Categorizing Ideas about Trees: A Tree of Trees

The aim of this study is to explore whether matrices and MP trees used to produce systematic categories of organisms could be useful to produce categories of ideas in history of science. We study the history of the use of trees in systematics to represent the diversity of life from 1766 to 1991. We apply to those ideas a method inspired from coding homologous parts of organisms. We discretize conceptual parts of ideas, writings and drawings about trees contained in 41 main writings; we detect shared parts among authors and code them into a 91-characters matrix and use a tree representation to show who shares what with whom. In other words, we propose a hierarchical representation of the shared ideas about trees among authors: this produces a “tree of trees.” Then, we categorize schools of tree-representations. Classical schools like “cladists” and “pheneticists” are recovered but others are not: “gradists” are separated into two blocks, one of them being called here “grade theoreticians.” We propose new interesting categories like the “buffonian school,” the “metaphoricians,” and those using “strictly genealogical classifications.” We consider that networks are not useful to represent shared ideas at the present step of the study. A cladogram is made for showing who is sharing what with whom, but also heterobathmy and homoplasy of characters. The present cladogram is not modelling processes of transmission of ideas about trees, and here it is mostly used to test for proximity of ideas of the same age and for categorization.


Introduction
Historians of Science used to categorize schools of thinking without any formal tools to do it (e.g., transformists, evolutionists, gradists, etc.). To produce such categories they had to compare ideas among authors, however, without any clear procedure. The same can be said about systematists, who have been categorizing themselves for long ago into schools like pheneticists, cladists, pattern cladists, synthetists, etc. [1], [2], [3], [4], [5]. Systematics, the science of classification, is using directed acyclic connected graphs to represent relationships among organisms, i.e. hierarchies in the distribution of shared attributes. From those figures systematists produce classifications (nested sets), which categorize organisms. The aim of this study is to explore whether the tools used to produce systematic categories of organisms could be useful to produce categories of ideas in history of science. The benefit should be the reproductiveness and testability of the consistency of the categories that are produced. We propose a testable way to categorize ideas, but we need a case study: what kind of ideas?
We chose the idea of ''tree'' used across two centuries and half by various authors to represent relationships among organisms. Our basic assumption is that the types of relationships (shown as graphs or branching diagrams) used through time have differed, but they themselves are somehow related. This study therefore focuses on the history of the use of trees to represent the diversity of life and applies to ideas about trees a method inspired from coding homologous parts of organisms. We discretized conceptual parts of the tree; we detected shared parts among authors; we coded those parts into a character matrix and we used a tree representation to show who shares what with whom. In other words, we propose a hierarchical representation of the shared ideas about trees among authors: this produces a ''tree of trees'' (which is, indeed not the ''tree of trees'' in the sense of Nye [6]). Then we categorize schools of thinking and discuss a possible phylogenetic interpretation of the representation of shared ideas under the form of a tree.
Authors writing their scientific ideas in books have not only collected data and facts: they also collected information (published or oral) from other authors of different times and places. Scientific ideas can be transferred in a vertical manner from one epoch to another; they can convergently appear at the same time; they can also be ''horizontally'' transferred in a same epoch from one author to another. When comparing ideas, two questions are then to be considered: i. Are we able to recognize the same idea through different words, and are we able to avoid the pitfall of using the same words used to express different ideas? This is a problem for every historian of ideas, here we propose to formalize shared ideas, i.e. to make explicit through character coding what is often implicitly accepted; ii. How to express shared ideas in a synthetic and consistent manner? Some ideas are widely shared; others are restricted to a few authors. A hierarchical distribution of sharings among authors is therefore needed, and a most parsimonious tree seems to be suitable because it shows who is sharing what with whom in a hierarchical manner… but what is the meaning of maximizing consistency among ideas?
Here we promote the formalizing step enabled by the parsimony approach to comparison, in a theory-free framework at least at the beginning (see discussion).

Materials and Methods
In the scientific field of Natural History we selected 41 books and papers from 1766 to 1991 where the idea of a ''tree of life'' was expressed and/or illustrated. The period was chosen because the metaphor or picture of ''tree'' became usual in natural history for those who wanted to organize the diversity of life. These were chosen because they encompass well known and/or fundamental literature in systematics, and they have a theoretical and/or educational content. Some of them even became elements of general scientific culture. Those works may talk about biology, paleontology, or even be philosophical or theological essays. They have in common to present trees of life. The XX th century was not sampled the same way as the XVIII th and XIX th . Indeed the explosion of tree reconstruction methods in the second half of the XX th century [7], [8] would require a specific study. Also, we limited the sampling to the modern scientific era. Trees used to support metaphysical views beyond science before the XVII th century (see [9] are out of the scope of the present analysis. In the same way, we chose to limit ourselves to Natural History: we study trees depicting the diversity of life, not trees organizing knowledge (e.g. [10], [11]), languages (historical linguistics) or any other kind of classificatory objects. The 41 works were selected as foreground ones in the field of systematics. The languages selected were English, French and Latin.

Terminal taxa, or ''Operational taxonomic units''
The operational taxonomic units used here are not authors or schools of classification, but books. More precisely, it is what a selfconsistent book says or draw about trees. The whole share the property of drawing or describing a classificatory tree based on a theory of classification.

The Outgroups
We aimed at classifying trees of life. Each of them must be based on a classificatory theory. Linnaeus elaborated a classification of life, but never made trees. For this reason, he was set in the ougroup. But for the same reason, we could not polarize states of characters for the questions about the tree graph. Zaluziansky has drawn dichotomic identification trees, with no objective classificatory purpose. This is the reason why Linnaeus and Zaluziansly have been set as outgroups.
