An outline history of phylogenetic trees and networks

This the 300th post on this blog, and so I thought we might have a bit of a summary. Here is the early history of phylogenetic trees and networks as we currently know it. There may, of course, be as yet undetected sources. Details of each of these historical notes (including illustrations) can be found elsewhere in this blog — you can use the search feature in the right side-bar to find them.

Biology

Genealogies as pedigrees (the history of individuals) have a long history. For example, they appear in inscriptions concerning the pharaohs of Ancient Egypt, although these are very imprecise and have caused many headaches for modern scholars. They appear as chains of ancestors and descendants in the Old Testament of the Christian Bible, often contradicting each other and claiming impossible lifespans. Most importantly for modern usage, they were employed in the New Testament to legitimize Jesus as the messiah foretold in the Old Testament. The first known illustration of this appeared in c.400 AD, and it was actually a network, as there were two lineages leading to Jesus (via both Joseph and Mary).

The apparent success of this application (later called the Tree of Jesse, pictures of which started appearing in the 10th century) has meant that both royalty and the nobility have subsequently used pedigrees to assert their own right to be regal and noble. The first known illustration of this is from c.1000 AD, in which Cunigunde of Luxembourg's ancestry was traced in a tree-like manner to include Charlemagne, thus legitimizing her claim to being royal.

Also, up until 1215 AD marriage within seven degrees of separation was not allowed by the christian church, and intestate inheritance applied the same relationship limit. So, a record of blood ties among relatives was often needed; and these started appearing in family bibles, for example. The first recorded tree-like illustrated pedigree was for Lambert of Saint-Omer, which appeared in 1122 AD in his personal copy of his book Liber Floridus.

It seems obvious, then, to also construct genealogies for groups of organisms, which we now call phylogenies (a word coined by Ernst Haeckel in 1866). The Great Chain of Being was for a long time the most popular iconography for relationships, mainly because it neatly tied in with the Christian philosophy of a chain of intellectual ideas, leading from pragmatic earthly concerns and culminating in the idealistic heavens. Humans were, of course, at the head of the chain of earthly beings, and capable of ascending to the heavens.

However, this did not work from a purely observational point of view. Observed pedigrees were not linear, but branched with each generation and often fused again via marriage. Furthermore, biodiversity (the patterns among groups of organisms) also seemed to have multiple relationships. This lead Vitaliano Donati in 1750 (Della Storia Naturale Marina dell' Adriatico) to suggest that:

In addition, the links of the chain are joined in such a way within the links of another chain, that the natural progressions should have to be compared more to a net than to a chain, that net being, so to speak, woven with various threads which show, between them, changing communications, connections, and unions. [from the original Italian]

He was not alone in this thought, although others chose different metaphors. For example, Carl von Linné in 1751 (Philosophia Botanica) wrote this:

All plants show affinities on either side, like territories in a geographical map. [from the original Latin]

Neither author published a reticulating diagram to illustrate their thoughts, although one of Linné's students subsequently produced a version of his ideas in 1792 (Caroli a Linné, Praelectiones in Ordines Naturales Plantarum).

So, it was Georges-Louis Leclerc, Comte de Buffon, who produced the first empirical phylogeny in 1755 (Histoire Naturelle Générale et Particulière, Tome V). This was a network showing the evolutionary origin of domesticated dog breeds. This was followed by Antoine Nicolas Duchesne in 1766 (Histoire Naturelle des Fraisiers), who produced a network showing the evolutionary origin of strawberry cultivars. In both cases the evolutionary process illustrated by the reticulations in the network was hybridization. Note that both of these diagrams refer to within-species genealogies, rather than to relationships between species; and neither author seems to have contemplated the idea of among-species phylogenies.

Thus, in both theory and practice modern phylogenetic metaphors started as networks, not trees. It was Peter Simon Pallas in 1776 (Elenchus Zoophytorum) who first suggested using a tree as a simplified metaphor:

As Donati has already judiciously observed, the works of Nature are not connected in series in a Scale, but cohere in a Net. On the other hand, the whole system of organic bodies may be well represented by the likeness of a tree that immediately from the root divides both the simplest plants and animals, [but they remain] variously contiguous as they advance up the trunk, Animals and Vegetables; [from the origina Latin]

Again, no diagram was forthcoming to illustrate this. It was Jean-Baptiste Pierre Antoine de Monet, Chevalier de Lamarck, who finally produced an empirical phylogeny in 1809 (Philosophie Zoologique). This was a small tree showing the evolutionary relationships among the major groups of animals. However, it represented what we would now call transformational evolution, as Lamarck did not believe in extinction, and thus he showed one group transforming into another. This differed from both Buffon and Duchesne, who were illustrating a process of increasing diversity of groups. It also differed by referring to supra-species relationships.

For the next 50 years, diagrams showing biodiversity relationships illustrated what we now call patterns of affinity, rather than showing historical relationships. These affinity diagrams showed apparent similarities among groups of organisms, without any implication that the relationships were the result of evolutionary history. The majority of these diagrams were networks rather than trees, indicating that groups of organisms had observed similarities with several other groups.

