Unattested character states

In an earlier post from January 2016, I argued that it is important to account for directional processes when modeling language history through character-state evolution. In previous papers (List 2016; Chacon and List 2015), I  tried to show that this can be easily done with asymmetric step matrices in a parsimony framework. Only later did I realize that this is nothing new for biologists who work on morphological characters, thus supporting David's claim that we should not compare linguistic characters with the genotype, but with the phenotype (Morrison 2014). Early this year, a colleague introduced me to Mk-models in phylogenetics, which were first introduced by Lewis (2001)) and allow analysis of multi-state characters in a likelihood framework.

What was surprising for me is that it seems that Mk-models seem to outperform parsimony frameworks, although being much simpler than elaborate step-matrices defined for morphological characters (Wright and Hillis 2014). Today, I read that a recent paper by Wright et al. (2016) even shows how asymmetric transition rates can be handled in likelihood frameworks.

Being by no means an expert in phylogenetic analyses, especially not in likelihood frameworks, I tend to have a hard time understanding what is actually being modeled. However, if I correctly understand the gist of the Wright et al. paper, it seems that we are slowly approaching a situation in which more complex scenarios of lexical character evolution in linguistics no longer need to rely on parsimony frameworks.

But, unfortunately, we are not there yet; and it is even questionable whether we will ever be. The reason is that all multi-state models that have been proposed so far only handle transitions between attested characters: unattested characters can neither be included in the analyses nor can they be inferred.

I have pointed to this problem in some previous blogposts, the last one published in June, where I mentioned Ferdinand de Saussure, (1857-1913), who postulated two unattested consonantal sounds for Indo-European (Saussure 1879), of which one was later found to have still survived in Hittite, a language that was deciphered and shown to be Indo-European only about 30 years later (Lehmann 1992: 33).

The fact that it is possible to use our traditional methods to infer unattested sounds from circumstantial evidence, but not to include our knowledge about them into phylogenetic analyses, is a huge drawback. Potentially even greater are the situations where even our traditional methods do not allow us to infer unattested data. Think, for example, of a word that was once present in some language but was later completely lost. Given the ephemeral nature of human language, we have no way to know this, but we know very well that it easily happens when just thinking of some terms used for old technology, like walkman or soon even iPod, which the younger generations have never heard about.

Colleagues with whom I have discuss my concerns in this regard are often more optimistic than I am, saying that even if the methods cannot handle unattested characters they could still find the major signal, and thus tell us at least the general tendency as to how a language family evolved. However, for classical linguists, who can infer quite a lot using the laborious methods that still need to be applied manually, it leaves a sour taste, if they are told that the analysis deliberately ignored crucial aspects of the processes and phenomena they understand very well. For example, if we detect that some intelligence test is right in about 80% of all cases, we would also abstain from using it to judge who we allow to take up their studies at university.

I also think that it is not a satisfying solution for the analysis of morphological data in biology. It is probably quite likely that some ancient species had certain traits which later evolved into the traits we observe which are simply no longer attested anywhere, either in fossils or in the genes. I also wonder how well phylogenetic frameworks generally account for the fact that what the evidence we are left with may reflect much less of what was once there.

In Chacon and List (2015), we circumvent the problem by adding ancestral but unattested sounds to the step matrices in our parsimony analysis. This is of course not entirely satisfactory, as it adds a heavy bias to the analysis of sound change, which no longer tests for all possible solutions but only for the ones we fed into the algorithm. For sound change, it may be possible to substantially expand the character space by adding sounds attested across the world's languages, and then having the algorithms select the most probable transitions. But given that we still barely know anything about general transition probabilities of sound change, and that databases like Phoible (Moran 2015)  list more than 2,000 different sounds for a bit more than 2,000 languages, it seems like a Sisyphean challenge to tackle this problem consistently.

What can we do in the meantime? Not very much, it seems. But we can still try to improve our methods in baby steps, trying to get a better understanding of the major and minor processes in linguistic and biological evolution; and not forgetting that, although I was only talking about phylogenetic tree reconstruction, in the end we also want to have all of this done in network approaches.

References

• Chacon, T. and J.-M. List (2015) Improved computational models of sound change shed light on the history of the Tukanoan languages. Journal of Language Relationship 13: 177-204.
• Lehmann, W. (1992) Historical linguistics. An Introduction. Routledge: London.
• Lewis, P. (2001) A likelihood approach to estimating phylogeny from discrete morphological character data. Systematic Biology 50: 913-925.
• List, J.-M. (2016) Beyond cognacy: Historical relations between words and their implication for phylogenetic reconstruction. Journal of Language Evolution 1: 119-136.
• Moran, S., D. McCloy, and R. Wright (eds) (2014) PHOIBLE Online. Max Planck Institute for Evolutionary Anthropology: Leipzig.
• Morrison, D.A. (2014) Are phylogenetic patterns the same in anthropology and biology? bioRxiv.
• Saussure, F. (1879) Mémoire sur le système primitif des voyelles dans les langues indo-européennes. Teubner: Leipzig.
• Wright, A. and D. Hillis (2014) Bayesian analysis using a simple likelihood model outperforms parsimony for estimation of phylogeny from discrete morphological data. PLoS ONE 9.10. e109210.
• Wright, A., G. Lloyd, and D. Hillis (2016) Modeling character change heterogeneity in phylogenetic analyses of morphology through the use of priors. Systematic Biology 65: 602-611.

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

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

Background

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

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

Do the data support a tree?

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

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

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

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

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

Do the data require a tree?

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

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

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

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

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

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

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

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

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

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

References

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

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

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

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

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

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

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

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

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

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

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

Models and processes in phylogenetic reconstruction

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

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

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

Lexical borrowing: direct transfer

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

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

Lexical borrowing: meaning transfer

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

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

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

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

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

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

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

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

References

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