1592: Adam Zaluziansky, ''Methodi Herbariae Libri Tres'', (Methods of herbs, manuscript three; only one edition). Adam Zaluziansky, botanist and doctor, separates botanics from medicine in his Methodi Herbariae. In this work, he elaborates several tree-shaped identification keys for the plants he describes.
Zaluziansky has been identified as an outgroup because he created trees, but not taxonomic classifications. This table is to be read neither strictly as a tree nor as a geographic map, but rather as a hybrid of both. A compass is represented on the table, but geographical content does not seem to be respected.
This table is a relative map: it is compass-oriented but does not represent a strict geographic map. Rather, it explains the various transfers that dogs races have undergone. The ''chien de berger'' (shepherd dog) is considered as the ancestor of all other dogs. The main lines are the first transfers of dogs: to the west, the east, the north, etc. Those transfers produce new dog varieties that are themselves transferred to other countries. Those second lines are much smaller: they do not indicate where dogs have been transferred. As relative coordinates, those lines are to be read as if the card was centered on the firstly-transferred dog, giving to the figure the aspect of an unrooted tree. The table is difficult to understand without Buffon's text, which comes with it.
This table is not a tree. However, Buffon describes it with words and concepts that are commonly used to describe trees, even if the tree is never used as a figure. We can study it as a tree-like extension of maps: it describes a tree-like classification of a part of life, dogs.
mankind at its top. The tree he describes is the first global tree of life, grouping plants, animals, and even minerals on its root. The content of trunk and of the main branches is described, as well as the classificatory mode.
Pallas concludes this introduction by strongly recommending the use of such classificatory trees. Interestingly, this written tree has never been drawn by the author.
1770: Buffon, ''Histoire Naturelle des Oiseaux'' (Natural History of birds), tome 16. (Only one edition). If the previous occurrence of a tree depiction in Buffon's works was located at the end of the volume, this one is situated in the introduction of the first volume of his Histoire Naturelle des oiseaux (Natural History of Birds), the sixteenth volume of his Histoire Naturelle. The scope of this tree is larger than the previous one: there is no more only a few species that are grouped together, but many avian species that are regarded as being from the same family. Buffon elaborates several trees, each one being the grouping of closely related species. Those family links are as much numerous as the bird species are small.
Buffon links this description to the organization of his work. In this study of birds, he prefers their grouping in genera and their global description versus a description of each species following another.
1774: Johannes Rü hling, ''Ordines Naturales Plantarum'' (Natural orders of plants). (only one edition). In his Ordines Naturales Plantarum, Rühling describes a classification method inspired from other botanists that he then applies to elaborate a succinct classification.
At the end of the preface, Rühling describes and draws a tree indicating ''quasi-inbred'' affinities between plants. But the classification is not an evolutionary one. Furthermore, the author describes his figure as a geographical table. But this figure is rooted; it contains nodes, branches and leaves. Its shape is the one of a tree.
1790: Johann Wolfgang von Goethe, ''Versuch die Metamorphose der Pflanzen zu erklä ren'' (Attempt to explain the metamorphosis of plants). (only one edition). Better known as a poet, playwright and writer, Goethe has also written a few books and essays about Natural Sciences. In his Metamorphose der Pflanzen (Metamorphosis of Plants), he studies the affinities between the organs of plants. Those affinities are a metaphor of the affinities and metamorphoses of plants themselves There is a tree-like metaphor of evolution in this work. 1801: Augustin Augier, «Essai d'une nouvelle classification des végétaux» (Experimentation of a new classification of plants). (Only one edition). French botanist, Augustin Augier elaborates an ''Experimentation of a new classification of plants'', which is described along with its pitfalls. Augier considers that classificatory tables failed. He then asserts that the only possibility is to classify plants by using a tree that he draws without any evolutionary consideration. This tree is guided by considerations of values -from the less perfect to the more perfect, in terms of complexity of organization (flowering system, complexity pattern of leaves…), through branches -but also the inclusion and the succession of ranks.
1809: Jean-Baptiste Monet, chevalier de Lamarck, «Philosophie Zoologique» (Zoological Philosophy). (only one edition). Lamarck's Philosophie Zoologique is an epistemological watershed in Life Sciences. In the first part of his work, he describes the mutations of bloodlines along generations of which taxon. Lamarck's theory is the first generalized theory of evolution -even if that word is not yet used in its present meaning. Evolution is seen as a mutation of organs of animals with an increasing complexity of them.
In the text, Lamarck describes his concept that the only possible classification of life is onto a scale of beings. But, in the addenda, he draws a tree illustrating the successive states of bloodlines.
1816: Charles Hélion de Barbançois, ''Observations sur la filiation des animaux'' (Remarks on the progeny of animals), in Journal de physique, de chimie, d'histoire naturelle et des arts. Barbançois is a follower of Lamarck. In a short paper, he more thoroughly investigates the succession of beings. He organizes them onto his own tree that follows, on the same page, Lamarck's one. Barbançois makes some modifications in Lamarck's classification.
1816: Charles Hélion de Barbançois, ''Observations pour servir à une classification des animaux'' (Remarks for use in a classification of animals), in Journal de physique, de chimie, d'histoire naturelle et des arts. Barbançois's second article, published a few months after the previous one does not contain the same tree, but much more a hierarchic key which makes gradations in terms of values within each group. He includes humans in his classification (which Lamarck did not do), splitting them into narrow-minded humans and clever ones.
1843: Louis Agassiz, «Recherches sur les poissons fossiles» (Research on fossil fishes), vol. 1. (Only one edition). Agassiz writes a five-volumes classification of fossil fishes based on the shape of their scales. There, he draws a tree that represents explicitly the occurrences of fossil species through geological times.