It is Charles Darwin and Alfred Russel Wallace who are credited with introducing, in 1858, the idea that natural selection could be the important process by which new species arise, although the idea of natural selection itself had been "in the air" for more than half a century with respect to within-species variation. (In the case of Patrick Matthew, he had also suggested a role in the origin of new species; 1831, On Naval Timber and Arboriculture; with Critical Notes on Authors who have Recently Treated the Subject of Planting).

As was by now becoming a tradition, neither Darwin nor Wallace (nor Matthew) produced a diagram to illustrate their thoughts. Darwin did draw a theoretical diagram in his subsequent 1859 book (On the Origin of Species by Means of Natural Selection), but he used it to illustrate continuity of evolutionary descent and the processes of extinction and diversification, rather than strictly as representing a phylogeny. His famous "Tree of Life" metaphor had nothing to do with the diagram (it was a Biblical metaphor, to stimulate the imagination of his readers).

The first person to get into print what we could call an empirical diagram representing Darwin's idea was Johann Friedrich Theodor Müller in 1864 (Für Darwin), who drew a small (three-species) tree of amphipods. This was followed by St George Jackson Mivart in 1865 (Contributions towards a more complete knowledge of the axial skeleton in the primates. Proceedings of the Zoological Society of London 33: 545-592). This was a much more extensive diagram illustrating possible evolutionary relationships among primate species (including humans) based solely on their body skeleton.

Confusion between trees and networks reappeared at this time. In particular, Franz Martin Hilgendorf had produced an unpublished PhD thesis in 1863 (Beiträge zur Kenntniß des Süßwasserkalkes von Steinheim) during which he constructed an empirical network of relationships among extinct snail species; but he rejected this because it did not match the Darwinian idea of an evolutionary tree. He later collected more data, and instead published a phylogenetic tree in 1866 (Planorbis multiformis im Steinheimer Süßwasserkalk: ein beispiel von gestaltveränderung im laufe der zeit).

Thus, we last saw an explicit evolutionary network in 1766, referring to with-species variation. The first person to publish an evolutionary network showing relationships among species was apparently Ferdinand Albin Pax in 1888 (Monographische übersicht über die arten der gattung Primula. Botanische Jahrbücher für Systematik, Pflanzengeschichte und Pflanzengeographie 10: 75-241). He produced 14 networks of various primula species, apparently showing affinity relationships, but three of these also illustrate hybridization, which is strictly an evolutionary process.

Anthropology

Genealogies appear in anthropology as well as in biology. Any human creation can be considered to have a history of "descent with modification" if copies are passed from generation to generation (eg. languages, books, tales). For our purposes here, the most important historical developments were in linguistics (languages studies) and in stemmatology (manuscript studies).

Georg Stiernhielm appears to have been the first linguist to draw a genealogy, when he produced a small network of Germanic languages in 1671 (De Linguarum Origine Præfatio, the preface to his edition of Evangelia ab Ulfila Gothorum). This was followed by Félix Gallet in c.1800 (Arbre Généalogique des Langues Mortes et Vivantes), who produced a single broadsheet with a network of Indo-European languages.

Note that, as for biology, the modern metaphors started as networks, not trees. More importantly, note that Stiernhielm's diagram pre-dated Buffon's dog network by more than 80 years — evolutionary ideas were less revolutionary in linguistics than they were in biology.

Darwin explicitly noted a connection between language genealogies and biology genealogies in 1859. However, the first people to get into print what we could call empirical diagrams representing Darwin's idea did so before Darwin published anything on the subject. In 1853 František Ladislav Čelakovský published a tree depicting a history of the Slavic languages (Čtení o Srovnávací Mluvnici Slovanské na Universitě Pražskě), and Auguste Schleicher published one on the development of the Indo-Germanic language family (Die ersten Spaltungen des Indogermanischen Urvolkes. Allgemeine Monatsschrift für Wissenschaft und Literatur 1853: 786-787).

Stemmatology differs from linguistics and biology in first producing a tree rather than a network. Hans Samuel Collin and Carl Johan Schlyter produced this in 1827 (first volume of Corpus Iuris Sueo-Gotorum Antiqui), with a tree of relationships among hand-written copies of documents containing the Medieval laws of Sweden. This was also a tree that represented Darwin's genealogical idea, and so it may be considered to be the first one of that type to be published (ie. 25 years before Čelakovský and Schleicher, and 30 years before Darwin).

This early lead was followed by the first network in 1832, when Friedrich Wilhelm Ritschl's stemma of a book by Thomas Magister (Thomae Magistri sive Theoduli Monachi Ecloga vocum Atticarum) explicitly showed sources of contamination among the manuscript copies — that is, different parts of a manuscript were copied from different sources, rather strict ancestor-descendant copying.

Interestingly, the tree metaphor didn’t endure in anthropology as well as it did in biology. It was quickly replaced by alternative metaphors, such as wave, web, warp & weft, lattice and other continuously reticulating images. Horizontal flow of information has always been seen as a dominant force in anthropological histories.

