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:

Petter.Hellstrom@idehist.uu.se

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.

A phylogenetic network outside science

I have written before about the presentation of historical information using the pictorial representation of a phylogeny (eg. Phylogenetic networks outside science; Another phylogenetic network outside science). These diagrams are often representations of the evolutionary history of human artifacts, and so a phylogeny is quite appropriate. They are of interest because:

• they are usually hybridization networks, rather than divergent trees, because the artifact ideas involve horizontal transfer (ideas added) and recombination (ideas replaced);
• they are often not time consistent, because ideas can leap forward in time, so that the reticulations do not connect contemporary artifacts (see Time inconsistency in evolutionary networks); and
• they are sometimes drawn badly, in the sense that the diagram does not reflect the history in a consistent way.

The latter point often involves poor indication of the time direction (see Direction is important when showing history), or involves subdividing the network into a set of linearized trees.

One particularly noteworthy example that I have previously discussed is of the GNU/Linux Distribution Timeline, which illustrates the complex history of the computer operating system. The problems with this diagram as a phylogeny are discussed in the blog post section History of Linux distributions.

In this new post I will simply point out that there is a more acceptable diagram, showing the key Unix and Unix-like operating systems. I have reproduced a copy of it below.

Click to enlarge.

This version of the information correctly shows the history as a network, not a series of linearized trees (each with a central axis). It also draws the reticulations in an informative manner, rather than having them be merely artistic fancies.

It is good to know that phylogenetic diagrams can be drawn well, even outside biology and linguistics.

The pedigree of grape varieties

We are all familiar with the concept of a family tree (formally called a pedigree). People have been compiling them for at least a thousand years, as the first known illustration is from c.1000 CE (see the post on The first royal pedigree). However, these are not really tree-like, in spite of their name, unless we exclude most of the ancestors from the diagram. After all, family histories consist of males and females inter-breeding in a network of relationships, and this cannot be represented as a simple tree-like diagram without leaving out most of the people. I have written blog posts about quite a few famous people who have really quite complex and non-tree-like family histories (including Cleopatra, Tutankhamun, Charles II of Spain, Charles Darwin, Henri Toulouse-Lautrec, and Albert Einstein).

Clearly, the history of domesticated organisms is even more complex than that of humans. After all, in most cases we have gone to a great deal of trouble to make these histories complex, by deliberately cross-breeding current varieties (of plants) and breeds (of animals) to make new ones. So, I have previously raised the question: Are phylogenetic trees useful for domesticated organisms? The answer is the same: no, unless you leave out most of the ancestry.

In most cases, we have no recorded history for domesticated organisms, because most of the breeding and propagating was undocumented. Until recently, it was effectively impossible to reconstruct the pedigrees. This has changed with modern access to genetic information; and there is now quite a cottage industry within biology, trying to work out how we got our current varieties of cats, dogs, cows and horses, as well as wheat, rye and grapes, etc. I have previously looked at some of these histories, including Complex hybridizations in wheat, and Complex hybridizations in barley and its relatives.

Grapes

One example of particular interest has been grape varieties. I have discussed some of the issues in a previous post: Grape genealogies are networks, not trees, including the effects of unsampled ancestors when trying to perform the reconstruction.

There are a number of places around the web where you can see heavily edited summaries of what is currently known about the grape pedigree. However, these simplifications defeat the purpose of this blog post, which is to emphasize the historical complexity. The only diagram that I know of that shows you the full network (as currently known) is one provided by Pop Chart (The Genealogy of Wine), a commercial group who provide infographic posters for just about anything. They will sell you a full-sized poster of the pedigree (3' by 2'), but here I have provided a simple overview (which you can click on to see somewhat larger).

You can actually zoom in on the diagram on the Pop Chart web page to see all of the details. This allows you to spend a few happy hours finding your favorite varieties, and to see how they are related. You will presumably get lost among the maze of lines, as I did.

A proper network of Europeans

Back in May this year, Iosif Lazaridis submitted a paper to the arXiv, called: "The evolutionary history of human populations in Europe". It is now online as part of the December 2018 issue of Current Opinion in Genetics & Development (53: 21-27).

Its interest for readers of this blog is the one and only figure that the paper contains. It is a genealogical network, showing the obvious — that the human "family tree" has quite a few reticulations, mostly due to introgression (or admixture, as human geneticists like to call it). Here is the figure, along with the legend. Note that not all of the edges in the network have a direction, so that it is not really a directed acyclic graph (see also First-degree relationships and partly directed networks).

A sketch of European evolutionary history based on ancient DNA
Bronze Age Europeans (~4.5-3kya) were a mixture of mainly two proximate sources of ancestry: (i) the Neolithic farmers of ~8-5kya who were themselves variable mixtures of farmers from Anatolia and hunter-gatherers of mainland Europe (WHG), and (ii) Bronze Age steppe migrants of ~5kya who were themselves a mixture of hunter-gatherers of eastern Europe (EHG) and southern populations from the Near East. Thus, we only have to go ~8 thousand years backwards in time to find at least four sources of ancestry for Europeans. But, each of these sources was also admixed: European hunter-gatherers received genetic input from Siberia and ultimately also from archaic Eurasians, and Near Eastern populations interacted in unknown ways with Europe and Siberia and also had ancestry from ‘Basal Eurasians’, a sister group of the main lineage of all other non-African populations. Dates correspond to sampled populations; in the case of a cluster of populations (such as the WHG), they correspond to the earliest attestation of the group.

Let's distinguish between Hennig and Cladistics

There are theoretically an infinite number of ways to mathematically analyze any set of data, and yet it is unlikely that all (or even most) of these will have any relevance to a study of biology. In this sense, the philosophy of phylogenetic analysis needs to show that there is a strong basis for treating any particular mathematical analysis as having biological relevance. This is a point that I have discussed before: Is there a philosophy of phylogenetic networks?

Willi Hennig clearly has some role to play here. However, his ideas are often treated as being solely related to one particular form of phylogenetic analysis — cladistics. In this post I will point out that his work has a much greater relevance than that — he provides a crucial logical step that applies to all phylogenetic inference.

The steps of phylogenetic inference are shown in the first figure, which is taken from my earlier post. The first step is a mathematical inference from character data to tree/network; the second step is a logical inference that the mathematical summary resulting from the first step has some biological relevance; and the third step is a practical inference that the biological summary applies to whole organisms as well as to their characters.

