Darwin's coral and seaweed metaphors

When challenging previous ideas about biological organization, Charles Darwin insisted upon both the origin of new biological forms and the extinction of some of the old forms. He used a multi-stemmed bush as his published metaphoric icon for these processes (in 1859), but we have always referred to it as a tree.

However, as noted in an earlier blog post (Charles Darwin's unpublished tree sketches), Darwin's first tree-like diagram (dated 1837-1838) was actually a drawing of a coral, accompanied by the text:

The tree of life should perhaps be called the coral of life, [with the] base of [the] branches dead; so that [the] passages cannot be seen

Darwin's specimen 1143, labelled Corallina officinalis.

As a geologist, Darwin had studied corals extensively in the Pacific and Indian Oceans, on the Beagle voyage (1831-1836). In May 1837 he read a paper before the Geological Society of London about his ideas for the development of reefs. This was then published in their journal:

Darwin, C.R. (1837) On certain areas of elevation and subsidence in the Pacific and Indian oceans, as deduced from the study of coral formations. Proceedings of the Geological Society of London 2: 552-554.

He subsequently published his book on the development of coral reefs in 1842 (this was his first monograph):

The Structure and Distribution of Coral Reefs. Being the first part of the geology of the voyage of the Beagle, under the command of Capt. Fitzroy, R.N. during the years 1832 to 1836. Smith, Elder and Co., London.

After this first use of a coral image, Darwin also tried a different marine metaphor:

a tree not [a] good simile — endless piece of sea weed dividing

He seems to have done nothing further with this particular idea.

What is most interesting for us is that the coral metaphor is not a strictly divergent model of evolutionary history. After all, there are many types of coral that form anastomoses. Indeed, there are also corals that do not even form a branching pattern. The neat divergent tree metaphor does not match the world of corals.

This point has been made at length by:

Horst Bredekamp (2003) Darwins Korallen: Frühe Evolutionsmodelle und die Tradition der Naturgeschichte. Verlag Klaus Wagenbach.

Horst Bredekamp (2005) Darwins Korallen: Die frühen Evolutionsdiagramme und die Tradition der Naturgeschichte. Verlag Klaus Wagenbach, second edition.

This book deals with the "aesthetic and political dimension of the coral", which the author (a philosopher and art historian) sees as "a model of anarchic evolution" that opposes the hierarchical metaphor of a tree.

Biologically, Darwin should have stuck to his original idea! However, it is undoubted that the Biblical association of the tree image was more likely to capture his readers' imaginations.

Naudin, Wallace and Darwin — the tree idea

Charles Darwin's most poetic published words concern his image of the Tree of Life. However, he did not claim to have originated the image. For example, Alfred Russel Wallace had already used it. Recently, the Natural History Apostilles blog has mentioned another important predecessor of both Englishmen, the Frenchman Charles Naudin, who deserves wider recognition.

Darwin's well-known words from On the Origin of Species (1859) are:

The affinities of all the beings of the same class have sometimes been represented by a great tree. I believe this simile largely speaks the truth. The green and budding twigs may represent existing species; and those produced during each former year may represent the long succession of extinct species ... As buds give rise by growth to fresh buds, and these, if vigorous, branch out and overtop on all sides many a feebler branch, so by generation I believe it has been with the great Tree of Life, which fills with its dead and broken branches the crust of the earth, and covers the surface with its ever branching and beautiful ramifications.

Wallace seems to have developed the Tree of Life metaphor quite independently (1855. On the law which has regulated the introduction of new species. Annals and Magazine of Natural History, 2nd series 16: 184-196):

"the analogy of a branching tree [is] the best mode of representing the natural arrangement of species ... a complicated branching of the lines of affinity, as intricate as the twigs of a gnarled oak ... we have only fragments of this vast system, the stem and main branches being represented by extinct species of which we have no knowledge, while a vast mass of limbs and boughs and minute twigs and scattered leaves is what we have to place in order, and determine the true position each originally occupied with regard to the others."

Darwin freely admitted having read Wallace's work. Moreover, he was well aware of the other of his predecessors, Charles Naudin, because on p.167 of his 'Books Read' and 'Books to be Read' notebook of 1852-1860 (see Darwin Online CUL-DAR128) he recorded:

"Revue Horticol Imp. 1852. p. 102. Naudin Consid. Phil, sur l'espèce"

Charles Naudin's words are these, roughly translated from the original French (1852. Considérations philosophiques sur l'espèce et la variété. Revue Horticole, 4th series 1: 102-109) [NB. the long convoluted sentences are in the original]:

This doctrine of inbreeding among organic beings of the same family, the same class, and perhaps of the same kingdom, is not new; men of talent, both in France as well as abroad, among them our learned Lamarck, have supported it with all of the authority of their names. We do not deny that, on more than one occasion, they have reasoned upon assumptions which were not adequately supported by observation, that they did sometimes apply to the facts forced interpretations, that finally resulted in exaggerations that have mainly helped to push their ideas. But these defects in details do not diminish the greatness and perfect rationality of the whole system that, alone, reflects, by the community of origin, the great fact of the organizational community of the other living beings of the same kingdom, the primary basis of our rankings of species into genera, families, orders and phyla. In the opposing system now in vogue, in this system which involves many partial and independent creations we recognize or think we recognize as distinct species, one is forced to be logical, to admit the similarities exhibited by these species are only fortuitous coincidence, that is to say an effect without a cause, concluding that the reason is not acceptable. In our own [system], on the contrary, these similarities are both the consequence and proof of a relationship, not metaphorical, but real, that they hold a common ancestor, which they left at times more or less remote and through a series of intermediaries greater or fewer in number; so they express the true relationships between species by saying that the sum of their mutual similarities is the expression of their degree of relationship, as the sum of the differences is that of the distance they are from the common stock from which they derive their origin.

Considered from this point of view, the plant kingdom would present, not as a linear series whose terms would increase or decrease in organizational complexity, according as we consider starting with one end or the other; it would not be more of a disordered tangle of intersecting lines, like a geographical map, whose regions, different in shape and size, would touch by a greater or lesser number of points; it would be a tree the roots of which, mysteriously hidden in the depths of cosmological time, would have given birth to a limited number of successively divided and subdivided stems. These first stems would represent the primordial types of the kingdom; their last ramifications would be the current species.

It follows from there that a perfect and rigorous classification of the other organized beings of the same kingdom, of the same order, of the same family, if something other than the family tree even of the species, indicates the relative age of each, its degree of speciation and the line of ancestors from which it descended. Thereby would be represented, in a manner of some sort so palpable and material, the different degrees of relationship of the species, such as that of groups of varying degrees, dating back to the primordial kinds. Such a classification, summarized in a graphical table, would be seized with much facility by the mind through the eyes, and present the most beautiful application of this principle generally accepted by naturalists: that nature is avaricious [stingy?] of causes and prodigal of effects.

This is quite clearly a description of a modern phylogenetic tree, and the taxonomic consequences of adopting that conception.

It is, however, rather a pity that he explicitly rejects a network ("a disordered tangle of intersecting lines") as a suitable model, along with the chain ("a linear series").

The first post-Darwinian phylogeny

It is tolerably well known that Alfred Russel Wallace developed the idea of evolution via natural selection quite independently of Charles Darwin, and that, indeed, it was Wallace's revelation of this fact that prompted Darwin to finally publish his ideas (Bannister et al. 2014).

