Abstract
The two great modern naturalists, Linnaeus and Darwin, expressed their intuition about how best to visualize patterns of affinities, that is, morphological similarities and divergences between taxa. Linnaeus suggested that “all plants show affinities on all sides, like a territory on a geographical map,” while Darwin thought that it was virtually impossible to understand the affinities between living and extinct species without a genealogical tree. Genealogical trees follow the diachronic, evolving logic of a timeline, whereas maps depict a synchronous pattern of extant taxa. Although the two seem unrelated, various naturalists made attempts to combine them. Surprisingly, these resulted in three-dimensional images that, in order to be observed, had to be projected on paper. The naturalists Max Fürbringer and Richard Bowdler Sharpe were aware of this fact, but even Darwin himself twice combined the basic intuitions underlying the two modes of representation to produce three-dimensional images. This article is a brief history of the efforts to merge genealogical trees and map-like cross sections of affinities into one three-dimensional image.
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Notes
Darwin ([1859] 2009, p. 431): “As it is difficult to show the blood-relationship between the numerous kindred of any ancient and noble family, even by the aid of a genealogical tree, and almost impossible to do this without this aid, we can understand the extraordinary difficulty which naturalists have experienced in describing, without the aid of a diagram, the various affinities which they perceive between the many living and extinct members of the same great natural class.”
Cambridge University Library MS.DAR.205.5.183r. Transcription by J. David Archibald (2014, p. 92).
Cambridge University Library MS.DAR.205.5.184r. Transcription by J. David Archibald (2014, p. 92; Archibald believes that the last word could be bird [p. 87]).
In “Three Pedigrees of Evolution, Observed from Above” and “1874: Garrod Reconstructs Both Ancestor and Offspring through a Tree and Its Cross Section”, we will encounter similar layer-like cross sections.
“Auf der beigegebenen Tafel (IV) enden die Auszweigungen des Stammbaumes in den Peripherieen 8 concentrischer Kreise und ist damit angedeutet, bis zu welcher Stufe jede einzelne Gattung sich entwickelt hat.”
See Winsor (2015a, b, c) for a detailed discussion of this map and of the concept of affinity from the 1820s, when William Sharp MacLeay launched his quinarian natural system until the publication of Darwin’s Origin. Her three-part article has the form of an amusing, imaginary dialogue between Darwin and Strickland. She also discusses Strickland’s later additions to his map, which eventually resulted in a map of the avian part of the animal kingdom. I will not discuss these additions, as they do not have direct relevance to the subject of this article.
I follow Sharpe’s use of italics for the scientific names of taxa regardless of their taxonomic rank.
The map shows three additional interesting features: (1) The “bridges” between the “islands,” e.g., between the pink Alcyone, Alcedo, and Corythornis. (2) The bright pink and green dots on both sides of the “straits” between the islands. These symbolize border-crossing affinities, shared by species in different genera. (3) The outward-pointing arrows that appear to suggest plate tectonics occurring in this region of a two-dimensional representation of the natural kingdom. In fact, however, the arrows represent affinity between the kingfishers and the “continents” on the map’s lower and right edges. Given the scope of this article, however, I cannot analyze these features in depth.
Garrod’s images can be explained without specifying their ornithological content and thus without decoding his character states. However, for readers who want to read their morphological details, the state of the common ancestor, 2. + . + . + , may serve as an example: 2 means in this case that the common ancestor possesses two carotid arteries; in other cases, Garrod used different numbers or letters to indicate particulars of the carotid arteries. The first + indicates the presence of an ambiens muscle (the thigh muscle of certain birds that bends the toes of the bird, so that the feet can clasp the perch on which the bird sits). The second + indicates the presence of a furcula or wishbone, a kind of strut between the bird’s shoulders. The last + stands for the presence of an oil gland which supplies oil to be spread on the wings (Garrod 1874, p. 595).
“Zur graphischen Darstellung der Stammbäume sei Folgendes kurz bemerkt. In Wirklichkeit wird jeder Stammbaum wie sein Vorbild in der Natur eine stereometrische Form haben, d. h. sich in den drei räumlichen Dimensionen erstrecken müssen. Gleich den linearen Systemen kann ein planer Stammbaum mit in nur einer Ebene stattfindenden Verästelungen den wirklichen Verhältnissen nicht entsprechen. Aus Draht angefertigte Modelle mit nach allen Richtungen gehenden Zweigen dürften die vollkommenste Darstellung des körperlichen Stammbaumes repraesentiren, während die graphische Reproduction sich—nach Art der Baupläne—mit der Vertical- und Horizontalprojection begnügen muss.”