Summary

Hennig's concept of "shared innovations" (which he called synapomorphies) is the only thing that allows us to use the mathematical phylogenetics in the pursuit of genealogical history. Without this concept, the mathematics could just produce something like the arithmetic mean, a mathematical concept with no connection to real objects (unlike the median or mode, which will always be real). The idea of shared innovations is what leads us to believe that the mathematical summary (whether tree or network) might actually also be a close approximation to the real thing. This is a separate concept from cladistics, which is simply a mathematical algorithm based on a particular optimality criterion (parsimony), just like maximum likelihood or bayesian approaches. So, shared innovations underlie the use of both parsimony, likelihood and distance methods — Willi Hennig (and, before him, Karl Brugmann in linguistics) is relevant no matter what algorithm we use.

Mathematical analyses

If they are to represent genealogical history, then all trees and networks in phylogenetics will be directed acyclic graphs (DAGs), mathematically. There are many ways to produce a DAG, some of which have had varying degrees of popularity in phylogenetics, and some of which have not been used at all.

To produce an acyclic line graph (in which nodes are connected by edges), we can start with character data or distance data. We can then use various optimality criteria to choose among the many graphs that could apply to the data, such as parsimony (usually ssociated with cladistics) and likelihood (either as maximum likelihood or integrated likelihood). We can also ensure that the graph is directed (ie. the edges have arrows), by choosing a root location, either directly as part of the analysis or a posteriori by specifying an outgroup.

All of these approaches are mathematically valid, as are a number of others. They all provide a mathematical summary of the data. This is step one of the phylogenetic inference, as illustrated above.

But what of step two? Biologists need a summary of the data that has biological relevance, as well, not just mathematical relevance. This has long been a thorn in the side of biologists — just because they can perform a particular mathematical calculation does not automatically mean that the calculation is relevant to their biological goal.

Consider the simplest mathematics of all — calculating the central location of a set of data. There are many ways to do this, mathematically — indeed, there are technically an infinite number of ways. These include the mode, the median, the arithmetic mean, the geometric mean, and the harmonic mean. All of these are mathematically valid, but do any of them produce a central location that describes biology?

The mode does, because it is the most common observation in the dataset. The median usually does, because it is the "middle" observation in the dataset. But what of the various means? There is no necessary reason for them to describe biology, although they are perfectly valid mathematics.

For instance, the modal number of children in modern families is 2, meaning that more families have this number than any other number of children. The median number is also 2, meaning that half of the families have 2 or fewer children and half of the families have 2 or more. So, these mathematical summaries are also descriptions of real families. But the means are not. For example, the arithmetic mean number of children is 2.2, which does not describe any real family. If you ever find a family with 2.2 children, then you should probably call the police, to investigate!

Mathematically valid data summaries have a lot of relevance, but they do not necessarily describe biological concepts. I can use the mean number of children per local family to estimate the number of schools that I might need in that area, but I cannot use it to describe the families themselves. This is a classic case of "horses for courses".

Hennig

So, in phylogenetics we need some piece of logic that says that we can expect our DAG (a mathematical concept) to be a representation of a genealogy (a biological concept). Our genealogical estimate may still be wrong (and indeed it probably will be, in some way!), but that is a separate issue. The DAG needs to a reasonable representation, not a correct one. Correctness needs to be a result of our data, not our mathematics.

This is where Willi Hennig comes in. Hennig's ideas, and the ideas derived from them, are illustrated in the second figure.

Hennig explicitly noted that characters have a genealogical polarity, with ancestral states being modified into derived states through evolutionary time. Furthermore, he noted that it is only the derived states that are of relevance to studying evolutionary history — the sharing of derived character states reveals evolutionary history, but shared ancestral states tells us nothing.

We have done two things with these Hennigian ideas. Some people have been interested in classification, for which the concept of monophyly is relevant, and others have been interested in reconstructing the genealogies, rather than simply interpreting them.

Phylogenetics

Reconstructing a tree-like phylogenetic history is conceptually straightforward, although it took a long time for someone (Hennig 1966) to explain the most appropriate approach. Interestingly, the study of historical linguistics has developed the same methodology (Platnick and Cameron 1977; Atkinson and Gray 2005), thus independently arriving at exactly the same solution to what is, in effect, exactly the same problem. From this point of view, the logical inference itself is uncontroversial; and its generic nature means that it can be used for any objects with characteristics that can be identified and measured, and that follow a history of descent with modification. I will, however, discuss this in terms of biology — you can make the leap to other objects yourself.

The objective is to infer the ancestors of the contemporary organisms, and the ancestors of those ancestors, etc., all the way back to the most recent common ancestor of the group of organisms being studied. Ancestors can be inferred because the organisms share unique characteristics (shared innovations, or shared derived character states. That is, they have features that they hold in common and that are not possessed by any other organisms. The simplest explanation for this observation is that the features are shared because they were inherited from an ancestor. The ancestor acquired a set of heritable (i.e. genetically controlled) characteristics, and passed those characteristics on to its offspring. We observe the offspring, note their shared characteristics, and thus infer the existence of the unobserved ancestor(s). If we collect a number of such observations, what we often find is that they form a set of nested groupings of the organisms.

Hennig, in particular, was interested in the interpretation of phylogenetic trees, rather than their reconstruction. He did this interpretation in terms of monophyletic groups (also called clades), each of which consists of an ancestor and all of its descendants. These are natural groups in terms of their evolutionary history, whereas other types of groups (eg. paraphyletic, polyphyletic) are not. So, a phylogenetic tree consists of a set of nested clades, which are the groups that are represented and given names in formal taxonomic schemes.

For phylogenetic trees, there is thus a rationale for treating a tree diagram as a representation of evolutionary history. For example, in a study of a set of gene sequences, first we produce a mathematical summary of the data based on a quantitative model. We then infer that this summary represents the gene history, based on the Hennigian logic that the patterns are formed from a nested series of shared innovations (this is a logical inference about the biology being represented by the mathematical summary). We then infer that this gene history represents the organismal history, based on the practical observation that gene changes usually track changes in the organisms in which they occur (ie. a pragmatic inference).

Mis-interpretations of Hennig

What I have said above has lead to various mis-interpretations of Hennig's role in phylogenetics.

First, he did not propose any specific method for producing a phylogenetic tree (or network). He was concerned about the logic of the diagram. not how to get it in the first place. He distinguished shared derived character states, or shard innovations, (he called them synapomorphies) from shared ancestral states (symplesiomorphies), and noted that only the former are relevant for phylogenies. So, distance methods will also work in phylogenetics provided the distances are based on homologous apomorphic features. If they are not so based, then they are simply mathematical constructions, which may or may not represent anything to do with phylogeny. Distances estimated from plesiomorphic features can be used to construct a tree, obviously, but there is no reason to expect that tree to represent a phylogeny.