Some people are even aware that Wallace developed the Tree of Life metaphor independently, as well (Wallace 1855), a fact of which Darwin himself was perfectly well aware (eg. Bradman and Bartlett 1998):

"the analogy of a branching tree [is] the best mode of representing the natural arrangement of species ... a complicated branching of the lines of affinity, as intricate as the twigs of a gnarled oak ... we have only fragments of this vast system, the stem and main branches being represented by extinct species of which we have no knowledge, while a vast mass of limbs and boughs and minute twigs and scattered leaves is what we have to place in order, and determine the true position each originally occupied with regard to the others."

What is less well known is Wallace's contribution to phylogenetic imagery.

The Darwinian version of a phylogenetic tree is, of course, something usually considered to post-date 1859, when Darwin published his best-known book. However, producing such a tree was apparently a rather slow process. For example, in 1863, Franz Hilgendorf wrote a PhD thesis for which he produced a hand-drawn phylogeny, but he did not actually include this in the thesis; and he significantly modified it for its publication in 1866. In 1864 Fritz Müller published a couple of three-taxon trees. Also in 1864, Ernst Haeckel claimed to have started work on his series of phylogenetic trees, but the resulting book was not published until 1866. This means that the first substantial tree to appear in print was that of Mivart (1865).

However, long before this, Wallace was already moving ahead. In 1856 Wallace took the tree imagery from his 1855 publication and applied it to the relationships among bird groups. This publication was his first clearly evolutionary empirical contribution. He adapted the unrooted diagram of Strickland (1841), which represented "the natural system" of bird relationships, and gave it a clearly evolutionary interpretation. So, while Strickland's work was strictly atemporal and non-evolutionary, Wallace produced an evolutionary view of the world, with his two trees representing the end-product of change through time.

Wallace was in South-East Asia at the time of this work, collecting specimens among the islands of what is now Indonesia. He returned to England in 1862, thus having been absent during Darwin's rise to fame. However, he did return before anyone else had tackled Darwin's ideas empirically, and he was in an ideal position to do so himself (Beckenbauer et al. 2010). It would therefore be surprising if he had not done so.

Recently, it has become clear, as a result of the work done for the Wallace Correspondence Project, that Wallace did, indeed, produce a post-Darwinian phylogenetic diagram before any of his contemporaries, although it remained unpublished (Becker and Borg 2014). Not unexpectedly, it also refers to the relationships among birds. What is most interesting for us, however, is that it was a phylogenetic network, not a tree.

You will note that it is an unrooted network, in the same manner as his unrooted bird trees from 1856. In this, his presentation differed from that of Müller, Hilgendorf, Mivart and Haeckel, who all indicated a common ancestor. On the other hand, the branch lengths represent the "relative amount of affinity" between the named taxa, unlike the diagrams of his contemporaries. This means that the diagram can, indeed, be interpreted (in modern terms) as an unrooted phylogenetic network.

In his bird paper, Wallace (1856) had noted that producing the tree diagrams is not easy, as "you will most likely find that you have set down some conflicting affinities, or that you have mistaken some mere analogies for affinities". This seems to be the origin of his interest in the alternative model of a network, rather than a tree (Brabham and Berger 2014), thus making him the first person the use a data-display network to represent conflicting character data.

This post was inspired by the work of Torvill and Dean (1996). Happy April 1.

References

Bannister RG, Ballesteros-Sota S, Bjørndalen OE (2014) Running, swinging and skiing — the private life of Alfred Russel Wallace. Studia Wallaceana 6: 82-96.

Becker BF, Borg BR (2014) The phylogenetics of A.R. Wallace, and its relation to the science of tennis. Journal of Phylogenetic Inference 13: 101-110.

Beckenbauer FA, Best G, Bruyneel J (2010) Association football as a metaphor for phylogenetics. Is it a sport or a science? Phyloinformatics 7:1.

Brabham JA, Berger G (2014) The speed required to achieve the publication rate of A.R. Wallace. Philosophy and History of Biology 102: 89-92.

Bradman DG, Bartlett KC (1998) Wallace Down Under: the work of Alfred Russel Wallace in the southern hemisphere. Systematic Zoology 47: 767-780.

Haeckel E (1866) Generelle Morphologie der Organismen. Verlag von Georg Reimer, Berlin.

Hilgendorf F (1866) Planorbis multiformis im Steinheimer Süßwasserkalk: ein beispiel von gestaltveränderung im laufe der zeit. Buchhandlung von W. Weber, Berlin.

Mivart, StG (1865) Contributions towards a more complete knowledge of the axial skeleton in the primates. Proceedings of the Zoological Society of London 33: 545-592.

Müller F (1864) Für Darwin. Verlag von Wilhelm Engelman, Leipzig.

Strickland HE (1841) On the true method of discovering the natural system in zoology and botany. Annals and Magazine of Natural History 6: 184-194.

Torvill J, Dean CC (1996) Skating on thin ice. Systematic Biology 45: 641-650.

Wallace AR (1855) On the law which has regulated the introduction of new species. Annals and Magazine of Natural History 16 (2nd series): 184-196.

Wallace AR (1856) Attempts at a natural arrangement of birds. Annals and Magazine of Natural History 18 (2nd series): 193-216.

Darwin's Finches, genomics and phylogenetic networks

As a means of motivating his interest in speciation, in The Origin of Species Charles Darwin highlighted the diversity of morphological forms among the finches of the Galápagos Islands, in the south-eastern Pacific Ocean, which he visited while circumnavigating the world in The Beagle. He considered this to be a prime example of biodiversity related to adaptation and natural selection, what we would now call an adaptive radiation.

Recently, the following paper, which provides a genomic-scale study of these birds, has attracted considerable attention:

Lamichhaney S, Berglund J, Almén MS, Maqbool K, Grabherr M, Martinez-Barrio A, Promerová M, Rubin CJ, Wang C, Zamani N, Grant BR, Grant PR, Webster MT, Andersson L (205) Evolution of Darwin's finches and their beaks revealed by genome sequencing. Nature 58: 371-375.

The authors note:

Darwin's finches are a classic example of a young adaptive radiation. They have diversified in beak sizes and shapes, feeding habits and diets in adapting to different food resources. The radiation is entirely intact, unlike most other radiations, none of the species having become extinct as a result of human activities.

Here we report results from whole genome re-sequencing of 120 individuals representing all Darwin's finch species and two closely related tanagers. For some species we collected samples from multiple islands. We comprehensively analyse patterns of intra- and inter-specific genome diversity and phylogenetic relationships among species. We find widespread evidence of inter-specific gene flow that may have enhanced evolutionary diversification throughout phylogeny, and report the discovery of a locus with a major effect on beak shape.

Sadly, the authors try to study the intra- and inter-specific variation principally using phylogenetic trees. They do this in spite of noting that:

Extensive sharing of genetic variation among populations was evident, particularly among ground and tree finches, with almost no fixed differences between species in each group.

Clearly, this situation requires a phylogenetic network for adequate study, as a network can always display at least as much phylogenetic information as a tree, and usually considerably more. The authors do recognize this:

A network constructed from autosomal genome sequences indicates conflicting signals in the internal branches of ground and tree finches that may reflect incomplete lineage sorting and/or gene flow ... We used PLINK to calculate genetic distance (on the basis of proportion of alleles identical by state) for all pairs of individuals separately for autosomes and the Z chromosome. We used the neighbour-net method of SplitsTree4 to compute the phylogenetic network from genetic distances.