Agassiz is not an evolutionist, and he refers to periods of supernatural disappearances and creations of species.
1845: Robert Chambers, ''Vestiges of Natural History of Creation'', 3rd edition. Published anonymously, the Vestiges work offers a history of Earth and Life. The author proposes a series of theories to explain the world and the universe, including various concepts about the evolution of life. Then, he proposes several recommendations about classification of life. Chambers explains evolution in terms of increasing complexity, and draws a tree to illustrate his words.
1850: Heinrich Georg Bronn, ''Recherches sur les lois d'évolution du monde organique pendant la formation de la croute terrestre'' (Research on the laws of evolution of the organic world during the formation of the Earth's crust), in Comptes rendus hebdomadaires des séances de l'Académie des sciences. Tome 2. The French Academy of Sciences proposed in 1850 a contest to researchers. They had to elaborate a classificatory system aimed at answering three queries: the position of fossils in sedimentary formations; the question of their appearance and disappearance; and relationships between the present shapes of living forms and the previous ones. The proposed system had to be based on one of the main phyla of life, at least one of the animal classes, but preferably treating life as a whole. The idea was not to propose a theory of evolution, but to offer a classification system suitable for all geological periods.
The price was awarded to Bronn in 1856, which based his system on the observations of successions of beings in strata since Cuvier and D'orbigny's works. The system he elaborates is not an evolutionary one but is based on times of extinctions and creations. Bronn proposes a classificatory tree-shaped system to illustrate his conclusions.

1853: Edward Hitchcock, ''Elementary Geology with an
Introductory Notice'', 8th edition. Edward Hitchcock was a geologist. In this work, he presents views on geological facts for the public and his students. This book was moreover destined to a Geology congress.
Describing geological data, Hitchcock presents the fossils found in each stratum and then elaborates a classificatory table. This table is then converted into a set of two grouped trees of life, titled ''Paleontological chart''. The first one is for animals, the second for plants. Those evolutionary trees are commented with Hitchcock's theory of evolution. In each one, two groups are crowned: Mammalia for animals, with Man on the crown, and Palms for plants.
1855: Alfred Russel Wallace, ''On the Law which has Regulated the Introduction of New Species'', in The Annals and Magazine of Natural History. Originally published in the Annals and Magazine of Natural History, Wallace's paper is an attempt to explain the formation of species from other ones. The system given describes the geological, geographical and anatomical arrangement of living forms. The notion of ''antitypes'', similar to our ''ancestor'' notion, guides the theoretical principle.
To illustrate those ideas, Wallace describes a theoretical figure, openly analogous to a branching tree, which is not drawn.
1856: Alfred Russel Wallace, ''Attempts at a Natural arrangement of Birds'', in The Annals and Magazine of Natural History. After a study of birds in Southern America, and during another one in the Indian Islands, Wallace begins a classification of bird groups. The finished work is not an evolutionary one but rather an arrangement of groups according to their morphological affinities.
In this article, Wallace draws two classificatory unrooted trees of birds.
1859: Charles Darwin, ''On the Origin of Species'', 1st edition. In this founder work for modern biology, Darwin proposes a theory for the evolution of species and their classification. The famous tree from that book functions as a conjecture about the general shape of the genealogical links if the theory is true [22], and it is followed by the required consequences for classification. Its status is theoretical. The first edition of this work is studied separately from the last one and appears in separate rows in the data matrix, because of numerous modifications that have been done in between. Among these changes, Darwin clearly expressed a requirement for monophyly of groups in the first edition [13] [14], a section that was removed in the sixth edition.
1866: Albert Gaudry, «Considérations générales sur les animaux fossiles de Pikermi» (General considerations on the fossil animals of Pikermi). (only one edition). Albert Gaudry was a paleontology professor at the French National Museum for Natural History, which he directed. In 1866, he published a genealogical classification of Pikermi (Greece) fauna. Benefiting from exceptionally preserved fossils, he attempted to arrange them following Darwin's prescriptions. His tree, considered as the first use of Darwin's one used for classifying, was lauded by Darwin.
Gaudry did not consider natural selection to be true, but rather believed in a deistic-guided harmony and regulation.  In this article, Cuénot describes the ideas directing the elaboration of the tree. He lends his own considerations about a direction in evolution and the idea that it is finished: there is no more evolution.

1953: Ernst Mayr, ''Methods and Principles of Systematic
Zoology''. (Only one edition). Ernst Mayr wrote a treatise about the principles of numerical taxonomy. This one is destined to teachers, biologists, and also amateurs. After a brief history of taxonomy, Mayr elaborates taxonomic procedures from the collection of specimens to the elaboration of taxonomic papers. He describes here the different analysis methods, and includes several trees in order to describe their elaboration. Then, he describes the process of zoological nomenclature following international rules.
1955: Pierre Teilhard de Chardin, «Le Phénomène Humain». (The human phenomenon). (only one edition). Teilhard de Chardin, paleontologist and Theologian, wrote two books aimed at explaining the conciliation between scientific knowledge and his personal religious believes. In this first one, written in 1947 and published as posthumous, he writes a history of the Universe. Linking theories in Physics and Biology with personal convictions, he writes an ''introduction to an explanation of the world'' and an attempt of general explanation of evolution. Teilhard de Chardin elaborates a theory to accommodate Darwinian natural selection to degrees of higher encephalization given to some species, until a cosmic «omega'' point. He represents this theory with several tree drawings.
1956: Pierre Teilhard de Chardin, ''Le Groupe Zoologique Humain'' (the human zoological group). (only one edition). In this second work, Teilhard de Chardin concentrates his study on mankind as a ''phenomenon''. He attempts at assigning the place of Homo sapiens in nature, among other forms of life. Teilhard de Chardin writes a story of the anthropogenesis in five steps: life in the universe, biosphere, appearance of mankind, expansion step of his ''noosphère'' and then its compression. More than a study of the past, the author aims at giving an interpretation of the appearance of mankind, and its future in a theological interpretation of life.