Second, parsimony analysis was developed independently of Hennig, by people such as Farris, Nelson and Platnick. This came to be called cladistics, intended by Ernst Mayr to be a derogatory term for the new form of analysis. The fact that the Willi Hennig Society is associated exclusively with cladistics has nothing to do with Hennig himself, or with the logic of his approach to phylogenetics. You need to clearly distinguish between Hennig and Cladistics!

Third, Hennig was more interested in classification than he was in phylogeny reconstruction. This seems to cause confusion for gene jockeys and linguists, in particular, who often associate phylogenetics solely with classification (see, for example, Felsenstein 2004, chapter 10). Sure, Hennig was primarily interested in the interpretation of phylogenies, rather than their construction. However, that was simply a personal point of view. The logic of his work transcends his own personal interests. Without him, no genealogical reconstruction makes logical sense, in genetics or linguistics. Mathematical methods for summarizing data were developed independently in genetics and linguistics, just as they were in other areas of biology and also in stemmatology. However, without the concept of shared innovations, these methods remain mathematical summaries, not estimates of genealogies.

Finally, Hennig's work was not original, being naturally a synthesis of much previous work. In biology, the work of Walter Zimmerman is frequently noted (eg. Donoghue & Kadereit 1992), and in linguistics the work of Karl Brugmann is obviously important (see Mattis' post Arguments from authority, and the Cladistic Ghost, in historical linguistics). Sometimes, wheels have to be re-invented many times before the general populace comes to realize just how important they are.

References

Atkinson QD, Gray RD (2005) Curious parallels and curious connections — phylogenetic thinking in biology and historical linguistics. Systematic Biology 54: 513-526.

Donoghue MJ, Kadereit W (1992) Walter Zimmermann and the growth of phylogenetic theory. Systematic Biology 41: 74-85.

Felsenstain J (2004) Inferring Phylogenies. Sinauer Associates, Sunderland MA.

Hennig W (1966) Phylogenetic Systematics. University of Illinois Press, Urbana IL. [Translated by DD Davis and R Zangerl from W. Hennig 1950. Grundzüge einer Theorie der Phylogenetischen Systematik. Deutscher Zentralverlag, Berlin.]

Platnick NI, Cameron HD (1977) Cladistic methods in textual, linguistic, and phylogenetic analysis. Systematic Zoology 26: 380-385.

Morgan Colman and English royal genealogies

I noted in an earlier post (Drawing family trees as trees) that from 1576 CE Scipione Ammirato, an Italian writer and historian, set up a cottage industry producing family trees for the nobility. Over the years, he was not the only person to try to make money this way.

In the English-speaking world, one of these was Morgan Colman (or Coleman), who produced an impressively large genealogy of King James I and Queen Anne, in 1608. Nathaniel Taylor has commented: "Of all the congratulatory heraldic and genealogical stuff prepared early in James’s reign, this might be the most impressive piece of genealogical diagrammatic typography."

Unfortunately, we do not have a complete copy of this family tree. It was published as a set of quarto-sized bifolded sheets that needed to be joined together. Below is a small image of the copy in the British Library, which gives you an idea of the intended arrangement, and its incompleteness (click to enlarge). Taylor has a larger PDF copy available here.

The WorldCat library catalog lists the work as "Most noble Henry ; heire (though not son)", which is the first line of the dedicatory verse at the top left. Elsewhere, I have seen it referred to as "The Genealogies of King James and Queen Anne his wife, from the Conquest".

It is usually described as "a genealogy of James I and Anne of Denmark in 10 folio sheets [sic], with their portraits in woodcut, accompanied by complimentary verses to Henry Prince of Wales, the Duke of York (Prince Charles) and Princess Elizabeth, and with the coats-of-arms of the nobles living in 1608 and of their wives."

A Christies auction notes the sale of an illuminated manuscript of the "Genealogy of the Kings of England, from William the Conqueror to Elizabeth 1", produced by Colman in 1592. The accompanying text reads (in part):

Colman, a scribe and heraldic painter, was steward and secretary to various eminent public figures, including successive Lord Keepers of the Great Seal, Sir John Puckering (1592-96) and Sir Thomas Egerton (1596-1603) who caused his election as MP for Newport, Cornwall in 1597. Heraldic and genealogical compositions were his speciality and in 1608 he had composed, and prepared for printing, genealogies of King James and his Queen published as ten large quarto sheets; in 1622 a payment records his work for James I in producing two large and beautiful tables for the King's lodgings in Whitehall and for making many of the genealogical tables for 'His Majesty's honour and service'. But these successes were a distant prospect in 1592 when he produced the present manuscript: in that year he petitioned for the post of York Herald and a second petition at about this date, possibly to Sir John Puckering, solicits the addressee's continued support for his advancement. This genealogy appears therefore to be part of a campaign to secure employment: the writer ends his summary of contents 'Wherein if the simplicity of well-meaning purpose, maie procure desired accept'on then rest persuaded that the industrious hand is fullie prepared spedelie to produce matter for more ample contentment.' The inclusion of Francis Bacon's arms at the end of his work shows that Colman had hopes of securing Bacon's patronage: by 1592 Bacon's political and legal career was well established, he was confidential adviser to the Earl of Essex, the Queen's favourite, and had hopes of high office. Colman, however, hedged his bets; another copy of this genealogy survives, though incomplete and lacking the arms of a recipient.

Colman apparently petitioned for the office of herald in the latter part of the reign of Queen Elizabeth I, but never obtained it.

The origin of an idea: reducing networks to trees

I have written a number of times in this blog about the strong tendency for people to present reticulating evolutionary relationships as trees rather than as networks. This involves them somehow reducing complex networks to bifurcating trees.

When referring to a "family tree", the most common way to reduce a network to a tree is simply to repeat people's names as often as necessary. That is, rather than have them appear once (representing their birth) with multiple reticulating connections representing their reproductive relationships, they appear repeatedly, once for their birth and once for each relationship, so that there are no reticulations. I presented a number of online examples of this process in my posts on Reducing networks to trees and on Thoroughbred horses and reticulate pedigrees.

Recently, Jean-Baptiste Piggin has pointed out that this approach actually has a very long history, indeed, actually dating back to what seems to be the first pictorial representation of a genealogy.

In an earlier post (The first infographic was a genealogy) I described Piggin's work on what he calls the Great Stemma, a diagram from c. 400 CE (Late Antiquity) representing the genealogy of Jesus as presented in the New Testament. In a recent update, Piggin reports:

The Great Stemma contains 13 doppelganger or fetches, that is to say, simultaneous appearances of the same person in two places, e.g. Hezron [as a] child, and separately as an ancestor of Jesus. This graphic method simplifies the layout, but forced the Late Antiquity reader to mentally register these virtual "hyperlinks".