However, this network is tucked away as Fig. 3 in the appendices. It is shown here in the first figure. The authors attribute the gene flow to introgression, but occasionally refer to hybridization and convergent evolution. Indeed, they suggest both relatively recent hybridization as well as the possibility of more ancient hybridization between warbler finches and other finches.

Clearly, this network is not particularly tree-like in places, especially with respect to the delimitation of species based on their morphology, as reflected in their current taxonomy. Nevertheless, the authors prefer to present as their main result as a:

maximum-likelihood phylogenetic tree based on autosomal genome sequences ... We used FastTree to infer approximately maximum-likelihood phylogenies with standard parameters for nucleotide alignments of variable positions in the data set. FastTree computes local support values with the Shimodaira–Hasegawa test.

This tree is shown in the second figure.

This apparently well-supported tree is not a particularly accurate representation of the pattern shown by the network. Indeed, it makes clear just why it is inadequate to use a tree to study the interplay of intra- and inter-specific variation. Gene flow requires a network for accurate representation, not a tree.

The authors do acknowledge this situation. While they try to date the nodes on their tree, they do note that:

Although these estimates are based on whole-genome data, they should be considered minimum times, as they do not take into account gene flow.

Actually, in the face of gene flow the concept that a node has a specific date is illogical, because the nodes do not represent discrete events (see Representing macro- and micro-evolution in a network). Given the authors' final conclusion, it seems quite inappropriate to rely on trees rather than networks:

Evidence of introgressive hybridization, which has been documented as a contemporary process, is found throughout the radiation. Hybridization has given rise to species of mixed ancestry, in the past and the present. It has influenced the evolution of a key phenotypic trait: beak shape ... The degree of continuity between historical and contemporary evolution is unexpected because introgressive hybridization plays no part in traditional accounts of adaptive radiations of animals.

Darwin, hybridization and networks

Charles Darwin's metaphor of the Tree of Life was not a tree, even in The Origin of Species. As noted by Franz Hilgendorf (see The dilemma of evolutionary networks and Darwinian trees) "the branches of a tree do not fuse again", and yet in his book Darwin discusses at least one circumstance when they do precisely that — hybridization.

Darwin's discussion of hybridization occupies all of chapter 8 of the Origin. His stated motivation is to address what many people might see as a fatal objection to his theory of species origins by means of natural selection. One of Darwin's main arguments in the book is that "descent with modification" is continuous, and therefore the distinction between species and varieties (and subspecies, etc) is an arbitrary cut in a continuum of biodiversity. However, it was conventionally accepted that varieties within the same species could cross-breed freely, but any attempt to hybridize distinct species would always fail. Darwin opposes this view by citing extensive evidence showing that varying degrees of sterility are encountered in efforts to cross-breed different species of plants (and a few birds) — if the species are closely related then often there will be a small degree of fertility in the hybrid offspring. So, as two related forms diverge from one another in the course of evolution, their ability to inter-breed gradually diminishes and eventually falls to zero (absolute sterility).

It is important to note that his motivation for writing about hybridization was independent of his ideas about phylogeny. So, he seems not to have noticed the consequence of hybridization for phylogenetic patterns.

This is similar to the situation regarding his so-called "tree diagram", in chapter 4. His motivation for the diagram (the only figure in his book) was a discussion of descent with modification, and particularly the continuity of evolutionary processes. He was expressing his idea about uninterrupted historical connections. In particular, this was part of his concern that there is no fundamental distinction between varieties and species, because evolutionary divergence is continuous — it is all a matter of degree, without sharp boundaries. His Tree of Life image expressed the continuity of evolutionary connections, not phylogenetic patterns. This is clear from his poetic invocation of the biblical Tree of Life, which is about the inter-connectedness of all living things along tree branches, not about patterns of biodiversity.

Implicit in this world view is the idea that the Tree of Life is still a tree in spite of hybridization. That is, Darwin failed to see that his "tree simile" (chapter 4) had to ignore hybridization (chapter 8) in order to work. His figure does not show any evidence of hybridization, only divergence. It was not intended to be what we would now call a phylogeny, but merely an idealized view of divergence and continuity of descent. When introducing the Tree of Life, he was using religious imagery to stimulate the imagination of his readers, and in so doing presented a contradictory argument — there is continuity along the branches as well as continuity of inter-connections.

The alternative conception is that Darwin's Tree of Life was never a tree — it was a network. From this world view, Hilgendorf's dilemma was actually irrelevant. He commented:

An observation which, as far as I know, contradicts these previously discussed views, [would be], that formerly separate species approach each other and finally merge with each other. This would not fit the beautiful image that Darwin presented about the connection of species in a branch-rich tree; the branches of a tree do not fuse again.

Well, they do, even in a Darwinian tree.

Update to Charles Darwin's unpublished tree sketches

This blog has previously reproduced some of the unpublished sketches by Charles Darwin that involve tree-like relationships:

• Part 1 — collected notebooks and notes
• Part 2 — a letter to Charles Lyell
• Part 3 — a reconstruction from one of his books

Recently, the first two of these posts have been updated.

Part 1 was updated to include three new sketches. I had previously encountered references to them but had not located them amongst the online Darwin documentation.

Part 2 was updated to include information from a paper on the same topic that was published several months after the blog post itself.

Predecessors of Charles Darwin

Charles Darwin and Alfred Russel Wallace are usually credited with independently developing the idea that natural selection could be the important process by which new species arise, although history has apportioned most of the fame to Darwin alone.

In the first edition of his most famous book Darwin (1859) cited no sources, and credited no-one except Thomas Malthus as a source of ideas. He was criticized for this, and from the third edition onwards he provided a historical essay mentioning a few more names.

The basic issue is that the idea of natural selection had been "in the air" for more than half a century, but only with respect to within-species variation. It was Darwin and Wallace who took the leap to consider between-species variation, on the basis that there is no historical boundary defining species — all individuals trace their ancestry back through a whole series of ancestors, including those who existed before the origin of their current species. That is, phylogenies trace back to the origin of life not just to the origin of each species.

So, who were the people who published, however briefly, a comment noting the idea of within-species natural selection? Joachim Dagg, of the Natural History Apostils blog, has recently been writing a series of posts discussing many of those publications that contain a clear description of selection. Here I have provided a convenient overview, in time order, with links to Joachim's blog for those of you who want more information.

Joseph Townsend

• (1786, republished in 1817) A Dissertation on the Poor Laws, by a Well-wisher to Mankind. London: Ridgways.

— a brief mention of selection in relation to the Poor Laws, not organic evolution, but he seems to have inspired Thomas Mathus (1798) Essay on the Principle of Population, the critical work cited by both Darwin and Wallace (Malthus does not write about heritable variation, and therefore does not cover selection)
Link 1 - Link 2

James Hutton

• (1794) Investigation of the Principles of Knowledge and of the Progress of Reason, from Sense to Science and Philosophy. Volume 2. Edinburgh: Strahan & Cadell. [section 13, chapter 3]

— advocated the idea of what we now call microevolution (related to heritable variation within species), especially in relation to agriculture, and suggested natural selection as the mechanism
Link 1

William Charles Wells

• (1813) An Account of a White Female, Part of Whose Skin Resembles that of a Negro. [talk]
• (1818) Two Essays: One Upon Single Vision with Two Eyes; the other on Dew. [plus] An Account of a Female of the White Race of Mankind, Part of Whose Skin Resembles that of a Negro. Edinburgh: Archibald Constable.