Timeline

Networks

1671 Georg Stiernhielm — small language network
1750 Vitaliano Donati — biology network suggestion
1751 Carl von Linné — biology map suggestion
1755 Georges-Louis Leclerc, Comte de Buffon — intra-species network
1766 Antoine Nicolas Duchesne — intra-species network
1792 Carl von Linné — map
1800 Félix Gallet — language network
1832 Friedrich Wilhelm Ritschl — small manuscript network
1863 Franz Martin Hilgendorf — unpublished inter-species network
1888 Ferdinand Albin Pax — inter-species network

Trees

1776 Peter Simon Pallas — biology tree suggestion
1809 Jean-Baptiste Pierre Antoine de Monet, Chevalier de Lamarck — small inter-species tree
1827 Hans Samuel Collin and Carl Johan Schlyter — manuscript tree
1853 František Ladislav Čelakovský — language tree
1853 August Schleicher — language tree
1859 Charles Robert Darwin — generalized tree
1864 Johann Friedrich Theodor Müller — small inter-species tree
1865 St George Jackson Mivart — large inter-species tree
1866 Franz Martin Hilgendorf — large inter-species tree

When infographics go wrong

Infographics have become very popular in recent decades, with the advent of computer graphics packages. Infographics combine data and pictures, trying to produce an aesthetically pleasing but still informative presentation of numeric information. Recently, the following book appeared:

The Infographic History of the World (2013)
by Valentina D’Efilippo & James Ball
HarperCollins (UK) / Firefly Books (US)

A selection of the the infographics can be perused at the senior author's web page:

http://www.valentinadefilippo.co.uk/ihw/

At the visual.ly blog the author also explains her intentions:

The Infographic History of the World is a new book that continues to push the field of infographics forward.

Our task required research, organization and the selection of topics. Then, we needed to decide how to display data in order to tell a coherent and compelling story. We have never considered this to be an alternative to tons of books of history, but hopefully a refreshing interpretation of what history is about.

With this book, we hope to lead readers on a journey, to interpret the data and find the implications that resonate with them. We don’t pretend that every set of data presents an unquestionable truth. And, rather than looking to define the world’s history, we were looking to present readers with an unconventional interpretation of the subject.

Sadly, these good intentions have not always been achieved. As noted by a review at Amazon:

the book showcases *clever* ways of displaying data, not *clear* ways of displaying it ... Far too often I had to pore over the graphic to figure out what it was trying to say.

What is worse for the readers of this blog, the information is not always correct. Consider this version of the Tree of Life, which has a long-standing tradition in systematics as one of the world's first examples of an infographic:

Click to enlarge.

Quite a number of the taxonomic labels are misplaced. You can check them for yourselves, but here is a selection of some of the surprising information contained in this infographic:

• Amphibians are not Tetrapods
• Humans are not Mammals
• Mammals are not Amniotes
• Turtles are not Reptiles
• Lobe-finned fishes are not Sarcopterygians
• Ray-finned fishes are not Bony Vertebrates
• Charophytes are Land Plants
• Hornworts are Vascular Plants
• Ferns and Horsetails are not only Seed Plants they are Gymnosperms
• Conifers, Gnetophytes, Gingko and Cycads are not Gymnosperms

 Clearly, little has been done to check the veracity of the information in this infographic, which completely defeats its purpose.

How confusing were the first written genealogies?

In a previous post I introduced the Great Stemma as the earliest known pedigree, being a genealogical view of biblical history (The first infographic was a genealogy). In it I noted that people were enclosed in circles, which were connected by lines showing relationships, much as we still do today. However, the lines combined marriage, parent-offspring and brotherly relationships without distinction. So, while it is a good first attempt, the Great Stemma leaves room for informational confusion, and this was not corrected at any time during its centuries of being copied. (In fact, confusion was increased through embellishments, deletions and modifications; but that is another story.)

To illustrate the potential problem of interpreting this early type of genealogy, I have included here a specific example.

The above excerpt from the Stemma shows the the children of Jacob by his wife Leah (who is shown at the top centre), and their subsequent children (ie. Leah's grandchildren). I have annotated the diagram to show parent-offspring (P), brother (B) and half-brother (HB) relationships. Note that all relationships are between males unless specified otherwise (so, half-brothers have the same father).

Leah is at the top [generation 1], with her six sons in a row below her (in birth order left to right), and her daughter to the side [generation 2]. Below this is the first-born son of each of the sons [generation 3], followed in columns down the page by their later sons, in birth order. Sons by later relationships are shown as half-brothers. At the bottom are two of Leah's great-grandchildren [generation 4].

Thus, the genealogical diagram does not effectively separate the generations visually, and parental and fraternal relationships are depicted in the same way. These days we solve this, of course, by keeping each generation as a single row and linking each child directly to the parent. It is easy to get used to the Stemma way of doing it, because it is fairly consistent about the arrangement. If there is confusion, then each circle does specify the relationship in words.

So, as I noted, this is a good first attempt, but some of the things that we now feel need distinguishing were not distinguished by the (unknown) original author.