If you view his diagram of the Great Stemma (Touring the Reconstruction), you can see on an overlay a set of links connecting the multiple appearances of the following people:
Athaliah, Gershon, Hezron, Judah, Kohath, Leah, Levi, Mahalath, Merari, Perez, Rachel, Rebekah, and Timna.

This repetition simplifies what is a rather complex diagram, which actually shows a network of family relationships. There is still one reticulation in the diagram, however, because it depicts Jesus' ancestry as described in the New Testament by both Matthew (labeled Filum C in the schematic below) and Luke (labeled Filum D), and these differ regarding the descendants of David (but not his ancestors).

The diagram contains more than just a genealogy (represented by Filum A-D), as it also displays other references from the Bible (indicated in yellow). Piggin is still working on his reconstruction (there are no known copies of the original, only later hand copies), and he continues to make discoveries.

Of especial interest in the genealogies is that Piggin now reconstructs the Great Stemma as having a strictly grid-like arrangement of the people, as discussed in his blog post Secret of the oldest infographic revealed: a grid. The placements of the lineages in the Stemma, and the connections between the people, are not always obvious to modern eyes (see my post on How confusing were the first written genealogies?), since we are used to the modern version of a "family tree" — it took another millenium after the Stemma to settle on the modern version. However, the use of a regular grid-like arrangement in the Stemma seems surprisingly modern by comparison.

Unfortunately, this arrangement seems to have become corrupted in the subsequent hand-made copies, suggesting that the scribes did not always appreciate the grid's organizational importance.

Drawing family trees as trees

In a previous blog post (Who first drew a family tree as a tree?), I pointed out that one of the candidates for drawing the first family tree as a tree (as opposed to a stick diagram) is Giovanni Boccaccio, in his Genealogia Deorum Gentilium (On the Genealogy of the Gods of the Gentiles) of 1370 CE.

However, there are arguments against this attribution. For example, Boccaccio's original pedigree was: (1) not about real people; (2) more like a vine rather than a tree; and (3) not rooted at the bottom. The first version of his pedigree that was actually tree-like and rooted at the bottom was in the Italian translation from 1547 CE (and again in the 1554 edition).

Recently, Jean-Baptiste Piggin has indicated in his blog that he is looking for the Oldest family tree. He writes:

What I am looking for here is the earliest example of a thing named "family tree" or "albero genealogico" or "Stammbaum" or "arbre de famille" ... these things had unwitting precursors in previous centuries. There were even 12th-century artists who took pre-existing stemmata and flipped them upside down to depict them as trees. But these were experiments or flukes, not genealogical trees as a general cultural phenomenon.

The conscious idea of presenting a complete family line connected by a woody trunk first shows up in southern German woodcuts in the late 15th century ... The tree as a recognizable category of art, a product where artist and customer know what to expect, only shows up later in the sixteenth century. It looks semi-natural, has a bottom root and clearly tiered generations.

In his blog post Piggin mentions various attempts (at drawing pedigrees) between their first known appearance in c. 1000 CE (see The first royal pedigree) and the late 1500s, when Scipione Ammirato (an Italian writer and historian) set up a cottage industry producing family trees for the nobility.

Highlights of the history of tree-like pedigree diagrams, as currently known, include (with links to copies of the diagrams):

1370 Boccaccio – first pedigree drawn as a vine, with the root at the top
1475 Rodericus (Der Spiegel des Menschlichen Lebens) – multiple intertwining vines
1492 Conrad Bote (Cronecken der Sassen) – first tree, using family shields in place of names
1515 Albrecht Dürer (Ehrenpforte, engraving) – unbranched woody vine
1536 Robert Peril (Family Tree of the House of Habsburg, engraving) – tree, with people along the trunk only, not on the branches
1547 Boccaccio – first version of his pedigree drawn as a tree
1576 Scipione Ammirato – first of his trees, with people along the trunk as well as the branches. Ammirato's first tree is shown above.

The 12th century pedigree that Piggin refers to, and dismisses as a candidate for a real tree, is discussed in his blog post on the Erlangen tree. This pedigree is from one of the copies of the Ekkehardi Chronicon Universale (Chronicle of Ekkehard of Aura, or Chronicle of Frutolf), drawn in c. 1140. The pedigree itself is based on the one shown in my post on The first royal pedigree, except that Cunigunde of Luxembourg (the focus of that earlier pedigree) is strangely absent. The version of interest is shown below, from the Universitätsbibliothek Erlangen-Nürnberg (manuscript 406, referred to as the Erlangen Codex, page 204v).

What is unique about this version of the pedigree is that it has been turned upside down, so that the root is at the bottom, making it look more tree-like. (See also my post on Does it matter which way up a tree is drawn?) As Piggin notes (NB: he uses the word "stemma" to refer to the early versions of pedigrees, with the names in roundels, connected by lines):

Other manuscripts of the Ekkehard Chronicle present the Stemma of Cunigunde more or less faithfully, but the scribe-artist of the Erlangen codex decided to have some fun with it. He inverted it, and drew the figure of Arnulph at the left and Arnulph's saintly mother Begga at right. [Arnulf is the person named at the root of the pedigree.]

What change in medieval culture had made this startling inversion of the stemma not just possible, but acceptable to the customer, probably the Cistercian Monastery of Heilsbronn in Germany, which became the long-term owner of this codex? Is this quirky conversion on an artist's desk the precise moment when the family tree, later to become a prestigious badge of nobility, was invented?

As I have already pointed out, inverted stemmata made to resemble trees with roots in soil are a rarity before the 16th century. It was 16th-century scholars like Scipione Ammirato who deserve the credit as the true originators of the family tree, not the medieval artists who created trees of ancestry more or less by fluke.

Grape genealogies are networks, not trees

I have noted before that the genealogies for all domesticated organisms are networks not trees, and specifically they are hybridization networks. That is, in sexually reproducing species, every offspring is the hybrid of two parents. If we include both parents in the pedigree, plus all of their relatives, then this will form a complex network every time inbreeding occurs.

I have previously illustrated this phenomenon using genealogies of grape cultivars:
     Are phylogenetic trees useful for domesticated organisms?
     First-degree relationships and partly directed networks

Reconstructing grape genealogies is often a tricky business. This was originally done using phenotypic characters and historical records, of course, but these days we use DNA from whatever cultivars are available for sampling. Perhaps the biggest problem is that many of the cultivars are no longer known (there have been at least 10,000 of them recorded at some time in history), so that the genealogies are full of question marks representing unknown (unsampled) parents.