1962: George Gaylor Simpson, ''Principles of animal taxonomy''. (2nd impression). In this work, Simpson develops classificatory models. From the original data to the tree and the classification, he gives instructions to proceed. This book is less an essay on classifications than a kind of handbook for students or researchers. There are several kinds of trees illustrating each step of the elaboration of a taxonomic work.
1963: Robert Sokal & Peter Henry Andrews Sneath, ''Principles of Numerical Taxonomy'', 1st edition. How can taxonomists make non-arbitrary groups? Tough they are convinced by evolution, Sokal and Sneath claim the impossibility to find the phylogeny of species. But they advocate for treeconstruction methods based on global similarity. Characters are not directly treated as such onto the tree because they have been previously mixed into a pairwise distances matrix. Thus their ''phenograms'' aren't phylogenies, what is assumed by the authors, but one of the first attempts to mathematize and objectivize the elaboration of taxonomic groups. American. Sokal's article develops the first principles of numerical taxonomy to match to new computation possibilities given by computers. Sokal develops much more this theory to make it able to classify imaginary animals, the famous ''Caminalcules''. Then, he proposes a mathematically and similaritybased ranking method.
1966: Willi Hennig, ''Phylogenetic Systematics''. (Only one edition). This English version of Hennig's ''Grundzüge einer Theorie der phylogenetischen Systematik'' proposes a novel classification method. It aims at reconstructing phylogeny, given as knowable, without the need of inclusion of pre-conceived groups into the procedure. He redefines monophyly, paraphyly and polyphyly and concepts of species and higher taxonomic groups.
Hennig's Phylogenetic Systematics has become the basis of modern classifications.

1967: Alfred Romer, ''Major Steps in Vertebrate
Evolution'', in Science. Romer explores, in this article, the origin of modern man in a succession of ''major steps'' since a ''metazoan ancestor''. He aims at reconstructing this sequence of selective steps from tunicates to vertebrates and from the rise of a bony structure to the emergence of terrestrial higher vertebrates, and then to primates and mankind.
1973: Alfred Romer, ''l'origine des classes de vertébrés'' (''The origin of Vertebrate classes''), in La Recherche. Are amphibians descended from a single common ancestor, or are they a polyphyletic group? In this article, Romer discusses, in terms of emergence of groups from other ones, the development of vertebrates and the search of intermediate forms. From fossils and paleontological data, he elaborates two trees: the first one for vertebrates, the second for tetrapods. Then, he discusses the production of ''natural classes'', descending from a common ancestor. Taxonomy'', 2nd edition. Ten years have passed since Sokal and Sneath's first Numerical Taxonomy. Technology has lead to the appearance of computers in laboratories, enhancing computational possibilities. Epistemological and mathematical novelties have been developed, such as the parsimony algorithm. Above all, Hennig's Phylogenetic Systematics emerged in the English-speaking world and totally remodeled the methodological landscape of Systematics.

1973: Sokal & Sneath, ''Numerical
The authors have corrected and enriched their own considerations. Especially, they develop in this work the idea of ''numerical cladism'' and its methodologies.
1982: Ernst Mayr, ''The Growth of biological thought: diversity, evolution and inheritance''. (Only one edition). Almost twenty years after the rise of cladism, after ten years of intense debates among the classificatory schools of pheneticists, cladists and synthetists, time has come to write a new history of biology. Mayr writes three books to do so. This one is about Evolution.
Well-known for his gradist classifications, Mayr casts a critical eye on other schools. This epistemological work deals about clades, grades, and their representation onto trees.

Vocabulary used
The analysis is based on 91 characters. Characters descriptions involve some specific vocabulary, which is explained here.
Blob, Bubble. A blob, or a bubble, is a bidimensional baloon. A ''bubble tree'', or ''romerogram'', is a tree made of such kinds of elementary objects, either linked to one another (e.g. in Romer) or independent (e.g. in Agassiz). Rather than linear branches, ''bubble trees'' are successions of closed two-dimensionnal shapes.
Discontinuities. A discontinuity is a gap, lack of continuity between two elements. Those elements can be genealogical links, blobs, groups based on global similarity, or in a chain of beings… Discontinuities are not ''vertical cuts'' (below): cuts are lines, not gaps.
Diversification axis. This axis of a tree represents diversification, i.e. the number of independent lines to the terminal leaves. This number, along this axis, does not increase with hierarchical resolution. An unresolved tree of 7 terminals has a value of 0 in the hierarchical axis and a value of 7 in the diversification axis. A fully resolved tree of 7 terminals has a value of 5 in the hierarchical axis and always a value of 7 in the diversification axis.
Groups. Groups are basically sets of objects gathered according to a given consistency. Thereby, for example, for phylogenetic systematics, taxa are sets of individuals grouped according to a principle of monophyly.
Hierarchical axis. The hierarchical axis of a tree is the one that counts the number of levels of inclusion implied by the various groups (or ranks), i.e. by the hierarchical resolution. An unresolved tree of 7 terminals has a value of 0 in the hierarchical axis and a value of 7 in the diversification axis. A fully resolved tree of 7 terminals has a value of 5 in the hierarchical axis and a value of 7 in the diversification axis.
Leaf objects (or ''tips''). The objects set on leaves are the kind of elementary entities classified. These can be taxa (when dealing with life), musical instruments, ideas… If they are taxa, they can be of several kinds: classes, families, species, populations, or openly one specimen.
Properties. Properties are attributes, qualities or characteristics of the classified objects.