However, the 24 extant copies of the Stemma are not identical, and two of them try to fit more information into Leah's family tree than is shown above. This information concerns the origin of the fourth generation, which is accurately depicted as far as it goes, but the above figure leaves out a lot. Some of the extra information is shown in the Stemma version below, which adds two extra people, both of them wives. I have annotated this version the same as the previous one, except that this pedigree adds one more relationship to the mix — marriage (M).

The extra details come from Genesis 38, which describes a set of relationships that would make a modern television soap-opera scriptwriter jealous. The story goes something like this (I have indicated the named people with letters in the diagram above, with Leah as L):

Judah (J) marries the [unnamed] daughter (W) of Shua. Judah and his wife have three children, Er (E), Onan (O), and Shelah (S). Er marries Tamar (T), but God kills him because he "was wicked in the sight of the Lord" (Gen. 38:7). Tamar becomes Onan's wife in accordance with the custom of the time, but he too is killed by God after he refuses to father children for his older brother's childless widow, and "spills his seed on the ground" instead (Gen. 38:8-10). Although Tamar should marry Shelah, the remaining brother, Judah does not consent, for fear of his son's life (Gen. 38:11). In response, after Judah's wife has died, Tamar deceives Judah into having intercourse with her, by pretending to be a prostitute (Gen. 38:12-23). When Judah discovers that Tamar is pregnant he prepares to have her killed, but recants and confesses when he finds out that he is the father (Gen. 38:24-26). The result is twin boys, Zerah (Z) and Perez (P) (Gen. 38:27), who are accepted as Judah's sons.

Biblically, this story is important because Judah became the founder of the Tribe of Judah, one of the twelve Tribes of Israel. Their land encompassed most of the southern portion of the Land of Israel, including Jerusalem. Both the Book of Ruth and the Gospel of Matthew identify Tamar's son Perez as an ancestor of King David, which makes Judah and Tamar also ancestors of Jesus.

For our purposes here, though, the interesting thing is the confusion caused by trying to add the two marriage relationships to the pedigree. These are in no way distinguished visually from the paternal and fraternal relationships, although the circled text does specify the relationship in words. Today, we solve this potential confusion by using horizontal lines for marriage relationships and vertical lines for parent-offspring relationships.

Equally importantly, note that Tamar's (legal) relationship supplants the (biological) parent-offspring relationship between Judah and her sons — you would never conclude from the diagram that Perez was Judah's son, for example, rather than Er's. However, note the neat attempt to keep Tamar's children in a single column by putting one twin above her and one below (perhaps also signifying simultaneous birth).

The above part of this post was inspired by a blog post from Jean-Baptiste Piggin (The Tamar Storyboard). The first picture above is from an unnamed manuscript in the Biblioteca Medicea Laurenziana, Florence, Plut.20.54, dated c. 1050 AD. The second picture if from an unnamed manuscript in the Pierpont Morgan Library, New York, M.644, dated 940-945 AD.

Moving on, the scribes of that time tried to go even further in complicating simple genealogies, as shown in the next figure. This is drawn by Stephanus Garsia Placidus, and is taken from the Saint-Sever Beatus in the Bibliothèque Nationale de France, Paris, ms. lat 8878, dated c. 1060 AD.

It shows the non-Semitic (ie. polytheistic) part of Noah's family. Noah is at the top right (sacrificing two doves), with his son Japheth (J) to the left and son Ham (H) below. Their wives (W) are indicated by intersecting circles, rather than by lines, which is a more successful approach than in the Stemma. Their descendants are shown in roughly the same style as above, with the first-born son followed by the later ones in order (so that the P and B relationships are not clearly distinguished) — Japheth has seven sons and Ham has four.

However, the illustrator has also tried to include a lot of history in this genealogy. For example, the sons of Ham's son Cush end with Nimrod (N), who has a small essay attached to his name. Among other things, he founded Babel, the city that plays an important role later in the Bible. Moreover, the sons of Ham's son Canaan (C) are shown as a reticulating network rather than as a simple chain. This apparently represents their roles as founders of the 11 tribes who originally occupied the ancient Land of Canaan, and who were later driven out and enslaved by the Israelites. These lines thus represent later history rather than parental or fraternal relationships.

This diagram is thus not a simple pedigree, as we would usually leave it today.

The first infographic was a genealogy (c. 400 AD)

The New Testament was originally written in Greek, and it apparently did not occur to the writers that a visualization of the many (and lengthy) Biblical genealogies would be helpful. They knew a lot about geometry but nothing about infographics.

Given the importance of the Old and New Testament genealogies for the foundation of Christianity (see The role of biblical genealogies in phylogenetics), it is not at all surprising that eventually someone had a go at summarizing them all in one place. However, this did not happen until several centuries later, when the Bible was being translated into Latin. Perhaps this delay had something to do with the biblical prohibition on images.

The first known attempt to draw a biblical pedigree, rather than writing out the relationships as text, also appears to have been the first attempt at a genealogy of any sort. Jean-Baptiste Piggin has been researching this document since 2009, and he has remarkably extensive notes about it at his web site Macro-Typography. Piggin dates the document to sometime in the decades before 427 AD, which is surprisingly early and thus unique in its historical context (Late Antiquity).