The practical consequence of this is that the time direction of the genealogy will be ambiguous whenever there is a missing parent. Estimates of identity-by-descent (IBD) are calculated based on linkage analysis for all pairwise comparisons of samples, and complex crossing schemes can generate IBD values that are indistinguishable from sibling relationships. So, in these cases we cannot distinguish parent-offspring relationships from sibling relationships.

A simple example is shown in the most detailed current book on grape cultivars:

Jancis Robinson, Julia Harding, José Vouillamoz (2012) Wine Grapes: a Complete Guide to 1,368 Vine Varieties, including their Origins and Flavours. Allen Lane / Ecco.

This example involves the grand-parentage of the Shiraz grape, usually called Syrah in the effete monarchies of the Old World. The authors present three possible scenarios, as shown here.

There are five sampled cultivars and two inferred unknowns, arranged in an unrooted network. Because the unknowns are inferred to be parents, the network can be rooted in any of three different places, as shown by the three Options illustrated.

The authors (or, more specifically, the third author, who is the one responsible for the genealogies) are in favour of Option A. This means that Mondeuse Noir and Viognier are Syrah's half-siblings rather than either being the grandparent.

This small genealogy is a tree, but when we move to larger genealogies the network nature of the cultivars should become obvious.

However, the authors resort to a standard subterfuge to hide this fact. This strategy is to show cultivars multiple times in the genealogies, to avoid drawing reticulate relationships. I have illustrated this approach a couple of times before in this blog:

     Reducing networks to trees
    Thoroughbred horses and reticulate pedigrees

In the following genealogy of the Pinot cultivar, the authors note: "For the sake of clarity, Trebbiano Toscano and Folle Blanche appear twice in the diagram."

Trees reign supreme as simplifications of networks!

Who first drew a family tree as a tree?

The Online Etymology Dictionary indicates that the English-language expression "Family tree" in the sense of "graph of ancestral relations" is first attested from 1752, in the novel A Genuine Account of the Life and Transactions of Howell ap David Price (which is available in Google Books).

Such pedigree diagrams have a much longer history, of course, but they were not called family trees, nor were they drawn with any particular tree-like imagery (except for the religious Tree of Jesse, pictures of which started appearing in the 10th century). See, for example:

• The role of biblical genealogies in phylogenetics
• The first infographic was a genealogy (c. 400 AD)
• How confusing were the first written genealogies?
• The first royal pedigree
• Another early noble pedigree
• The first known pedigree of a non-noble family

This leaves open the question of who first drew a tree-like family tree. [Note: see also the later post Drawing family trees as trees.]

Ernest H. Wilkins (1925. The genealogy of the genealogical trees of the Genealogia deorum. Modern Philology 23: 61-65) has suggested that it might be the Italian author and poet Giovanni Boccaccio (1313-1375), in his Genealogia Deorum Gentilium (On the Genealogy of the Gods of the Gentiles).

This Renaissance book was an "encyclopedic compilation of the tangled family relationships of the classical pantheons of Ancient Greece and Rome" (according to Wikipedia). It was written in Latin, apparently starting in c. 1350, and then continuously corrected and revised until the author's death. In c. 1370 an apograph [ie. perfect copy] was made of an autograph manuscript [ie. in the author's own hand], and from that first apograph other copies were made.

The 1370 autograph is not known to still exist; but a second autograph manuscript, showing later revisions, is in the Laurentian Library in Florence (MS. LII, 9). There are some three dozen extant apographs from the 1300s and 1400s, all based on the lost first autograph. The first printed edition was produced in Venice in 1472, followed by an edition of 1473 printed in Leuven. At least seven other editions appeared during the 1400s and 1500s. A French translation was published in Paris in 1498, and an Italian translation appeared in Venice in 1547. (See Ernest H. Wilkins. 1919. The genealogy of the editions of the Genealogia Deorum. Modern Philology 17: 425-438.)

The illustrations shown here are from various versions of the book.

Wilkins (1925) notes:

The extant autograph manuscript of the Genealogia Deorum of Boccaccio is illustrated by thirteen genealogical trees, designed certainly and drawn in all probability by Boccaccio himself. At the top of each tree is a large circle, in which is written the name of a divinity. From this circle descends a stem which now expands into other lesser circles, now sends forth leaves, and now branches, which in their turn expand into circles and send forth leaves and lesser branches. In the center of each circle or leaf a name is written. The circles are used for those divinities whose progeny is represented in the same tree; the leaves, for divinities whose progeny is not represented. In the circles the words qui genuit [ie. who fathered] follow each masculine name, and the words quae peperit [ie. who bore] each feminine name. Similar trees certainly appeared in the earlier lost autograph, from which all the apograph manuscripts are derived; and similar trees appear in several apographs, and in the fourth and all later editions of the Genealogia.

So far as I can ascertain, Boccaccio's trees are the earliest secular genealogical trees properly so called: that is to say, the first non-biblical genealogical charts in which stems, branches, and leaves appear.

This claim of priority has apparently gone unchallenged by later workers; eg. Christiane Klapisch-Zuber (1991. The genesis of the family tree. I Tatti Studies in the Italian Renaissance 4: 105-129) notes:

It may well be that Boccaccio was the first to combine the old graphic system of medallions in the descending order typical of medieval genealogies with the implications of a vegetal theme.

The vegetal image is quite obvious, although the leaves do vary widely in form within any one manuscript, and also from copy to copy. In the autograph they are palmately five-lobed. In some trees the different generations are indicated by variation in the colour of the branches.

Personally, to me each of these diagrams looks more like a vine than a tree, especially with the root at the top.

Moreover, some of the printed editions do not contain the genealogies, and in others their form is modified. For example, some have a portrait of the progenitor divinity, and others bear scrolls or circles instead of leaves. Some of the trees have extra (empty) leaves or scrolls. It is thus quite clear that the tree metaphor for the pedigrees was not seen as important at the time.

Nevertheless, it is important to note that in the first two editions of the Italian translation by Giuseppe Betussi (1547 & 1554; but not in later editions) the first genealogy is drawn as an actual tree rooted in the ground, with the name of the progenitor appearing at the base of the trunk. Klapisch-Zuber notes:

In comparison with Boccaccio's divinely radiant foliage, this image must strike us as mean and desiccated. And yet, it is the triumph of the genealogical tree as we know it, planted right side up; and any one in the modern world can use it to evoke his ancestors and to express his faith in the survival of his lineage.

GeneaQuilts

The drawing of large genealogies is not easy, and phylogeneticists (among others) have tried a number of solutions, including circular diagrams as we as interactively zoomable displays. One interesting solution that does not appear to have yet been used in phylogenetics is the concept of GeneaQuilts.