— a talk read before the Royal Society of London in 1813, and apparently referenced by Adams, but not put into print until 1818 — discusses selection in relation to human skin color
Link 1 - Link 2

Joseph Adams

• (1814) A Treatise on the Supposed Hereditary Properties of Diseases. London: J. Callow.

— does not actually use the expression "selection" but briefly describes the process in relation to climate-related human variation, tucked away in the notes
Link 1 - Link 2 - Link 3

Patrick Matthew

• (1831) On Naval Timber and Arboriculture; with Critical Notes on Authors who have Recently Treated the Subject of Planting. Edinburgh: Adam Black.

— explicitly used the phrase "natural process of selection" in relation to the origin of timber varieties, with a discussion tucked away in an appendix — as noted by Joachim Dagg, Matthew explicitly included the possible origin of new species via selection, thus being a literal predecessor of Darwin and Wallace, although they appear to have been unaware of his work [until Matthew advertised it to the world after Darwin published his book: (1860) Nature's law of selection. Gardeners' Chronicle and Agricultural Gazette (7 April): 312-313]
Link 1 - Link 2 - Link 3 - Link 4 - Link 5
You can learn more about him at The Patrick Matthew Project.

John C. Loudon

• (1832) [Book review of] Matthew, Patrick: On Naval Timber and Arboriculture; with Critical Notes on Authors who have recently treated the Subject of Planting. The Gardener's Magazine 8: 702-703.

— a book review mentioning Matthew's idea of natural selection (he was the only contemporary commenter known to do so) and noted it explicitly as being concerned with "the origin of species and varieties"
Link 1 - Link 2

Edward Blyth

• (1835) An attempt to classify the "varieties" of animals, with observations on the marked seasonal and other changes which naturally take place in various British species, and which do not constitute varieties. The Magazine of Natural History 8: 40-53.*
• (1836) Observations on the various seasonal and other external changes which regularly take place in birds, more particularly in those which occur in Britain; with remarks on their great importance in indicating the true affinities of species; and upon the natural system of arrangement. The Magazine of Natural History 9: 393-409.*
• (1837) On the psychological distinctions between man and all other animals; and the consequent diversity of human influence over the inferior ranks of creation, from any mutual or reciprocal influence exercised among the latter. The Magazine of Natural History, new series, 1: 1-9.*

— discusses the effects of artificial selection, but describes the process in nature as restoring organisms in the wild to their archetype (rather than forming new species)
Link 1

Herbert Spencer

• (1852) A theory of population, deduced from the general law of animal fertility. Westminster Review 57: 468-501.

— published his article in order to show that the adaptedness or fitness of organisms results from the principle discussed by Malthus — Spencer later coined the expression "survival of the fittest" as a synonym of natural selection (in 1862)
Link 1


* Full title: The Magazine of Natural History and Journal of Zoology, Botany, Mineralogy, Geology, and Meteorology

Goofy genealogies

Family pedigrees seem to be confusing things, because there are two distinct interpretations of the expression "family tree".

First, the pedigree tree could be drawn with a particular contemporary person at the root of the tree, so that the tree expands backwards in time to increasing numbers of ancestors at the leaves (ie. an "ascent tree"). In some ways this seems quite illogical as an analogy, given that the base of a real tree is the origin of its growth.

Second, the pedigree tree could be drawn with a particular ancestor at the root of the tree, so that the tree expands forwards in time to increasing numbers of descendants at the leaves (ie. a "descent tree"). This is more logical, although we often draw the root at the top. (The following example is actually a network, rather than strictly a tree; see also Pedigrees and phylogenies are networks not trees.)

Pedigrees are generally somewhat different from phylogenies, but in phylogenetics we do choose the latter option for interpreting trees — we start with a collection of contemporary leaves and try to reconstruct the tree backwards towards the common ancestor. Thus the root is at the "base" of the tree, even when we draw the root at the top of the diagram.

In popular usage these distinctions are often blurred. Consider this "family tree" of the Disney character Goofy. It is taken from Gilles R. Maurice's Calisota web page, where the character names are listed clearly.

This is based on the first usage described above, since Goofy himself is at the base and his ancestors are at the leaves. This is actually closer to a lineage rather than a tree, especially as no females seem to be involved at any stage.

However, roughly the same information can be presented the other way around. This cartoon is taken from a different Calisota page.

Here, Goofy is now at the top of the tree and his ancestry proceeds downwards, with the oldest ancestor at the base (except for his son!). This really is confusing.

Reducing networks to trees

I have commented before about the perceived tendency to resist thinking about evolutionary relationships as networks (Resistance to network thinking), and even to present reticulating evolutionary relationships as trees rather than as networks (The dilemma of evolutionary networks and Darwinian trees). Charles Darwin seems to be the guilty party in starting this phenomenon.

This behavior becomes particularly obvious when we consider family genealogies. A good example appears when we consider the family relationships of the Olympian gods of Ancient Greece. Several illustrations of these relationships are gathered together on the Olympian Gods Family Tree web page.

Noteworthy is the particularly frisky nature of Zeus, who "got around a bit", to put it mildly. As shown in the first diagram, Zeus was the offspring of Cronus and Rhea. However, he then fathered children with at least nine people, including two of his own sisters, an aunt, a first cousin, and several first cousins once removed, among others. This creates the complex network shown.

However, not everyone wants to draw family genealogies as reticulating networks. After all, they are usually called "family trees". As shown by the examples below, 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 will leave it to you to count how often Zeus appears in each of these so-called family trees.

Clearly, this is misleading, and it makes no sense to obscure the fact that a so-called tree is actually a reticulate network. If relationships are reticulate then it is best to illustrate them that way, rather than to disguise the networks as trees.

The role of biblical genealogies in phylogenetics

Phylogeneticists treat the tree image as having special meaning for themselves. Conceptually, the tree is used as a metaphor for phylogenetic relationships among taxa, and mathematically it is used as a model to analyze phenotypic and genotypic data to uncover those relationships. Irrespective of whether this metaphor / model is adequate or not, it has a long history as part of phylogenetics (Pietsch 2012). Of particular interest has been Charles Darwin's reference to the "Tree of Life" as a simile, since that is clearly the key to the understanding of phylogenetics by the general public.

The principle on which phylogenetic trees are based seems to be the same as that for human genealogies. That is, phylogenies are conceptually the between-species homolog of within-species genealogies. As far as Western thought is concerned, human genealogies make their first important appearance in the Bible, with a rather specific purpose. The Bible contains many genealogies, mostly presented as chains of fathers and sons. For example, Genesis 5 lists the descendants of Adam+Eve down to Noah and his sons, which can be illustrated as a pair of chains (as shown in the first figure); and the rest of Genesis gets from there down to Moses' family, for which the genealogy can be illustrated as a complex tree.

The genealogy as listed in Genesis 5.
Cain's lineage was terminated by the Flood.

However, the theologically most important genealogies are those of Jesus, as recorded in Matthew 1:2-16 and Luke 3:23-38. Matthew apparently presents the genealogy through Joseph, who was Jesus' legal father; and Luke apparently traces Jesus' bloodline through Mary's father, Eli. These two lineages coalesc in David+Bathsheba, and from there they have a shared lineage back to Abraham. Their importance lies in the attempt to substantiate that Jesus' ancestry fulfils the biblical prophecies that the Messiah would be descended from Abraham (Genesis 12:3) through Isaac (Genesis 17:21) and Jacob (Genesis 28:14), and that he would be from the tribe of Judah (Genesis 49:8), the family of Jesse (Isaiah 11:1) and the house of David (Jeremiah 23:5).