“Könnte ich einen solchen, sich nach allen drei Dimensionen erstreckenden Stammbaum als ein körperliches, aus Draht oder einem ähnlichen Materiale angefertigtes Modell beigeben.... Auch stereoskopische Ansichten eines solchen Modelles würden wenigstens einen allgemeinen Eindruck der betreffenden Verhältnisse gewähren. Beides ist leider bei der auf einfache Flächen angewiesenen graphischen Methode nicht möglich.”
The footer “Max Fürbringer fec.,” at the bottom left of the images, indicates that he himself was the draftsman of the views, which were transferred by an unknown lithographer to the offset plates used in printing them.
“Sein Stamm, seine Äste, Nebenäste und groberen und feineren Zweige geben einen klaren Einblick in das mannigfache Gewirr der phylogenetischen Entwicklungsbahnen und zugleich der näheren oder ferneren genealogischen Relationen, welche die einzelnen Abtheilungen unter einander verbinden; je kurzer oder je länger dabei die Äste und Zweige sind, je weniger weit oder je weiter sie sich von ihrem Ausgangspunkte verbinden, desto niedriger oder höher ist die morphologische Stellung der durch sie repraesentirten Formen; je weniger oder je mehr sie gegenseitig divergiren, desto minder oder mehr differiren die denselben Ahnen entsprossenen Abkömmlinge.”
“Dünne und dicke, durchlaufende, gestrichelte und punktirte Linien umschliessen Subfamilien, Familien, Gentes, Subordines und Ordines.”
We need not be surprised that Fürbringer mentioned Garrod’s “horizontal projection,” along with Sharpe’s (Fürbringer 1888, p. 1123).
“Um in das Gewirr der verticalen Ansichte grössere Deutlichkeit zu bringen, müssten einige Äste, die sich sonst verdeckt haben würden, oder einander zu nahe gekommen wären, etwas beiseite gebogen werden.”
“einerseits erscheinen manche in Wirklichkeit weit aus einander liegende Zweige auf den verticalen Ansichten, wo die körperliche Tiefe nicht ausgedrückt werden könnte, allzusehr genähert...; andererseits scheinen auf den horizontalen Projectionen manche Familien dicht neben einander zu liegen, die wegen der sehr verschiedenen Höhe ihrer Entwicklung oder wegen ihrer Abstammung von ganz verschiedenen Zweigen in Wirklichkeit von einander recht entfernt sind.”
“Die Grösse dieser Kreise sind verschiedene, je nach dem ungefähren Umfange der durch sie ausgedruckte Familien; ... Die Kreise selbst sind etwas zu gross, die Zwischenräume zwischen ihnen zu klein angegeben; eine grössere Entfernung verbot sich durch die Rücksicht auf den beschränkten Umfang der Tafel.”
The potential added value of a real three-dimensional model is questionable. Admittedly, it would have been possible to view it from all sides and therefore no branch would have remained hidden behind others. But otherwise it would have been nothing other than a “manifold tangle” of, say, iron wire. Moreover, it is hard to imagine how syntheses at horizontal levels in the form of circles or irregular islands could have been integrated in the model itself without hiding other parts of it from sight. In this respect the two-dimensional horizontal projections perform even better.
The purport of Sharpe’s statement is similar to Darwin’s observation, quoted in the opening line of this article, that naturalists cannot do without the aid of genealogical trees when trying to describe “the various affinities which they perceive between the many living and extinct members of the same great natural class.” In fact, Fürbringer’s Stammbaum may be considered the special, ornithological illustration of Darwin’s general statement, by which he introduced the famous diagram in Origin. In this special case, Sharpe, confronted with the challenge of understanding and presenting Fürbringer’s overwhelming number of findings on the phylogeny of birds to the congress, stated that he could not meet this challenge without the latter’s Stammbaum.
The quotations in this section are from the printed report, not from Sharpe’s spoken address.
I thank an anonymous referee for this interesting suggestion.
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Acknowledgements
I would like to express my sincere thanks to Prof. Carla Rita Palmerino and Prof. Christoph Lüthy, at the Center for the History of Philosophy and Science, Radboud University, Nijmegen, The Netherlands. Without their unfailing confidence and continuous inspiration, this article would not have been produced. I also owe a lot to Jasper C. van Putten, PhD, Basel, Switzerland, who made some indispensable illustrations. I also thank two anonymous reviewers whose suggestions contributed to the quality of this article.
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van Putten, K. Three-Dimensional Phylogeny in Two Dimensions: How Darwin and Other Nineteenth-Century Naturalists Created Three-Dimensional Figures of the Natural System by Combining Trees of Life and Maps of Affinity. J Hist Biol 54, 639–687 (2021). https://doi.org/10.1007/s10739-021-09662-5
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DOI: https://doi.org/10.1007/s10739-021-09662-5