Steps. A step is an evolutionary stage. It generally implies a progression toward a goal, a more complex evolutionary stage.
Value. An ''evolutionary value'' is the quality of something that renders it, in fine, closer to mankind's abilities.
Vertical cut. A ''vertical cut'' is a vertical line that cuts a tree into «paraphyletic'' groups, i.e. a node but not all its descending branches. A vertical cut is not what we call above a ''discontinuity''. A discontinuity is a gap, not a line.

Characters classified into thematic areas
To allow a better understanding of the ideas that are coded into the character matrix, we classified the 91 characters into five thematic areas: The elements of the tree, The meaning of the tree, The content of the tree, Trees and taxonomy, The methodology employed. Through these five thematic areas, and to facilitate understanding of characters, the characters are themselves grouped into 33 sections. Each of them is a question about the tree.
Elements of the Tree. Here we detail each component of the tree, whether they are general (root, leaves, branches, nodes, etc.) or specific to certain authors (''blobs'', cuts across the tree, etc.). We also code the meaning of the tree root in terms of whether it implies an object or concept. If its meaning is an object, it is either considered as being (or having been) alive or an inert entity (such as minerals, molecules, etc). If the root refers to a concept, it is either an initial state of characters or a type.
Section ''Meaning of the root'' (Characters 1 to 7). The root is the base of the tree. It is the point from which emerge the first branches and thus all the potential extent of their diversification.
Section ''Meaning of the lines'' (i.e. branches; Characters 8 to 10). The term ''lines'' refers to the branches of trees. They represent links between roots, leaves or trunk. Links carry a message: they are the expression of a purely logical relationship among objects or branches bear a content. This content changes along the branch: bloodlines, or gradation (or not) in terms of perfection.
Section ''Meaning of the internal nodes'' (Characters 11 to 14). Nodes are, topologically, the point from where branches emerge. As they are a-dimensional objects, they cannot express any gradation. However, they carry information. As trees express relationships among the various entities of life, nodes can refer to species, races and varieties or groups of larger size. They can also bear concepts: mass extinctions, characters, etc. Finally, nodes are sometimes linked to a notion of ancestor: these two ideas can then be confused and a ''concrete'' ancestor be placed at this point.
Section ''Meaning of the leaves'' (Characters 15 to 19). Leaves are, in a tree, objects connected to a line and only one. They are moreover located opposite to the root. In addition, leaves can be related either to current times or past ones. They can explain the end of an evolutionary pathway, its finality or merely its most recent expression. Indeed they can furthermore be the expression of an evolutionary destiny, a teleological apex of evolution, the ultimate ending of a progression. Leaves may symbolize groups or species. They can also consider time, reflecting changes in species and their reasons. Finally, some of authors regard leaves as the only detectable objects.
Section ''Meaning of vertical cuts'' (Character 20). A ''vertical cut'' is a split between two parts of the tree. If present, they symbolize a break-up between either groups or kingdoms.
Section ''Meaning of ''blobs'' (Characters 21 to 22). A ''blob'', or a ''bubble'', is a swelling in size into the tree. They most often replace branches. As bi-dimensional objects -branches are unidimensional ones -they so express a second message. Bubbles may thus refer to a numerical quantity of species within a given group over the generations. They may furthermore bear a message of gradation.
Section ''Meaning of the ancestor'' (Characters 23 to 26). With the idea of a chronology in evolution comes the one of the ancestor. This one is narrowly linked to a concept of descent.
Section ''Orientation of the tree'' (Characters 27 to 31). How is the tree to be read? There are rules guiding the reading of the tree, and those one admit an orientation for reading -basically from the root to the leaves. However, a tree is always drawn in two dimensions and we need here to name the two dimensions. The dimension along which hierarchical levels are embedded into one another can be called the ''hierarchical axis'' (Fig. 1). This axis increases in number of steps (or in length) as the hierarchical resolution increases. This is, most often, the axis along which authors place time when it is the case. The other dimension is called here ''diversification'' axis. This axis does not increase in number of steps (or length) when the hierarchical resolution increases. It increases only with the number of leaves.
Section ''Diversification axis of the tree'' (Characters 32 to 35). There is a message set on the two axes of the tree, its abscissa and its ordinate. The diversification axis may take various meanings. It may thus symbolize just diversification of species or groups from their common base, but may also illustrate properties or a value gradation in a value system. It may exceptionally be the result of the necessity of nesting different groups into each other (in Haeckel or Wallace). Finally, on the diversification axis may also contain a notion of time (for example in Haeckel).
Section ''Hierarchical axis of the tree'' (Characters 36 to 40). This character is independent from the characters 28-32. Indeed the meaning given to the diversification axis is independent from the meaning given to the hierarchical axis.
Section ''Well-marked discontinuities'' (Characters 41 to 42). Drawing a tree implies accepting a continuity and a discontinuity in life. A ''well-marked'' discontinuity must be identified by an empty space between two branches of the tree. Discontinuities are not splits superimposed to the graph; they are empty spaces into the graph itself. They may appear either horizontally or vertically.
Meaning of the tree. What is the tree made for? We will focus on the use of trees for classification.
Section ''Classificatory aim'' (Characters 43 to 44). Has the tree been drawn in order to classify a content? (in opposite to a merely illustrative tree, for example).
Section ''Status of the tree's graph'' (Characters 45 to 46). As mentioned above, trees can have a theoretical and/or an epistemological status: epistemological trees propose classifications of concrete objects, animals, plants, sharks, etc. On the opposite, a theoretical tree models the shape that a classification might have if the theory about the processes of diversification is true. Trees can be only theoretical, only epistemological, or be a combination of the both.