Importantly, the pedigree is actually an infographic in the modern sense, in that the figure itself conveys almost all of the information, with the text acting as a supplement. Thus, a single image allows the viewer to grasp the overview (of biblical history in this case), as well as providing access to the details. This is an idea that did not really catch on until the Medieval period, when Latin manuscripts started to use images as pedagogic devices, in addition to their textual descriptions. An obvious example is the so-called Tree of Porphyry in logic, which was first described in words by Porphyry of Tyre in c. 270 AD (Isagoge), sketched by Boëthius c. 520 AD (In Porphyrium Commentariorum), and finally reproduced as an actual tree diagram in Medieval manuscripts (being named arbor Porphyrii by Petrus Hispanus in 1240, in Summulae Logicales).

Sadly, there is no extant copy of this early biblical pedigree, and so we do not know who produced it or exactly when; nor do we have any of the copies made during the following 500 years. We do, however, have 24 complete or partial copies from the period 950-1250, many of them incorporated into Spanish editions of the Bible. Piggin has studied these copies extensively, and tried to reconstruct what he thinks the original document most probably looked like.

Piggin reconstructs the document (shown above), which he calls the Great Stemma, as a single scroll made from papyrus, designed to be unrolled and read from the upper left towards the middle right. All extant copies, however, break the figure up into sections, for inclusion as pages in a parchment manuscript (a codex) typical of the Medieval period.

Reconstruction was not an easy task, given the later modifications, digressions and embellishments, made with each successive hand-drawn copy. In particular, the process of reducing the long scroll to sequential pages apparently introduced many errors; and subsequent modifications degraded the logic of the original intention. Incidentally, embellishments do not improve the communication of information (see Mistaken improvements), and nor necessarily do modifications, since in this case they often created contradictions.

Above is a schematic overview of the reconstructed original scroll, but you can zoom in to all of the details by visiting Piggin's original reconstruction. Each circle represents one person (out of 540), with connecting lines showing their genealogical relationships — marriage, parent-offspring or brotherly (these are inter-mixed). Time is read left to right along the top (Adam is at the top-left), with vertical excursions downwards for lineages that do not lead to Jesus (who is at the middle-right). Note that the pedigree is drawn using nodes and lines, as we still do, but it is not drawn anything like a tree (ie. a "family tree"). Indeed, it is actually a network, since two ancestral lineages converge on Jesus (via Joseph and Mary), and elsewhere there are 13 simultaneous appearances of the same person in two places (to avoid complicated connections; see Reducing networks to trees).

The diagram also has a distinct timeline superimposed, shown as the elements without circles, which attempts to synchronize biblical events with contemporaneous secular history. So, Piggin notes that the Stemma it is "not just a genealogy, but a graphic version of the universal chronicles which attempted in antiquity to cross reference the histories of different civilizations to establish an overview of Middle Eastern and Graeco-Roman history." However, the timeline is not calibrated in any way (ie. time changes are not constant).

[Note: There is an update about the reconstruction in this blog post: The origin of an idea: reducing networks to trees]

Below, I have included pages from some of the extant manuscripts, to show their variety after more than 500 years of scribes making copies.

The above figure is the first page from the Roda Codex, in the Real Academia de la Historia (Madrid) cod.78 (dated 990 AD). This is the start of the genealogy, with Adam at the top-left, and illustrating his family.

The above figure is the third page from an unnamed manuscript in the Pierpont Morgan Library (New York) M.644 (dated 940-945 AD). This one shows Noah and his non-Semite descendants.

The above figure is the final page from an unnamed manuscript in the Plutei collection at the Biblioteca Medicea Laurenzian (Florence) Plut.20.54 (dated 1050 AD). This shows the incarnation of Jesus, at the end of the genealogy, illustrating the confluence of the lineages described by Matthew (at the top) and Luke (at the bottom).

Piggin notes that here may actually have been few early copies of the Stemma, because of the difficulty of transcribing illustrations by hand. That is, it is very difficult to accurately hand-copy a diagram, as opposed to copying text (where only the words matter not their visual style). Indeed, to what extent did the scribes actually understand that they needed a precise copy? Copying complex technical drawings requires careful measurement and layout, and yet some of the copies seem to have been very badly planned. Piggin suggests that "the serious corruption done to the Great Stemma early in its diffusion led to it ultimately being discarded and begun all over again by medieval writers such as Peter of Poitiers." The reference is to the Compendium Historiae in Genealogia Christi by Petrus Pictaviensis (Peter of Poitiers) produced in c.1185 AD, and for which there are many extant copies dated from that time to 1650 AD — he used long rolls for his genealogies.

Finally, Piggin even has a suggestion for a small ancient board game that might have provided inspiration for the form of the infographic (see Board Game). This is important, because there are no known prior models for constructing such a diagram — apart from geometry, no-one had previously produced an image that illustrated non-corporeal ideas.

Footnote: The word stemma referred originally to an ancient Roman genealogy (displayed in noble homes), which is roughly how it is used by Piggin. However, these days the word is more commonly used in anthropology to refer to a genealogy of manuscript copies. A genealogy of manuscripts is more properly called a stemma codicum.