That is, these genealogies legitimize Jesus as the prophesied Messiah. Following this lead, subsequent use of genealogies has commonly been to legitimize someone as a monarch, so that royal genealogies have been of vital political and social importance throughout recorded history (see the example in the next figure). This importance was not lost on the rest of the nobility, either, so that documented genealogies of most aristocratic families allow us to identify the first-born son of the first-born son, etc, and thus legitimize claimants to noble titles — genealogies are a way for nobles to assert their nobility.

The genealogy of the current royal family of Sweden. [Note: most children are not shown]
The lineage of the recent monarchs is highlighted as a chain, with an aborted side-branch dashed.

If we focus solely on the line of descent involved in legitimization, then genealogies can be represented as a chain (as shown in the genealogy above). However, if we include the rest of the paternal lines of descent then family genealogies can be represented as a tree. However, if we include some or all of the maternal lineages as well, then family genealogies can be represented as a network. For example, the biblical genealogies only rarely name women, but where females are specifically named the genealogies actually form a reticulated network. Jacob produced offspring with both Rachel and Leah, who were his first cousins; and Isaac and Rebekah were first cousins once removed. Even Moses was the offspring of parents who were, depending on the biblical source consulted, either nephew-aunt, first cousins, or first cousins once removed. These relationships cannot be represented in a tree. (See also the complex genealogy of the Spanish branch of the Habsburgs, who were kings of Spain from 1516 to 1700.)

This idea of genealogical chains, trees and networks was straightforward to transfer from humans to other species. Originally, biologists stuck pretty much to the idea of a chain of relationships among organisms, as presented in the early part of Genesis. Human genealogies were traced upwards to Adam and from there to God, and thus species relationships were traced upwards to God via humans. However, by the second half of the 1700s both trees and networks made their appearance as explicit suggestions for representing biological relationships. In particular, Buffon (1755) and Duchesne (1766) presented genealogical networks of dog breeds and strawberry cultivars, respectively.

However, these authors did not take the conceptual leap from within-species genealogies to between-species phylogenies. Indeed, they seem to have explicitly rejected the idea, confining themselves to relationships among "races". It was Charles Darwin and Alfred Russel Wallace, a century later, who first took this leap, apparently seeing the evolutionary continuum that connects genealogies to phylogenies. In this sense, they both took ideas that had been "in the air" for several decades, but previously applied only within species, and applied them to the origin of species themselves. [See the Note below.] Both of them, however, confined themselves to genealogical trees rather than using networks. It seems to me that it was Pax (1888) who first put the whole thing together, and produced inter-species phylogenetic networks (along with some intra-species ones).

In this sense, the biblical Tree of Life has only a peripheral relevance to phylogenetics. Darwin used it as a rhetorical device to arouse the interest of his audience (Hellström 2011), but it was actually the biblical genealogies that were of most practical importance to his evolutionary ideas. Apart from anything else, the original biblical tree was actually the lignum vitae (Tree of Eternal Life) not the arbor vitae (Tree of Life). Similarly, the tree from which Adam and Eve ate the forbidden fruit was the lignum scientiae boni et mali (Tree of Knowledge of Good and Evil), not the arbor scientiae (Tree of Knowledge) that was subsequently used as a metaphor for human knowledge.

Note. Along with phylogenetic trees, Darwin and Wallace did not actually originate the idea of natural selection, which had previously been discussed by people such as James Hutton (1794), William Charles Wells (1818), Patrick Matthew (1831), Edward Blyth (1835) and Herbert Spencer (1852). However, this discussion had been in relation to within-species diversity, whereas Wallace and Darwin applied the idea to the origin of between-species diversity (i.e. the origin of new species).

References

Buffon G-L de. 1755. Histoire naturelle générale et particulière, tome V. Paris: Imprimerie
Royale.

Duchesne A.N. 1766. Histoire naturelle des fraisiers. Paris: Didot le Jeune & C.J. Panckoucke.

Hellström N.P. 2011. The tree as evolutionary icon: TREE in the Natural History Museum, London. Archives of Natural History 38: 1-17.

Pax F.A. 1888. Monographische übersicht über die arten der gattung Primula. Bot. Jahrb. Syst. Pflanzeng. Pflanzengeo. 10:75-241.

Pietsch T.W. 2012. Trees of life: a visual history of evolution. Baltimore: Johns Hopkins University Press.

The sex life of Charles Darwin

Charles Darwin's sex life is of interest because of his consanguineous marriage (to his first cousin), which seems to have resulted in genetic problems for his children, due to inbreeding (see Charles Darwin's family pedigree network). The children of this marriage have recently been discussed in the book by Tim Berra (Darwin and His Children: His Other Legacy). This book discusses Darwin's children mainly in the context of Darwin's own life. Unfortunately, it does not delve much into his personal relationship with either them or his wife, Emma. His private life remains fairly private.

In particular, the book fails to draw any inference from the obvious fact that there were 10 of these children, plus two possible miscarriages. However, obviously we do learn indirectly about a certain part of Mr Darwin's private life. After all, one does not get a woman pregnant accidentally (no matter what your friends try to tell you) -- there are certain biological procedures that you need to go through, and it is fairly difficult to carry these out accidentally. Clearly, Charles and Emma were familiar with this particular activity, and carried it out successfully on numerous occasions.

Charles Darwin, 2 years before the
birth of his last child

The question is: how many occasions? We know the minimum number, but what about the average rate, for example? The Darwin cottage industry has apparently produced speculations about his sex life before (see Wikipedia), but I have not read about them. Instead, I will provide my own analysis of the situation.

Background

Charles and Emma married on 29 January 1839, when Charles was 29 years and 11 months old and Emma was 30 years and 8 months old. This is pretty late to be starting a family, although not necessarily unusual, and it does have an influence on the calculations.

Emma realized during the following April that she was pregnant (ie. within 3 months); and during the subsequent 18 years she was pregnant a total of 11 more times. On average, there were 500 days between each of the first nine pregnancies, as shown in the first graph. This means that during those 12 years she spent 55% of her days being pregnant and 45% of them not pregnant.

Wikipedia paints an interesting picture of marriages in Victorian Britain (Women in the Victorian era):

When a Victorian man and woman married, the rights of the woman were legally given over to her spouse. Under the law the married couple became one entity where the husband would represent this entity, placing him in control of all property, earnings and money. In addition to losing money and material goods to their husbands, Victorian wives became property to their husbands, giving them rights to what their bodies produced: children, sex and domestic labour. Marriage abrogated a woman's right to consent to sexual intercourse with her husband, giving him 'ownership' over her body. Their mutual matrimonial consent therefore became a contract to give herself to her husband as he desired.

The extent to which Emma was involved in the decision to spend more than half of her time pregnant is therefore open to debate. Both her letters and those of her husband do not, as far as I know, reveal any marital difficulties — indeed, quite the contrary. However, Charles' has left us written evidence of his pre-marital ideas about marriage (Darwin’s notes on marriage), which indicate his specific intention to have a family available in his old age.