Section ''Does the tree intends to illustrate the natural order?'' (Characters 47 to 48). An intrinsic ''order of the Nature'' is supposed and is what classification is expected to reflect using a tree. Moreover this term ''natural order'' must be explicitly mentioned. Note that the link between the order in Nature and classificatory purposes is not unequivocal. For instance, for pheneticists there is a natural (genealogical) order in Nature however it is not what classification intends to reflect.
Section ''The tree is genealogical'' (Characters 49 to 50). The tree is theoretically based on a genealogical background: if species do evolve, there thus must be bloodlines, implying kinship. We must define genealogy here. It is a ancestor-descendant relationship between two concrete individuals. However here that relationship can be either thought as merely theoretical or thought by the author as a concrete empirically accessible link.
Section ''Are Beings steps of a value system?'' (Characters 51 to 52). In some authors there can be a value gradation among beings reflecting a value system; for instance gradation in perfection. The notion of perfection is then expressed through various means: roots, branches, bubbles, leaves, clippings, ordinate or abscissa.
Section ''Teleology: direction in evolution?'' (Characters 53 to 54). Is evolution guided by a specific direction or is it the mere product of fortuity?
Content of the tree. We will focus here on contents of a tree: fossils, kingdoms, ancestors, etc. That's what is carried -or notby the tree which will target our interest.
Section ''Do fossils belong to the classification?'' (Characters 55 to 56). Are fossils taken into consideration, or merely ignored?
Section ''Trees take into consideration the extinctions of species'' (Character 57). Do trees consider the possibility of the complete disappearance of a species?
Section ''Is the ancestor concrete?'' (Characters 58 to 59). A ''concrete'' ancestor is an organism, extinct or alive, assigned as the ancestor of a group. Its body, complete or lacunar has been found and a name has been attributed to it.
Section ''Consideration of time in the tree'' (Characters 60 to 61). Larger than the mere genealogy, is there a notion of time carried by the tree? Here we code 1 if time is present whatever the axis (hierarchical or diversification, see characters 36 and 39).
Section ''Kinship between plants and animals?'' (Characters 62 to 63). One of the most recurrent questions in ancient authors is the relationship between plants and animals. It is therefore necessary to examine relationships between the two life's kingdoms that are embedded into our pre-scientific cultural background.
Section ''Ability to interbreed'' (Character 64). In some ancient authors interbreeding is the ability for groups (larger than mere species) to cross one another. A global ability to interbreed is never found. Meanwhile, the question is here to know if interbreeding (including between distant groups) is possible or not.
Section ''Extent of the tree'' (Characters 65 to 66). The tree aims here at studying a larger or a smaller group. Is the group studied the ''largest'' one, including all beings, or does the tree incarnate only a small part of life? Typically, some authors make a distinction between plants and animals in the applicability of their method, which restrict the extent of the classificatory program. In some works, there are several trees; one for each different part of life.
Section ''Special position assigned to mankind'' (Characters 67 to 68). Is mankind set at the top of the tree? Is its place a privileged one? This question is recurrent among authors.
Trees and taxonomy. Obtaining data and relationships is not an isolated activity. Authors may also create groups.
Section ''Reality given to categories'' (Characters 81 to 82). Are the categories given as real, non-arbitrary elements of life, or are they seen as arbitrary concepts? (for instance, categories are real for Linnaeus and closer to us, for Dubois [43] the genus is a real evolutionary unit in Nature).
Methodology Employed. Section ''Use of parsimony (character 83). Although this criterion is, from all, the most recent one, the use of parsimony principle appears as being rich enough to be set in our characters matrix. The use of this principle must be openly asserted.
Section ''Classification based on presence of characters'' (Characters 84 to 85). Is classification based on presence or lack of characters? Section ''Classification (i.e. arrangement) by global similarity'' (Characters 86 to 87). A classification can also be elaborated according to global similarity.
Section ''Use of monophyly'' (Characters 88 to 89). Monophyly is the property of grouping to an ancestor all its descent and nothing less; to group entities by the mere consideration of bloodlines. If the modern meaning of this term is rather recent, we will here consider the idea of monophyly, whatever its name could be.
Section ''Consideration of homoplasies'' (Characters 90 to 91). Homoplasies are similar character states that have not been inherited from a common ancestor.

Description of characters
Character 1: A concrete species or ancestral group is referred to at the root. A concrete form is seen as a being able to reproduce its own kind. Here, this is a concrete being that the author assigns to the root. This is, for example, what Darwin does (0), whereas Hennig does not. Yes = 0; No = 1 Character 4: If the root carries the idea of a being: is this one still alive (even as a ''living fossil'') or extinct?. As an example, Buffon considers that the being set at the basis of the tree is still alive (the horse, the shepherd dog…) whereas, according to Darwin, this species is extinct. Extant = 0; Extinct = 1 Character 5: Root taxon of higher value. A ''value'' is ideological expression. A value is given according to a value system, most often implicitly. Here a value is some combination of the ideas of perfection and complexity. In the case where the root starts a value gradation, the other entities are then viewed as ''degenerate'', or less perfect than the original entity. Is the taxon at the root seen as more complex and/or more perfect than the others on the tree? Buffon adheres to this idea, whereas Darwin or Lamarck disagrees with it. No = 0; Yes = 1 Character 6: Root taxon of lesser value. In the case where the root starts a value gradation, the other entities are then viewed as more progressive and/or complex than the original entity. Is the taxon at the root seen as less complex and/or less perfect than the others on the tree? Lamarck thinks so whereas Darwin does not. No = 0; Yes = 1 Character 7: No value. There is absolutely no gradation in terms of value between the root and the rest of the tree. Darwin adheres to this idea, whereas Chambers disagrees with it. Yes = 0; No = 1 Character 8: Genealogical kinship links. The link between the two extremities of the line is conveyed by a genealogical process. There is an idea of descent that is set into branches. For instance this idea is not accepted by Pallas or Augier, but it is by Darwin or Haeckel.