These were introduced by the Visual Analytics Project:

A. Bezerianos, P. Dragicevic, J.-D. Fekete, J. Bae, B. Watson (2010) GeneaQuilts: a system for exploring large genealogies. In: IEEE InfoVis '10: IEEE Transactions on Visualization and Computer Graphics, Oct 2010, Salt-Lake City, USA.

The web page has a video introducing the concept, which does a better job than I can do here. The basic idea is to abandon the tree / network representation, and to use a diagonally-filled matrix instead, where the rows are individuals and the columns show parent-offspring relationships.

Here is an example genealogy, based on the reported relationships among the Greek Gods.

If the relationships are tree-like then the diagram will be concentrated on the diagonal of the matrix. However, network relationships (inbreeding) will cause off-diagonal elements, two of which are shown in the example: one involves Hades and his niece Persephone.

Several, much larger examples are displayed on the GeneaQuilts website. There is a program that can be downloaded, which takes as its input standard family-history files.

There seems to be no intrinsic reason why this display form could not also be used in phylogenetics.

The phylogeny of elves and other fantastic figures

I have previously pointed out that phylogeny reconstructions exits for legendary figures, cartoon animals, Donald Duck, Pokémon, and dragons (see Faux phylogenies). Another popular topic has been the figures of fantastical literature such as elves, dwarves, goblins, gnomes and trolls. Here I present a few of the better-known ones from around the web.

Elves

The first one comes from Dominic Evangelista's blog post at The Eco Tome called Phylogeny of elves finds that santa’s workers are actually dwarves. The original data matrix is provided, but the comments on that post point out a few errors in the character coding.

Dungeons & Dragons Elves

This next one comes from Limey Boy's blog, and specifically pertains to the D&D Elven Phylogenetic Genealogical Tree.

There is a related post on the D&D Human Phylogenetic Genealogical Tree, with a much more extensive genealogy.

Fairyland

Next we have a small tree from Terry Newman covering The Natural History of Fairyland.

Fantasy Races

Then we have a somewhat bigger tree from Reddit covering the Evolutionary Phylogeny of Fantasy Races. This seems to have multiple roots, unlike the other genealogies above.

Lord of the Rings

Finally, we have the genealogy to end all fantasy genealogies. The Lord of the Rings Project has a complete interactive genealogy of all of the works of J.R.R. Tolkien. It is way too large to show here, even in miniature, and is actually a series of genealogies that are not connected. However, it is worth noting that, unlike the above genealogies, while most of the genealogies are tree-like many are actually networks because both sexes are included.

Is the Ring of Life a network?

Ten years ago, Rivera and Lake decided to emphasize the series if genome fusions that seem to have been involved in the origin of the major phylogenetic groups by calling it the ring of Life rather than the Tree of Life:

Maria C. Rivera and James A. Lake. 2004. The Ring of Life provides evidence for a genome fusion origin of eukaryotes. Nature 431: 182-185).

This terminology has been repeated in a number of subsequent papers, including:

James McInerney, Davide Pisani and Mary J. O'Connell (2015) The Ring of Life hypothesis for eukaryote origins is supported by multiple kinds of data. Philosophical Transactions of the Royal Society of London B 370: 20140323.

However, life is not that simple, and it has more recently become accepted that a set of inter-connected rings is involved in the metaphor, rather than the simple ring originally presented. Thus we now have the plural Rings of Life, instead.

James A. Lake and Janet S. Sinsheimer (2013) The deep roots of the Rings of Life. Genome Biology and Evolution 5: 2440-2448.

James A. Lake, Joseph Larsen, Brooke Sarna, Rafael R. de la Haba, Yiyi Pu, HyunMin Koo, Jun Zhao and Janet S. Sinsheimer (2016) Rings reconcile genotypic and phenotypic evolution within the Proteobacteria. Genome Biology and Evolution (in press).

I think that the rest of us would still call each of these diagrams a network. Indeed, most of the metaphors that have been used over the years can also be called a network (see Metaphors for evolutionary relationships).

The Tree of Architecture

The following diagrams are taken from the book A History of Architecture on the Comparative Method for the Student, Craftsman, and Amateur. This book is considered to be "a canonical text that has played a formative role in the education of generations of architects" because it really does "cram everything into a single volume". The first edition of the book appeared in 1896, with the 20th edition appearing in 1996.

The first picture is from the 5th edition (1905), and the second one is from the 16th edition (1954).

As noted in the first figure, these trees purport to show the "evolution" of the various architectural styles. However, they do no such thing.

At the base of the tree trunk is a set of individual architectural styles that apparently led nowhere, while at the crown of the tree several styles are repeated. Each of the latter styles exist on two side-branches from the main trunk, each pair connected by vertical tendrils. So, this is a network, at least. However, the meaning of this network is not immediately obvious. Indeed, even a short perusal of the diagram should lead you to the idea that the meaning is contained more in cultural bias than in the actual history of architecture.

The history of the book itself is somewhat complex. The first edition was written by the father and son team of Banister Fletcher & Banister F. Fletcher. Subsequent editions were revised by Banister F. Fletcher (the son), with the 6th edition (1921) being rewritten by Fletcher and his first wife (who got no credit, even though the father's name was then dropped). After Fletcher's death in 1953, the 17th edition (1961) was revised by R.A. Cordingley, the 18th (1975) by James Palme, the 19th (1984) by John Musgrove, and the 20th (1996) by Dan Cruickshank. The tone and arrangement of the book was changed with each edition.

The tree has been analyzed in detail by Gülsüm Baydar Nalbantoglu (1998. Toward postcolonial openings: rereading Sir Banister Fletcher's "History of Architecture". Assemblage 35: 6-17). She notes the following:

Until the fourth edition of 1901, A History of Architecture had been a relatively modest survey of European styles. The fourth edition, however, appeared with an important difference: this time the book was divided into two sections, "The Historical Styles", which covered all the material from earlier editions, and "The Non-Historical Styles", which included Indian, Chinese, Japanese, Central American, and Saracenic architecture. 

The "Tree of Architecture" has a very solid upright trunk that is inscribed with the names of European styles and that branches out to hold various cultural / geographical locations. The nonhistorical styles, which unlike others remain undated, are supported by the "Western" trunk of the tree with no room to grow beyond the seventh-century mark. European architecture is the visible support for nonhistorical styles. Nonhistorical styles, grouped together, are decorative additions, they supplement the proper history of architecture that is based on the logic of construction. 

In the posthumously published seventeenth edition of 1961, the two parts were renamed "Ancient Architecture and the Western Succession" and "Architecture in the East", respectively. The nineteenth edition of 1987, on the other hand, consisted of seven parts based on chronology and geographical location. Cultures outside of Europe included "The Architecture of the Pre-Colonial Cultures outside Europe" and "The Architecture of the Colonial and Post-Colonial Periods outside Europe".