Note that there are reported to have between two miscarriages between the 9th and 10th births, one in 1852 (when Emma was 44 years old) and one in 1854 (when she was 46). Emma was 48 years and 7 months old when she delivered her final child. Along with the miscarriages, it is worth noting that the final child was born mentally disabled (probably Down's syndrome, for which there is a 1 in 11 chance at age 49), and he died after 18 months. Also, the third child was born after only 36 weeks of pregnancy (instead of the "normal" 40 weeks), and lived for less than a month. Darwin's favorite child was his 2nd (Anne), who unfortunately died of tuberculosis at age 10. The remaining seven children survived to adulthood.

We can also note that the children were born during most periods of the year, as shown in the next graph. However, five of the births were during the 3-month period from early July to late September, implying conception during the period October to December.

In English-speaking countries there is a peak of births in late September, 9 months after the Christmas celebrations (Wellings et al. 1999; Tita et al. 2001). (In Scandinavia, the birth peak is 9 months after the mid-summer celebrations.) Given that two of the births were in this period, we might accuse the Darwins of fitting into this behavioral cliché. However, one of the these two births was the shortened pregnancy, so that conception in that case was on or near to their 3rd wedding anniversary, rather than Christmas. The other conception dates do not fit any pattern that I can see.

All of the above data lead me to the conclusion that most, if not all, of the pregnancies were the result of more-or-less continuously ongoing sexual activity, rather than being the result of deliberate attempts to conceive, or being incidental by-products of celebratory activity. That is, the pregnancies occurred as chance dictated, given the night-time activities being undertaken.

This leads us to the key question of how often these activities took place. We can do some general calculations that might be informative.

Calculation

We now know that the potentially fertile period of human female ovulation is 12 days out of every 28, and vaginal sex during this period should be avoided if you do not wish to be involved in a pregnancy (Arévalo et al. 1999). Within this window of opportunity there is a 6-day period during which conception is most likely (Dunson et al. 2002; Stirnemann et al. 2013), and if you are trying to conceive a child then sex at least twice during this period is the recommended strategy. (Each egg lasts 1 day, but sperm last for 3 days, so that sex more than 2-3 times doesn't seem to improve your chances.) Clearly, sex once during this 6-day period is a reasonable minimum expectation for conception.

However, the probability of conception even under these minimum circumstances is very dependent on the age of the female involved. (The eggs are produced early in the female's life, and the eggs age along with the woman, so that older eggs have reduced fertility; Broekmans et al. 2009.) For example (Siebler 2009; Sozou & Hartshorne 2012), in her early 20s a healthy fertile woman has a 20–25% probability of conception each month. The average time to achieve conception for this age group is 4 months, and the likelihood of conception within one year is 93–97%. More importantly, in her early 30s (as Emma was when she married) the probability of conception each month drops to 10–15%, so that the average time of conception is 10 months and the likelihood of conception within one year is c.72%. The probability keeps dropping until menopause (where it reaches zero), so that, for example, the likelihood of conception within one year is c.65% for a woman in her late 30s.

Emma, near the time of her marriage

This means that, given her age, Emma had to receive sperm during every ovulation cycle, in order to maintain a 50% chance of getting pregnant within any one year (she got pregnant on average every 9-12 months). If you know the ovulation times, then that rate requires sex 13 times per year. If you don't know the times, or you don't know anything about ovulation cycles (and it seems likely that Victorian women did not), then it requires sex at least once per week in order to hit them all by random chance.

So, I arrive at the conclusion of weekly sex for the Darwins throughout the first 12 years of their marriage, and possibly for 18 years. Calculations seem to be much more difficult after that, due to lack of suitable data.

I have no idea whether this weekly rate was normal for Victorian couples, but it certainly seems to be quite normal in the modern world, for people of their age. As shown in the next graph, people in their 30s and 40s currently report having sex every 4-5 days throughout the year (Mosher et al. 2005; Schneidewind-Skibbe et al. 2008). So, Charles' sex life would fit perfectly into the 21st century.

From Mosher et al. (2005)

Postscript

Finally, it is interesting to note that Charles started writing what he called his "Big Species Book" shortly after the birth of his final child. Furthermore, he converted this incomplete manuscript into what is now known as On the Origin of Species after the early death of that same child. Other events were involved in these decisions, of course, but his changing family life is unlikely to have been the least important of them.

References

Arévalo M, Sinai I, Jennings V (1999) A fixed formula to define the fertile window of the menstrual cycle as the basis of a simple method of natural family planning. Contraception 60: 357-360.

Broekmans FJ, Soules MR, Fauser BC (2009) Ovarian aging: mechanisms and clinical consequences. Endocrine Reviews 30: 465-493.

Dunson DB, Colombo B, Baird DD (2002) Changes with age in the level and duration of fertility in the menstrual cycle. Human Reproduction 17: 1399-1403.

Mosher WD, Chandra A, Jones J (2005) Sexual behavior and selected health measures: men and women 15–44 years of age, United States, 2002. Advance Data From Vital and Health Statistics 362. National Center for Health Statistics, Hyattsville, MD.

Schneidewind-Skibbe A, Hayes RD, Koochaki PE, Meyer J, Dennerstein L (2008) The frequency of sexual intercourse reported by women: a review of community-based studies and factors limiting their conclusions. Journal of Sexual Medicine 5: 301-335.

Siebler SJ (2009) How to Get Pregnant. Little, Brown and Co, New York, NY.

Sozou PD, Hartshorne GM (2012) Time to pregnancy: a computational method for using the duration of non-conception for predicting conception. PLoS One 7: e46544.

Stirnemann JJ, Samson A, Bernard JP, Thalabard JC (2013) Day-specific probabilities of conception in fertile cycles resulting in spontaneous pregnancies. Human Reproduction 28: 1110-1116.

Tita AT, Hollier LM, Waller DK (2001) Seasonality in conception of births and influence on late initiation of prenatal care. Obstetrics & Gynecology 97: 976-981.

Wellings K, Macdowall W, Catchpole M, Goodrich J (1999) Seasonal variations in sexual activity and their implications for sexual health promotion. Journal of the Royal Society of Medicine 92: 60-64.

The dilemma of evolutionary networks and Darwinian trees

I have noted before that Franz Hilgendorf (1839-1904), a German palaeontologist, was apparently the first person to publish a Darwinian tree based on the fossil record, in 1866 (Who published the first phylogenetic tree?). Indeed, among the people who first produced trees inspired by Darwin's work, Hilgendorf seems to have been the only "real" Darwinian — St George Mivart later became a strong anti-Darwinist, Albert Gaudry accepted Darwin's genealogical ideas but rejected the idea of natural selection, and Ernst Haeckel was in practice more of a Lamarckian than a Darwinian. Hilgendorf, on the other hand, continued to pursue Darwinism throughout the rest of his career, even being the first to introduce evolutionary theory into Japan (c. 1873) .

What I wish to point out here is that he was also the first person to face what I will now christen "Hilgendorf's Dilemma", which is a problem that phylogenetics has faced ever since the publication of Darwin's book in 1859. Hilgendorf solved the problem in the same way that later phylogeneticists also did — it is only in the last 2-3 decades that a different solution has been widely adopted.

The problem is this: what do you do when your data are not tree-like but you accept the evolution-as-tree paradigm? The solution of choice has been: publish a tree anyway.

The history of phylogenetic metaphors

I have previously emphasized the important point that the earliest genealogical diagrams were networks, published in 1755 and 1766 by the Frenchmen Buffon and Duchesne, respectively (Networks of genealogy). However, genealogical diagrams were then mostly ignored for the next century, except by Lamarck — most published relationship diagrams were affinity networks rather than representing genealogy (see Affinity networks updated).