Archiving of phylogenetics data

The draft Minimum Information about a Phylogenetic Analysis standard (Leebens-Mack et al. 2006) suggests that all relevant information about each and every published phylogenetics analysis should be archived, so that it can be scrutinized by later researchers, either for validation or for re-use. The issues here are both preservation of the information (data and analysis protocols) and open access to it.

In this blog we have already pointed out that there has been criticism of the bioinformatics part of this archiving, where there have been repeated claims that many computer programs are poorly maintained (Poor bioinformatics?) as well as poorly archived (Archiving of bioinformatics software).

Anyone who has ever tried to get data out of a biologist will know that the data-related part of the standard is no better. My own success rate, at requesting data from all areas of biology not just phylogenetics, is less than 20% over the past 25 years. The responses have been, in order: (i) no response (>50%), (ii) "a student / postdoc / colleague has the data not me", and (iii) "I have moved recently and don't know where the data are". My most recent attempt, to get the data from Collard et al. (2006), was ultimately unsuccessful even after several attempts.

For phylogenetics, this situation has recently been quantified and analyzed by Magee et al. (2014). They tried to collect phylogenetic data (comprising nucleotide sequence alignment and tree files) from 217 published studies. Of these, 54 (25%) had at least some part of the data (alignment or tree) archived in an online repository, and 91 (42%) were obtained by direct solicitation, but in 72 (33%) of cases nothing could be obtained even after three requests. Overall, complete datasets (both tree and alignment) were available for only 40% of the studies.

The authors note that the data were more likely to be deposited in online archives and/ or shared upon request when the publishing journal has a strong data-sharing policy. Furthermore, there has been a positive impact of recent policy initiatives and infrastructural changes involving data repositories. The TreeBASE phylogenetic-data repository has existed for more than 20 years, but its use has been sporadic. However, the recent establishment of the Joint Data Archiving Policy by a consortium of journals, which requires the submission of data to online archives as a condition of publication, and the concomitant establishment of the Dryad repository for evolutionary and ecological data, has seen a surge in the archiving of data.

So, all in all, things have been no better on the bio side than the informatics side of bioinformatics.

Stoltzfus et al. (2012) have identified a number of possible barriers to successful data archiving, including lack of awareness of options and policies, perception that benefits do not justify burden, and an active desire to restrict data access. Importantly, there are also a number of practical issues even for those people who do wish to archive their data:

• inconvenience of gathering complete data and metadata
• inconvenience of format conversions needed for archiving
• frustration when some data don't fit the archive's data model
• poor and undocumented archive submission interfaces.

For the readers of this blog, issue three is possibly the most important one — all current repositories are based on a tree model for phylogenetics, and therefore network phylogenies are frustrating to deal with.

In order to improve the overall situation, there are explicit suggestions from Cranston et al. (2014) for best practices when archiving. They have ten simple guidelines that, if followed, will result in you providing open access to your data and analyses, even if the publishing journal does not force you to do it.

Footnote: I have been reminded that archiving data in PDF format is inappropriate. Trying to extract text (such as a dataset) from a PDF file can be difficult, because there is no standard format for storing the text. Consequently, different PDF readers will extract the text in different ways, and it is possible that in all cases the output will need extensive manual re-formatting, in order to recover the original text formatting that went into the PDF file. In my experience, Google Chrome may do the least-worst job.

References

Collard M, Shennan SJ, Tehrani JJ (2006) Branching, blending, and the evolution of cultural similarities and differences among human populations. Evolution and Human Behavior 27: 169-184.

Cranston K, Harmon LJ, O'Leary MA, Lisle C (2014) Best practices for data sharing in phylogenetic research. PLoS Currents Jun 19;6.

Leebens-Mack J, Vision T, Brenner E, Bowers JE, Cannon S, Clement MJ, Cunningham CW, dePamphilis C, deSalle R, Doyle JJ, Eisen JA, Gu X, Harshman J, Jansen RK, Kellogg EA, Koonin EV, Mishler BD, Philippe H, Pires JC, Qiu YL, Rhee SY, Sjölander K, Soltis DE, Soltis PS, Stevenson DW, Wall K, Warnow T, Zmasek C (2006) Taking the first steps towards a standard for reporting on phylogenies: Minimum Information About a Phylogenetic Analysis (MIAPA). OMICS 10: 231-237.

Magee AF, May MR, Moore BR (2014) The dawn of open access to phylogenetic data. PLoS One 9: e110268.

Stoltzfus A, O'Meara B, Whitacre J, Mounce R, Gillespie EL, Kumar S, Rosauer DF, Vos RA (2012) Sharing and re-use of phylogenetic trees (and associated data) to facilitate synthesis. BMC Research Notes 5: 574.

Trees as art

Trees can be many things: objects, symbols, art, or information.

As objects, they act as homes and shelter, they provide food and oxygen, and they bind soil to hold topography in place. They even provide somewhere to sit while you are waiting to discover gravity. Their most famous use as symbols is the Tree of Life, which recurs in many cultures throughout the world. This was later extended to the Tree of Knowledge, a potent intellectual symbol throughout Western history. In the modern world this latter use has been expanded, so that trees are mathematical representations of the relationships among information.