That is, "architecture" for the Banisters was defined as being about a building's construction, not its decoration. European cultures focused on construction, and they developed their styles through time. Other cultures focused on decoration, and were therefore not a proper part of architecture, and had no historical development. This is what the tree attempts to show.

This cultural bigotry was corrected in the final few editions of the book (after the Fletchers were no longer involved), where all architectural styles were considered more-or-less equal.

Rivers of Life, instead of trees

In an earlier blog post, I discussed some of the evocative Metaphors for evolutionary relationships, particularly reticulating ones.

In that post I listed the concept of a "braided river", and mentioned a 1994 paper by John Moore as my earliest source for the image. However, the metaphor actually goes back more than 100 years earlier. It occurs as the central metaphor in this quite remarkable book on comparative religion:

Forlong, J.G.R. (1883) Rivers of Life: or Sources and Streams of the Faiths of Man in All Lands, Showing the Evolution of Faiths from the Rudest Symbolisms to the Latest Spiritual Developments. 2 vols. Bernard Quaritch: London.

James George Roche Forlong was a Scottish engineer serving in the British army that occupied India during the 19th century. He apparently had a life-long interest in comparative religion, and his book arose from his personal experience of non-Christian religions (facilitated by his knowledge of several languages). The book involves a serious re-interpretation of the evolutionary history of world religions, as a series of six inter-connecting rivers running from ancient times into the modern world, each river representing a different type of worship.

The illustrative chart that accompanies the book can be viewed here. A low-resolution copy is shown below.

Wigwag, and the Family Tree

I have noted before that common usage of expressions like "family tree" often extend far beyond actual pedigrees. This particular expression is often used to describe any sort of historical relationship, not just genealogical ones. It is also sometimes used simply to describe any sort of personal inter-connection. All of these usages occurred in a short-lived magazine from 25 years ago called Wigwag.

Wigwag magazine formally debuted in October 1989 (after a test issue in 1988), and published its last issue in February 1991, for a total of 15 issues. It was a sort of cozy version of the New Yorker magazine. Similarly, it had a number of regular features, such as the Road Trip, the Map, and Letters From Home. The one that is of interest to us was called The Family Tree.

This feature mapped cultural relationships, having been described as "a field guide to the genealogy of influence in American life". It included human relationships, but it also included things like cars (the tree of which is reproduced in the book by Nobuhiro Minaka & Kunihiko Sugiyama. 2012. Phylogeny Mandala: Chain, Tree, and Network) and comic-book superheroes.

I have been unable to locate any decent copies, but four of the "trees" are included below.

As you can see, sometimes The Family Tree was actually a genealogical tree, but just as often it was simply a network of pairwise cultural connections. The latter, of course, usually formed a complex network that did not really map historical relationships.

This last Family Tree is from the original trial issue, and shows the inter-relationships of the writers and producers of American TV sitcoms.

You can read a bit more about the magazine, and its history, here:

• Design Magazines
• The Awl
• Folio
• Chicago Tribune

An unusual genealogy

"Genealogies" produced on the web are frequently no such thing, they are merely timelines. However, the following alleged Genealogy of Automobile Companies seems to really be one, and it has a number of odd characteristics. These characteristics are quite common among manufactured products.

It is described as "A flowing history of more than 100 automobile companies across the complete time span of the automobile industry." Actually, it focuses on companies in the USA, up to 2012. You can zoom in on the details by visiting the original image at HistoryShots InfoArt.

First, note that the genealogy has multiple roots. Second, lineages coalesce forwards through time rather than diverging, so that the lineages become clustered. Moreover, some lineages do not connect to any others. Finally, there is horizontal transfer, because parts of companies get sold to other companies.

There is also a similar Genealogy of US Airlines, and a Genealogy of International Airlines.

Consanguinity and incest can produce the same effects

I have noted before that Pedigrees and phylogenies are networks not trees. For example, a human family "tree" is a tree only if it includes one sex alone. Otherwise, it must be a network when traced backwards from any single individual through both parents, because the lineages must eventually coalesce in a pair of shared common ancestors.

This potentially creates a problem for maintaining genetic diversity within species. If a pedigree is tree-like, then each person would, for example, have 32 great-great-great grand-parents. These 32 people's genes are mixed more-or-less randomly (depending on recombination and assortment) to produce the great-great-great grand-child. This heterozygosity is a good thing, evolutionarily, because there is then genetic diversity within that person.

However, inbreeding turns a tree into a network. This increases the probability that identical alleles will be paired in any one individual. If deleterious recessive alleles are thereby expressed, then genetic problems can ensue, which is called inbreeding depression. However, this situation is not inevitable, but depends on the probability of alleles becoming paired. Indeed, for domesticated organisms, inbreeding is the norm (see Thoroughbred horses and reticulate pedigrees).

I have discussed examples of well-known historical figures who have encountered the unfortunate effects of inbreeding, including Charles Darwin (Charles Darwin's family pedigree network) and Henri Toulouse-Lautrec (Toulouse-Lautrec: family trees and networks). In both cases the problems arose because of consanguineous relationships, which involve people who are first cousins or more closely related.

I have also discussed the extreme case of consanguinity, incest. In particular, royalty have often been exempt from taboos against sibling and parent-child couplings, as noted in Tutankhamun and extreme consanguinity and also in Cleopatra, ambition and family networks. At least for Tutankhamun there is evidence of genetic problems (an accumulation of malformations is evident), but apparently not in Cleopatra's case (there is no convincing evidence of infertility, infant mortality or genetic defects, for example). Royalty have not been the only exceptions to the incest taboo (see Evolutionary fitness and incest).

In Tutankhamun's case it has been suggested that his mother was his father's (Akhenaten) sister (name not known), which is surprising, because only two wives of Akhenaten, Nefertiti and Kiya, are known to have had the title of Great Royal Wife, which the father of the royal heir should bear. As a way out of this dilemma, Marc Gabolde has suggested that the apparent genetic closeness of Tutankhamun's parents is because his mother was his father's first cousin, Nefertiti. The apparent genetic closeness is then not the result of a single brother-sister mating but instead is due to three successive instances of marriage between first cousins.

To explain this idea we can look at an actual example. An historical example of how consanguinity can produce the same genetic effects as incest is provided by the Spanish branch of the Habsburg dynasty in 1700, as discussed in Family trees, pedigrees and hybridization networks.