One of Darwin's main goals in 1859 was thus to re-introduce genealogy as being the most important relationship concept in biology. However, he chose the tree as his metaphor rather than the previously proposed network. This seems to have been a rhetorical device as much as anything else, alluding to the biblical Tree of Life (Hellström 2011, Penny 2011). Darwin succeeded in his goal, and genealogical trees have been the dominant metaphor since that time, rather than genealogical networks.

Franz Martin Hilgendorf

Hilgendorf knew and apparently accepted Darwin's ideas (Heinrich Bronn's German translation of the Origin had appeared in 1860), and he applied them to his PhD studies in 1862. He was investigating the fossil gastropods of the middle Miocene basin at Steinheim, in southern Germany. He studied the morphological variation, in the different stratigraphic layers, of the various fossil forms of what he referred to as Planorbis multiformis. Importantly, he recognized that the different morphological forms (which he called varieties) occurred exclusively in different stratigraphic layers. Thus, what he saw in the stratigraphy could be translated into a phylogenetic diagram, as shown in this next figure.

Adapted from Rasser (2013).

On the face of it, Hilgendorf's work provides strong support for Darwinism, and in his thesis (Hilgendorf 1863) he explicitly noted the relationship to Darwin's ideas. However, he did not include his phylogenetic diagram, and he did not publish his thesis. The 42-page thesis was hand-written, and he did not even leave a copy behind at the University of Tübingen. The only known copy (presumably the original) is now in the Museum für Naturkunde, Berlin, where Hilgendorf later worked, donated by Hilgendorf's heirs. It was discussed by Reif (1983), and has recently been transcribed by Glaubrecht (2012).

The usual explanation given for Hilgendorf's decision not to publish is the controversial nature of the subject of evolution (eg. Weltner 1906, Reif 1983, Janz 1999, Glaubrecht 2012), which was not even supported by his own supervisor (Friedrich von Quenstedt). However, it seems equally likely that the explanation was Hilgendorf's Dilemma.

Hilgendorf's Dilemma

Hilgendorf refers to this dilemma in the penultimate paragraph of his thesis. After discussing the Darwinian ideas that species are connected with each other through intermediate stages, and have evolved apart over time, he says:

Eine Beobachtung die, so viel ich weiß, mit den bisher aufgestellten Ansichten nicht stimmt, [wäre], daß früher getrennte Arten sich einander nähern und endlich miteinander Verschmelzen können. Darauf würde das schöne Bild, das Darwin uns vom Zusammenhange der Species in einem Zweige=reichen Baume vorführt, nicht passen; die Zweige eines Baumes wachsen nicht wieder zusammen.

An observation which, as far as I know, contradicts these previously discussed views, [would be], that formerly separate species approach each other and finally merge with each other. This would not fit the beautiful image that Darwin presented about the connection of species in a branch-rich tree; the branches of a tree do not fuse again.

The problem for Hilgendorf was that this is precisely what happened in his reconstructed phylogeny. Among the Hilgendorf artifacts found in the Institut und Museum für Geologie und Paläontologie, Tübingen, as discussed by Reif (1983), is a series of cards attributed to the time of his thesis work. These mostly illustrate some of Hilgendorf's proposed morphological transformation series, but one of them represents a phylogeny. This is shown in the next figure. This phylogeny shows gradual transformation of lineages (anagenesis), splitting of lineages (cladogenesis), and one lineage fusion. The diagram seems to accurately reflect the discussion in Hilgendorf's thesis, and so it is considered to be the phylogeny "missing" from that thesis.

The dilemma for Hilgendorf, then, was that he saw his work as supporting Darwin's evolutionary ideas but not supporting his metaphor. Under these circumstances, he decided not to rush into print. (Why publish on a controversial subject when you are not convinced by your evidence?)

What he did, instead, was return to Steinheim two years later (1865) and collect more data. This time his phylogenetic method produced a tree instead of a network (illustrated in Gastropods on Monday), and he subsequently published the result (Hilgendorf 1866, 1867). This paper makes no mention of Darwin at all. Interestingly, the first version had a subtitle ("an example of morphological change through time") that was not used in the final version, thus expunging all explicit references to evolutionary theory. It was not until Hilgendorf (1879) that he once again placed the Steinheim work into an explicitly Darwinian framework.

Hilgendorf could thus have been the third person to publish a genealogical network. Instead, he became the second person to publish a post-Darwinian phylogenetic tree. (Mivart had published the first tree in 1865, while Hilgendorf was prevaricating.)

Hilgendorf continued to defend his work in print against attacks from a number of people, notably Carl Sandberger, another German (who rejected transmutation entirely), and Alpheus Hyatt, an American (who was a Lamarckian) (see Reif 1983, Janz 1999, Rasser 2013). Ironically, these two anti-Darwinians seem to have convinced Darwin himself that Hilgendorf's work was not worthwhile (see Rasser 2013), and the only comment that Darwin added to later editions of his book was: "Hilgendorf has described a most curious case of ten graduated forms of Planorbis multiformis in the successive beds of a fresh-water formation in Switzerland [sic!]." As a result, Hilgendorf and his work have been ignored by most biologists.

Note that Darwin consistently down-played the importance of fossil evidence for his theory — he seemed to think that biogeographic evidence, for example, would be more convincing (as independently suggested by Alfred Russel Wallace). He thus failed to give due credence to the work of both Hilgendorf and Gaudry (a Frenchman digging in Greece), who each provided the first good examples of Darwinian evolution based on fossil stratigraphy.

The general Dilemma

I see Hilgendorf's personal history as the first example of a dilemma that all subsequent phylogeneticists have potentially faced, and when necessary have usually resolved in a similar manner. Darwin inappropriately changed the phylogenetic metaphor from a network to a tree, even in the face of then-known reticulation processes such as hybridization and introgression. And every time we are confronted with non-tree-like data we face the same dilemma; and most people have resolved it in the same way by publishing a tree instead of a network (see Phylogenetic networks 1900-1990).

It is only in the past couple of decades that we have started to behave in a more rational manner, and have returned to publishing networks instead of trees.

References

Darwin C. (1859) On the Origin of Species by Means of Natural Selection. John Murray, London.

Glaubrecht M. (2012) Franz Hilgendorf's dissertation "Beiträge zur Kenntnis des Süßwasserkalks von Steinheim" from 1863: transcription and description of the first Darwinian interpretation of transmutation. Zoosystematics & Evolution 88: 231-259.

Hellström N.P. (2011) The tree as evolutionary icon: TREE in the Natural History Museum, London. Archives of Natural History 38: 1-17.

Hilgendorf F. (1863) Beiträge zur Kenntniß des Süßwasserkalkes von Steinheim. Unpublished PhD Dissertation. Philosophische Fakultät, Universität Tübingen, 42 pp.

Hilgendorf F. (1866) Planorbis multiformis im Steinheimer Süßwasserkalk: ein beispiel von gestaltveränderung im laufe der zeit. Buchhandlung von W. Weber, Berlin, 36 pp.

Hilgendorf F. (1867) Über Planorbis multiformis im Steinheimer Süsswasserkalk. Monatsberichte der Königliche Preussischen Akademie der Wissenschaften zu Berlin 1866: 474-504.

Hilgendorf F. (1879) Zur Streitfrage des Planorbis multiformis. Kosmos 5: 10-22, 90-99.

