usual history of genealogical trees, as this blog recognizes them, denoting a chronological history. They, would, however, fir neatly into the post on Relationship trees drawn like real trees.

Monday, October 7, 2019

A recent thesis about Trees of Knowledge

Recently, Petter Hellström successfully defended his doctoral thesis:
Trees of Knowledge: Science and the Shape of Genealogy
Department of the History of Science and Ideas
Uppsala University, Sweden
The thesis itself is obviously of great interest to readers of this blog. It is not currently online, but you can obtain a printed or electronic copy by contacting:

Here is the abstract:
This study investigates early employments of family trees in the modern sciences, in order to historicise their iconic status and now established uses, notably in evolutionary biology and linguistics. Moving beyond disciplinary accounts to consider the wider cultural background, it examines how early uses within the sciences transformed family trees as a format of visual representation, as well as the meanings invested in them.
Historical writing about trees in the modern sciences is heavily tilted towards evolutionary biology, especially the iconic diagrams associated with Darwinism. Trees of Knowledge shifts the focus to France in the wake of the Revolution, when family trees were first put to use in a number of disparate academic fields. Through three case studies drawn from across the disciplines, it investigates the simultaneous appearance of trees in natural history, language studies, and music theory. Augustin Augier’s tree of plant families, Félix Gallet’s family tree of dead and living languages, and Henri Montan Berton’s family tree of chords served diverse ends, yet all exploited the familiar shape of genealogy.
While outlining how genealogical trees once constituted a more general resource in scholarly knowledge production — employed primarily as pedagogical tools — this study argues that family trees entered the modern sciences independently of the evolutionary theories they were later made to illustrate. The trees from post-revolutionary France occasionally charted development over time, yet more often they served to visualise organic hierarchy and perfect order. In bringing this neglected history to light, Trees of Knowledge provides not only a rich account of the rise of tree thinking in the modern sciences, but also a pragmatic methodology for approaching the dynamic interplay of metaphor, visual representation, and knowledge production in the history of science.
The trees of Augier and Gallet have been covered in this blog, but that of Berton has not. I will discuss it in the next post.