This example can be explained using inbreeding F values. For any specified offspring, these indicate the probability of paired alleles being identical by descent (ie. due to the close relationship of the parents). For close family relationships the F values are:

self parent-offspring siblings uncle-niece = aunt-nephew double first cousins first cousins first cousins once removed second cousins

0.500 0.250 0.250 0.125 0.125 0.063 0.031 0.016

Note that incest produces F values of 0.250 while consanguinity values are 0.063 or greater.

If we consider the case of King Charles II of Spain (1661-1700), then his inbreeding F = 0.254, which was achieved entirely without incestuous relationships. His pedigree is shown in the post Family trees, pedigrees and hybridization networks.

This pedigree shows that the parents of each person had the following relationships:

himself = uncle-niece [ie. his parents were uncle and niece]

father = first cousins once removed [ie. his father's parents were first cousins once removed]
mother = first cousins

father's father = (a) = uncle-niece
father's mother = (b) = uncle-niece
mother's father = first cousins
mother's mother = first cousins once removed

father's father's father = not closely related
father's father's mother = first cousins
father's mother's father = not closely related
father's mother's mother = not closely related
mother's father's father = uncle-niece
mother's father's mother = second cousins
mother's mother's father = see person (a)
mother's mother's mother = see person (b)

Thus, on his father's side he was the third generation of consecutive consanguinity, and on his mother's side he was the fourth generation of consecutive consanguinity. This is simply an accumulating series of probabilities — consanguinity potentially produces problems and consecutive consanguinity simply increases the probability.

It is not surprising, then, that Charles suffered genetic problems (he was disfigured, physically disabled and mentally retarded) to such an extent that his royal lineage came to an end, and the Spanish branch of the Habsburg dynasty ceased to rule.

Incidentally, the scientist who devised the quantity F, Sewall Wright, himself had a rather high amount of inbreeding — his parents were first cousins.

Does it matter which way up a tree is drawn?

To a modern phylogeneticist the answer to this question is obviously "no". Phylogenetic trees occur in the literature with their root at the top, the left or the bottom, and more rarely on the right. The graph has the same interpretation no matter where the root is placed, as all of the edges are implicitly directed away from the root. The tree can even be circular, with the root in the centre and the tree radiating outwards.

However, this was not always so for genealogies, and indeed this freedom seems to be a product of the past 200 years or so. The history of tree orientation has been discussed in detail by Christiane Klapisch-Zuber (1991. The genesis of the family tree. I Tatti Studies in the Italian Renaissance 4: 105-129).

Originally, genealogies were drawn with the root at the top, as shown in previous blog posts: The first royal pedigree, and The first known pedigree of a non-noble family. These pedigree trees (ie. genealogies of individuals) have a particular ancestor at the root of the "tree", so that the tree expands forwards in time down the page, to increasing numbers of descendants at the leaves (ie. a "descent tree"). This made linguistic sense, because people "descended" from the ancestor down the page. In European languages pages are read top to bottom, and so the natural reading order was the same as the time sequence.

However, this arrangement makes no sense if one refers to the graph as a "tree". Trees have their root at the bottom, not the top. Trying to draw the pedigree as a tree while retaining the original orientation could lead to unusual results, as shown in the first figure, from the end of the 1300s CE (from Universitätsbibliothek, Innsbruck, ms. 590, folio 116r). This is actually an Arbor Consanguinitatis rather than an empirical pedigree — it shows the various relatives of a nominated individual (the man pictured in the center) and their degree of relationship to that person. These diagrams have been used to compute which relatives can marry without committing incest, or which can inherit if a person dies intestate. Jean-Baptiste Piggin, at his web site Macro-Typography, has noted that the earliest known examples are from the 400s CE.

In order to match a real tree, the genealogy has to be read from bottom to top. This implies an ascent through time, instead, with a spreading out of the family upwards through time.

The first known empirical pedigree in which the ancestor is at the base is the Genealogia Welforum, the pedigree of a dynasty of German nobles and rulers (Dukes of Bavaria, and Holy Roman Emperors, successors of the Carolingians). The earliest known example, drawn as part of the Historia Welforum [Welf Chronicle], is shown in the second figure (from Hessische Landesbibliothek, Fulda, ms. D.11 folio 13v). The original text version of the pedigree is dated 1167-1184 CE, with the miniatures added sometime from 1185-1191 CE.

Clearly, this diagram is only sketchily like a tree, with many of the people placed along the main trunk, and medallions hanging off for other relatives. This seems to arise from the pedigree's origin as prose, and the subsequent literal illustration of that prose.

The ancestor is labeled "Welf Primus", and he apparently lived in the time of Charlemagne (the best known of the Carolingian dynasty). The empty space at the top of the chart was apparently intended for a picture of Emperor Frederick I Barbarossa, of the House of Hohenstaufen. The woman at the top right is Henry the Black's daughter Judith, who was the mother of Barbarossa. Intriguingly, the final bend of the Welf trunk to the left, combined with Barbarossa at the top, seems to imply that it is the descendants of Barbarossa who continue the Welf lineage, rather than those bearing the Welf name.

Historically, it seems to have been the proliferation, after about 1200 CE, of illustrations of the biblical Tree of Jesse that popularized the idea of "pedigrees as trees". The next figure shows such a tree from c. 1320 CE (from a Speculum Humanae Salvationis manuscript, Kremsen ms. 243/55). Jesse lies at the base of the tree, and the tree actually arises from him. His descendants then ascend to Jesus, shown at the crucifixion, with Heaven illustrated at the top. The tree thus uses Christ's pedigree to symbolize the ascent of humans to heaven (via his crucifixion), rather than simply the descent of humans through time. That is, the tree correctly represents ascent (as well as descent).

This leaves us contemplating just when we added the final twist to the iconography, by putting a single descendant at the base of the tree, and having the ancestors branching out above as leaves (ie. an "ascent tree"). This means that time flows from the top to bottom of the figure, even though the tree is oriented from bottom to top. This is quite illogical as an analogy, given that the base of a real tree is the origin of its growth (see Goofy genealogies). This particular iconography is not used for phylogenies but is very commonly used for pedigrees.

I have no idea when this first occurred. However, David Archibald (2014. Aristotle's Ladder, Darwin's Tree: The Evolution of Visual Metaphors for Biological Order. Columbia Uni Press) draws attention to a very tree-like pedigree of Ludwig (Louis III), fifth Duke of Württemberg, from the late 1500s, shown here as the final figure (from Württembergisches Landesmuseum, Stuttgart). Ludwig is at the base of the tree, and ironically he had no descendants (although he married twice). His parents are above him in the tree (Christoph, Duke of Württemberg, to the left, and Anna Maria von Brandenburg-Ansbach, to the right), followed by four further ancestral generations. Note the leaves and hanging fruits, which highlight the tree metaphor.