No = 0; Yes = 1 Character 9: Purely logical links. A ''logical link'' is the use of branches in order to represent only a hierarchy. Hierarchies in the form of a tree are used to express the sharing of features, identification keys, etc. Hennig or Agassiz use such links, whereas Buffon or Darwin do not. Yes = 0; No = 1 Character 10: Value gradation within a branch. Are branches tools to express a value system? In other words, do branches express differences in values among entities? If yes, there are differences between the values of the entities at the beginning and at the end of the branch. Note that trees that depict an overall gradation in value at the scale of the whole tree (character 51) do not necessarily include such a gradation within a single branch: character 10 is not redundant with character 51. As an example, Buffon considers that there is such a gradation whereas Darwin does not see any gradation within branches. No = 0; Yes = 1 Character 11: Nodes as species, races, varieties. Do internal nodes refer to populations or individuals that are able to interbreed? This is the case with Hennig but not with Haeckel, for example. No = 0; Yes = 1 Character 12: Nodes as groups of higher rank. Nodes are groups above the mere species level. It can be genera, or higherranked groups. If the rank isn't mentioned, a ''group'' is essentially composed of several species. Such groups at nodes give birth to other groups without including them (they are not groups in a cladistic sense). Lamarck or Hitchcock see such groups at nodes, whereas Hennig or Darwin do not. Yes = 0; No = 1 Character 13: Nodes as concepts. Nodes are ''concepts'', either a list of characters or a property. A ''concept'' may be a hypothetical common ancestor, a reconstructed entity, character states, or a property used in a determination key. Note that the informative content of a node in a phenogram could appear difficult to interpret at the first glance. Clearly the node of a phenogram is made of global similarity, and as such it is a concept. This idea is not accepted by Haeckel, but it is by Sokal and Sneath.
No = 0; Yes = 1 Character 14: When the node corresponds to an ancestor, is it actually found or not?. Has the ''ancestor'' been found? Is it a discovered fossil? Gaudry thinks so whereas Darwin does not. No = 0; Yes = 1 Character 15: Group at the leaves. A group at the leaves has an upper rank than the mere species. If the rank isn't specified, a group is basically composed of several species. Darwin considers that species are at the leaves whereas Buffon sees groups on leaves. Groups = 0; Species = 1 Character 20: Vertical cuts enhance differences between groups, whatever kind they are (1); between kingdoms of life (2). A ''kingdom'' isn't seen as a mere group because it carries a cultural burden that dates back before elaboration of taxonomical rules. As a result, it has nothing to do with phylogeny and there are presumptions of polyphyly concerning kingdoms elaborated until the XIX th century.
No vertical split: 0; Vertical splits between groups = 1; between kingdoms = 2. As an example, there is no vertical split for Darwin, splits between groups in Haeckel's Anthropogenie and between kingdoms for his Monophyletischer Stammbaum der Organismen.
Character 21: Blobs reflecting amounts of beings by generation. The more there are entities into the group, the broader the ''blob'' is. This is the case with Agassiz, for example. Yes = 0; No = 1 Character 23: Ancestor as an ancestral species or as past state of the same group. An ''ancestral species'' carries a concept of mutation, of fundamental difference between a mother and a daughter species. A ''past state'' insists on the continuity of a group or a family. Its name remains the same whereas the family's content has evolved. Buffon sees the ancestor as an ancestral species, whereas Lamarck sees it as the past state of the same group. Ancestral species = 0; Past state of the group = 1 Character 24: Ancestors organized into succession of types in a genealogical way: 0; ancestors seen as sets of plesiomorphies: 1. ''Ancestors'' can bear several interpretations on the tree. They can be concrete individuals organized in a genealogical way that will set what are plesiomorphies (they express primitive steps or states). Alternatively, plesiomorphies refer to an hypothetical ancestor (which is expressed by them.) Mayr considers that ancestors are organized into successions of types in a genealogical way whereas Hennig considers ancestors as sets of plesiomorphies.
Character 25: Primitiveness of lesser value. Do primitiveness, ancestral states or plesiomorphies include an idea of lesser value and/or imperfect state of adaptation? As an example, Mayr thinks that primitiveness do so whereas Hennig does not think that plesiomorphies do so. Yes = 0, No = 1 Character 45: Tree's graph has an epistemological status (i.e. classifying concrete organisms, 0); Theoretical (i.e. model, 1). Our trees can be either epistemological or theoretical. ''Epistemological'' trees are classifying concrete things: they depicts a hierarchy in shared attributes among known concrete entities (a dog, a cat, a mouse…), interpreted through a given model. Those trees authors, such as Mayr in his ''Methods and Principles of Systematic Zoology'', want to represent a pattern of life much more than to explain the process of its diversification. On the opposite, a ''theoretical'' tree will not deal with concrete objects but with abstractions (A, B, C…) and aim at illustrating or supporting a theory about processes of diversification. It represents a model or the theoretical background itself: it makes conjectures about how should patterns be organized according to the known processes. This is, in particular, what Hennig does. Epistemological = 0; Theoretical = 1 Character 46: Tree's graph has both status, one of them being much heavier. Finally, some authors aim to be simultaneously theoretical and epistemological. These authors will be coded 1. The most notable of the two components is coded in character 45. This is the case of Lamarck, who presents a theoretical and epistemological tree. Because his figure is more theoretical (the theory of increasing complexity) than epistemo-logical (an idea of the sequence of concrete groups through generations), it is coded 1 for character 45 and 1 for character 46. No = 0; Yes = 1 Character 47: The tree intends to illustrate the natural order. The tree illustrates a fundamentally ordered nature for Darwin, whereas it can't illustrate this order for Sokal & Sneath. For instance, for Darwin Nature is intrinsically ordered and we should have access to this order; for Sokal and Sneath Nature is intrinsically ordered however we do not have access to this order; and for Linné Nature is intrinsically ordered however this order has a supernatural origin and we have access to it. No = 0; Yes, Nature is fundamentally ordered = 1.