Trees have also long played a role in art, which continues in the modern works of, for example, Vincent van Gogh and Gustav Klimt.

My first introduction to this was the book The Tree (1979, Aurum Press, UK / Little, Brown and Co, USA) by John Fowles (text) and Frank Horvat (photographs). This is a meditation on the connection between the natural world and human creativity. Horvat provides moody views of trees with (almost) no human objects in sight, and Fowles (the novelist) provides a provocative essay on trees as representations of art, revealing in his usual erudite manner that he particularly dislikes the "taming the wild" aspects of horticulture and science.

More recently, there has been the hand-lithographed book The Night Life of Trees (2006, Tara Books, Chennai, India). This contains a series of tribal-art images from three Gond people of central India (Bhajju Shyam, Durga Bai and Ramsingh Urveti). (And yes, the land of the Gond is Gondwanaland, which was the source of our name for the southern land masses.)

The Gond people have previously decorated their house walls and floors with traditional tattoos and motifs; and these motifs have made their way onto paper as modern representations of the tribal art form. Other tribal art forms that have followed a similar transfomation include the Aboriginal art of Australia, which bears a strong stylistic resemblance to some of the Gond art.

The Gonds are traditionally forest dwellers, and so the lives of humans and trees have been seen as closely entwined. Their lore suggests that trees are hard at work during the day providing shelter and nourishment, but at night they finally rest and their spirits are revealed. It is these spirits that the artists have tried to capture in their book.

I have reproduced two of the images here, because it is clear that the inter-twining reveals a very network-like aspect of the trees. The accompanying text is taken from the book.

Snakes and Earth

The earth is held in the coils of the snake goddess. And the roots of trees coil around the earth too, holding it in place. If you want to depict the earth, you can show it in the form of a snake. It is the same thing.

The Binding Tree

Mahalain trees are found deep inside the thickest jungles, holding each other in a tight embrace. Because it clings and binds so well, Mahalain bark is known for its strength. Our ancestors from earliest times searched for it in the deep jungles and used it to build houses. A house built well with Mahalain bark is said to last a hundred years.

Both books are worth seeking out if you value art as well as science. The Gond book is now in its 9th hardback edition, and is widely available in bookstores. The Fowles book (without the photographs) is currently available as a 30th anniversary paperback edition; but you are better off finding a second-hand hardback with the pictures.

Finally, just by way of contrast, here is the Albero Trinità from Joachim of Fiore's Liber Figurarum (published in 1202), a book that uses many different visualizations to display human knowledge.

My daughter was the inspiration for writing this blog post.

Massive citations of bioinformatics in biology papers

For those of you who have missed it, the magazine Nature has recently looked at the 100 most highly cited science papers of all time (across all fields):

van Noorden R, Maher B, Nuzzo R (2014) The top 100 papers: Nature explores the most-cited research of all time. Nature 514: 550-553.

The list is dominated by biology papers, with biochemical laboratory techniques taking all of the top spots. However, it also worth noting that bioinformatics papers produce a very good showing, and so I have extracted 10 of them here.

If you have ever wondered what phylogenetic tree-building method is most used then it is at #20, while the most-used tree-building program is at #45 (having got there in only 7 years). You may also wonder why sequence alignment programs (#10 & #28 for Clustal; #12 & #14 for BLAST) do much better than tree-building programs (#45 for MEGA; #75 for GCG; #100 for MrBayes).

As for journals, the papers appeared in Nucleic Acids Research (4), Molecular Biology & Evolution (2), Bioinformatics (2), Journal of Molecular Biology (1) and Evolution (1). This list only partially matches their Journal Citation Reports current 5-Year Impact Factors: 8.378, 10.494, 6.968, 3.795 and 5.469, respectively.

Rank: 10 Citations: 40,289
Clustal W: improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice.
Thompson, J. D., Higgins, D. G. & Gibson, T. J
Nucleic Acids Res. 22, 4673–4680 (1994).

Rank: 12 Citations: 38,380
Basic local alignment search tool.
Altschul, S. F., Gish, W., Miller, W., Myers, E. W. & Lipman, D. J.
J. Mol. Biol. 215, 403–410 (1990).

Rank: 14 Citations: 36,410
Gapped BLAST and PSI-BLAST: A new generation of protein database search programs.
Altschul, S. F. et al.
Nucleic Acids Res. 25, 3389–3402 (1997).

Rank: 20 Citations: 30,176
The neighbor-joining method: A new method for reconstructing phylogenetic trees.
Saitou, N. & Nei, M.
Mol. Biol. Evol. 4, 406–425 (1987).

Rank: 28 Citations: 24,098
The CLUSTAL_X Windows interface: Flexible strategies for multiple sequence alignment aided by quality analysis tools.
Thompson, J. D., Gibson, T. J., Plewniak, F., Jeanmougin, F. & Higgins, D. G.
Nucleic Acids Res. 25, 4876–4882 (1997).

Rank: 41 Citations: 21,373
Confidence limits on phylogenies: an approach using the bootstrap.
Felsenstein, J.
Evolution 39, 783–791 (1985).