Janz H. (1999) Hilgendorf's planorbid tree — the first introduction of Darwin's theory of transmutation into palaeontology. Paleontological Research 3/4: 287-293.

Penny D. (2011) Darwin's theory of descent with modification, versus the biblical Tree of Life. PLoS Biology 9: e1001096.

Rasser M.W. (2013) Darwin's dilemma: the Steinheim snails' point of view. Zoosystematics & Evolution 89: 13-20.

Reif W.-E. (1983) Hilgendorf's (1863) dissertation on the Steinheim planorbids (Gastropoda; Miocene): the development of a phylogenetic research program for paleontology. Paläontologische Zeitschrift 57: 7-20.

Weltner W. (1906) Franz Hilgendorf. 5 Dezember 1839 – 5 Juli 1904. Archiv für Naturgeschichte 72(1): I-XII.

Pierre Trémaux, the unknown phylogeneticist

Pierre Trémaux is a name that most of you will not have heard of, and yet he was a remarkable man. Or, rather, he wrote one remarkable book that has been almost completely ignored by history.

Trémaux (1818-1895) has been described as "a French architect, orientalist and photographer", but in his late 40s he also became a theoretical biologist, and it is this latter context that is of interest here. His best-known book is Origin et Transformations de l'Homme et des Autres Êtres (1865, L. Hachette, Paris). The ambitious nature of this book is indicated by its subtitle: Indiquant la transformation des êtres organisés, la formation des espèces, les conditions qui produisent les types, l'instinct et les facultés intellectuelles, la base des sciences naturelles, historiques, politiques, etc. [Indicating the transformation of organized beings; the formation of species; the conditions that produce the types, the instinct and the intellectual faculties; the base of natural sciences, history, politics, etc.]

In this book the author did four noteworthy and original things regarding phylogenetics:

1. he drew the first "proper" post-Darwinian phylogenetic tree (ie. showing speciation and extinction, with the internal branches as ancestors and the leaves as extant organisms), which connects all of the historical branches back to a single origin (which Darwin's diagram does not show)
2. he discussed the idea that speciation is concentrated at certain times in the geological record (the boundaries between "ages") and that there is effectively evolutionary stasis at other times, which presages Eldredge and Gould's theory of punctuated equilibrium by more than a century
3. he presented the idea that species form in geographically isolated populations, thus beating Moritz Wagner to the idea of allopatric speciation by 3 years
4. he applied Darwinian ideas to the evolution of Homo sapiens, 6 years before Darwin explicitly did so himself. (Thomas Henry Huxley contributed to the topic in 1863, but his book is best known for its infamous frontispiece illustrating transformational evolution among apes.)

Points (1) and (2) are illustrated in the only diagram in Trémaux's book, as reproduced here.

Trémaux's phylogenetic tree (from Google Books)

The text translates as:

Origin and Transformations of Beings

Synoptic figure of the transformation of species, by P. Trémaux

Species of different branches of the animal kingdom, arising from the same origin (the primordial cell or utricle), subdivide age by age; some of the species become extinct in every age, the others continue to grow and to divide and diverge more and more in their characters.

As far as point (1) is concerned, it is important to note that Darwin's 'tree' diagram is not connected to his description of the Tree of Life. The diagram is used to describe his vision of divergence, and descent with modification; at no stage does he refer to it as a "tree". His dry-as-dust description of the diagram and his poetic evocation of the biblical Tree thus have nothing to do with each other. It is merely a modern fancy to suggest that Darwin drew what we would now call a phylogenetic tree.

Therefore, Trémaux seems to have been the first to publish an illustration of the concept of a phylogenetic tree, in the form in which we know it today. St George Mivart, on the other hand, seems to have been the first to publish an empirical phylogenetic tree, in the same year (1865; see Who published the first phylogenetic tree?).

Darwin's diagram is not even connected at the base, as must be a genealogical tree. This presumably reflects his idea, as he put it in Notebook C in 1838: "The bottom of the tree of life is utterly rotten & obliterated in the course of [the] ages." His predecessors also had doubts about the base of the tree (notably Louis Agassiz and Edward Hitchcock), so that when they drew their diagrams of the fossil history of organisms they also were not connected to a single origin. Trémaux had no such doubts, and explicitly indicated a single origin and connected all of his lineages to it.

Ironically, Trémaux actually produced (quite independently) a finished version of an idea that Darwin sketched in one of his notebooks. This is on a page numbered 184 (probably from the early 1850s; see Charles Darwin's unpublished tree sketches). As shown below, it also considers the relationship between genealogical trees and geological history. Darwin owned a copy of Trémaux's book but apparently saw nothing of worth in it (Wilkins & Nelson 2008), in spite of the obvious relationship to his own idea!

Darwin's sketch

Circular trees apparently did not re-appear until the work of Engler (1881), where the concentric circles represented different morphological features, instead of geological time, thus showing phenotypic divergence from the common ancestor (along with the genealogy represented by the tree itself).

Conclusion

It is of some concern that Trémaux's book is so poorly known and the author himself almost unheard of. He does not appear in any of the standard histories of biology (see Wilkins & Nelson 2008), and his entry in the English-language Wikipedia has only two lines (he fares better in the French version)

In his 1874 book (Origine des Espèces et de l'Homme, avec les Causes de Fixité et de Transformation, et Principe Universel du Mouvement et de la Vie ou Loi des Transmissions de Force) Trémaux makes it clear that the [French] Académie des Sciences had rejected his work. Thereafter, few people seem to have read any of it, relying instead on the correspondence of Karl Marx (who thought the book was great) and Friedrich Engels (who though that it was rubbish) to pass judgement. Wilkins & Nelson (2008) have tried to redress the problem to some extent.

The rejection by the Académie is likely to have been because they did not accept the application of Darwinian evolution to humans. Indeed, it has been noted (see Hull 1988) that French biologists did not embrace Darwin's ideas in general. More particularly, Darwin himself realized that most of the problems engendered by his work would surround the idea of human evolution. Indeed, it was one major area where he and Alfred Russel Wallace (who independently developed the idea of natural selection) disagreed, as Wallace refused to apply the idea to humans.

Wilkins & Nelson (2008) wisely suggest that much of the confusion also comes from translating Trémaux's use of the French word "sol" as "soil" rather than as "habitat", thus leading to the conclusion that Trémaux was claiming that it is the nature of the soil alone that affects evolution. This was certainly done by Stephen Jay Gould (1997, 1999), who commented that: "I have never read a more absurd or more poorly documented thesis." Trémaux and his book deserve a better epitaph than that, because Trémaux certainly meant much more than most of the historical commentators have credited him with.

References

Engler A. (1881) Über die morphologischen Verhältnisse und die geographische Verbreitung der Gattung Rhus, wie der mit ihr verwandten, lebenden und ausgestorbenen Anacardiaceae. Botanische Jahrbücher für Systematik, Pflanzengeschichte und Pflanzengeographie 1: 365-426.

Gould S.J. (1997) Redrafting the Tree of Life. Proceedings of the American Philosophical Society 141: 30-54.

Gould S.J. (1999) A Darwinian gentleman at Marx's funeral. Natural History 108(7): 32-41. [Reprinted as "The Darwinian gentleman at Marx's funeral" in the book I Have Landed (2002).]

Hull D.L. (1988) Science as a Process: An Evolutionary Account of the Social and Conceptual Development of Science. University of Chicago Press, Chicago.

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