Rank: 45 Citations: 18,286
MEGA4: Molecular Evolutionary Genetics Analysis (MEGA) software version 4.0.
Tamura, K., Dudley, J., Nei, M. & Kumar, S.
Mol. Biol. Evol. 24, 1596–1599 (2007).

Rank: 75 Citations: 14,226
A comprehensive set of sequence analysis programs for the VAX.
Devereux, J., Haeberli, P. & Smithies, O.
Nucleic Acids Res. 12, 387–395 (1984).

Rank: 76 Citations: 14,099
MODELTEST: Testing the model of DNA substitution.
Posada, D. & Crandall, K. A.
Bioinformatics 14, 817–818 (1998).

Rank: 100 Citations: 12,209
MrBayes 3: Bayesian phylogenetic inference under mixed models.
Ronquist, F. & Huelsenbeck, J. P.
Bioinformatics 19, 1572–1574 (2003).

On partitioning incongruent data into congruent blocks

In a recent article (by myself, Leo van Iersel, Nela Lekić and Simone Linz) we stumbled upon the following problem which appears to touch upon some interesting biological issues.

A rooted triplet xy|z is a rooted binary tree in which x and y have a common parent p, p is a child of the root, and z is the other child of the root. A rooted phylogenetic tree T displays (informally: agrees with) xy|z if the common ancestor of x and y is a strict descendant of the common ancestor of x and z (or y and z). See the figure below: the tree on the right displays triplet xy|z.

Suppose we are given a set of rooted triplets S on a set X of taxa. Suppose we have reason to believe that the set of triplets S have been obtained from different sources (e.g. genes), where the genes have different evolutionary histories due to reticulate phenomena. This means that, for a given subset of 3 taxa {x,y,z} from X, S will contain zero, one, two or three of the possible triplets {xy|z, xz|y, yz|x}.

Crucially, suppose we do not know which gene generated each triplet in S. This might sound artificial, but if some of the rooted triplets have been generated from phenotypic data, or have been obtained from inherently complex data (such as metagenomic data), then the genomic origins of the triplets might not be readily available.

Under such circumstances it is tempting to obtain a lower bound on the number of incongruent gene topologies by answering the following question. What is the minimum number of blocks that we can partition the triplets into, such that the triplets in each block are compatible with a tree (i.e. can all be displayed by the same tree)? It's easy to see that the worst case is when all 3(n 3) possible triplet topologies are present in S, where n is the number of elements in X. Let tau(n) denote this worst case.

We computed tau(n) exactly for small n. For n equal to 3 or 4, tau(n) is 3. For 5 <= n < = 12, tau(n) is 4. For 13 <= n <= 20 we only have an upper bound: tau(n) <= 5.

We know that tau(n) never stops growing: you can always find a larger value of n to force tau to rise even further. However, tau(n) seems to grow extremely slowly as a function of n. We have reason to believe that tau(n) grows far more slowly than O(log n).

The bottom line is that, for any n that might be encountered in a real-world experiment, it could well be that tau(n) <= C where C is a small constant. Suppose, for the sake of argument, that C is 10. This would mean that even the most incredibly diverse and incongruent real-world dataset could be 'explained' by (at most) 10 underlying tree topologies, even when - in truth - there are hundreds or even thousands of different tree signals within the dataset. In other words, tau(n) is potentially a massive underestimation of underlying incongruence.

The problem here is that rooted triplets only carried limited information about the underlying trees that generated them. Specifically, a large amount of information is lost if we do not know which gene tree generated which triplet.

One possible response to this problem is to explicitly incorporate topology. Suppose, for example, that a set of triplets S can be partitioned into 2 trees, but any rooted phylogenetic network displaying these two tree topologies (where each tree is on the full set of taxa X) must have a huge amount of reticulation, due to the fact that the 2 trees are highly incongruent to each other. On the other hand, suppose there exists a partition of S into 4 trees such that the trees are relatively congruent and thus can be displayed by a rooted phylogenetic network with a much smaller amount of reticulation. Depending on where we lay the emphasis we might prefer one solution over the other. Indeed, at one extreme we can completely ignore the number of trees in the underlying partition, and seek only to pack the rooted triplets into a rooted phylogenetic network with as little reticulate activity as possible: a well-studied problem. At the other extreme we are back with the original problem, i.e. of minimizing the number of trees needed to cover/generate the triplets in S, irrespective of how incongruent they are relative to each other.

As far as we know hybrid approaches — constructing rooted phylogenetic networks from triplets, but insisting that the triplets originate from a constrained number of trees within that network — have not yet received any significant research attention and could be interesting to investigate.

To conclude, rooted triplets are mathematically and experimentally seductive due to the hope that on one hand they can be experimentally inferred with high accuracy (due to their small size) but on the other hand still carry enough evolutionary signal to be puzzled together into large, accurate phylogenetic trees (or even networks). However, they carry limited information and this means that one must be careful when using them for hypothesis generation. Explicitly incorporating tree or network topology into triplet-based methods is potentially a way of strengthening their inference power.