Character 48: explicit tree. Is the tree explicit, i.e. drew or described, or is it merely evoked through ''reading between lines''? The tree is implicit for Goethe, whereas it is explicit for others, for example, clearly described by Buffon or drew by Darwin.
Yes, drew or written = 0; No, implicit = 1 Character 49: the tree is genealogical. As an example, the tree is genealogical for Darwin, but it is not for Sokal  Character 69: Groups are really in Nature. If groups are not in Nature, they are openly considered as virtual. Note that considering groups as really in Nature or not is not necessarily linked to a position concerning the character 47, i.e. if there is a fundamental natural order or not. For instance, for Darwin groups are virtual but Nature is fundamentally ordered by genealogy, while for Buffon groups are virtual and Nature is disordered ( Table 2). In parallel, groups are really in a perfectly ordered Nature for Linnaeus (a consequence of his creationism, fixism and essentialism). Finally, groups can really be in Nature but disordered by several exceptions, as for É tienne Geoffroy Saint-Hilaire (Table 2). According to Geoffroy Saint-Hilaire in his ''Principes de philosophie zoologique'', Nature is fundamentally disordered: ''La nature ne se laisse imposer aucune règle arbitraire'' (p. 8) ''Nature refuses to be imposed of any arbitrary rule'' But most groups are really in Nature: ''Chaque classe, non comprise celle des reptiles qui est artificiellement formée, voit pour elle revenir un nombre donné de matériaux, neuf, huit et sept: si cela n'est pas toujours à l'égard de quelques familles, l'exception vient confirmer la règle'' (p. 175) ''Each class, excluding that of the reptiles that is artificially formed, sees the presence of a given number of materials, nine, eight and seven, if this is not always towards some families, the exception confirms the rule''.
Some species can exceptionally belong to several groups at the same time, such as Monotremes (''Cours de l'histoire naturelle des mammifères'', 4 e leçon, p. 11): ''[Les mammifères] enfantent leurs petits vivans; les oiseaux pondent des oeufs. Nous trouvons dans ce fait les moyens d'établir une ligne de démarcation bien tranchée entre les deux classes d'animaux à coeur bi-loculaire; toutefois quand nous parlerons des monotrêmes et des marsupiaux, peut-être serons nous forcés de reconnaître que cette distinction n'est point établie sur des caractères aussi nets et aussi précis'' '' [Mammals] give birth to their young alive, the birds lay eggs. We find in this fact the means to establish a strict line of demarcation between the two classes of animals at heart bi-celled; but when we speak of Monotremes and marsupials, perhaps will we have to recognize that this distinction is not based on so clear and accurate characters''.
Groups are virtual = 0; Groups represent a non-arbitrary order = 1 Character 70: Groups are not used a priori but created with a classificatory purpose and justified by properties. This is especially what Buffon does when grouping together the horse, the donkey and the zebra: the group is supported by properties (the whole of their similarities). Yes = 0; No = 1 Character 71: Groups aimed at assigning a specimen. Groups are given a-priori and imply some properties. The purpose is to assign specimens to some of them according to the properties found. Typically, this is what Lamarck does within the framework of his theory of evolution. No = 0; Yes = 1 Character 72: Groups made according to genealogical links joining entities. In an evolutionary consideration, there are genealogical links between entities. Do groups refer to this genealogy? It is the case for Darwin, for whom ''All true classification is genealogical''. No = 0; Yes = 1.
Character 73: Mode of ranking (how ranks are made). Ranking can be performed according to global similarity or to kinship links. This is for instance one of the oppositions between Linnaeus and Buffon: according to the first one, ranks are made according to global similarity; whereas, for Buffon, ranks should be made according to genealogical links. Ranking made according to global similarity = 0; To hierarchy from kinship links = 1.
Character 74: Geometry of classification. A branching graph must carry information on its terminal/lateral branches. If there is no such information, i.e. if there is no difference between Table 2. Distribution of some major authors according to species realism and taxonomic groups realism. leaves and the basement of branches, such as Romer's tree in his ''Major steps in vertebrate evolution'', then the content of the trunk becomes mono-dimensional, and the scheme becomes assimilated to a ladder (scala) and used as such for classification. Classification under the form of a ladder (scala) of beings = 0; Made from a tree = 1.
Character 75: Groups made according to shared characters. There are numerous authors creating groups according to shared properties (character 70), however these properties can be diverse. They can be shared characters or shared degree of perfection. For instance, if Hennig elaborates his groups only according to shared characters, Lamarck groups animals according to an idea of perfection degree. Yes = 0; No, groups are made by perfection degree or adaptive level = 1 what differs between what they contain? Ranks can be assigned to groups in an agglomerative procedure (0), according to shared characters. Ranks can also be assigned according to a divisive procedure (1). This is for instance what is done when classifiers confuse identification keys and phylogenies. They insist more heavily on what distinguishes groups, degrees of divergence between entities to classify (taxa). In the agglomerative approach there will be many nested ranks (like in cladistics), while in the divisive approach the trend will be to multiply groups of equal rank (like in phenetics). For instance, the divisive logic by which the class of birds is justified by Mayr explains why birds and reptiles have both the rank of a class. Ranks express a sharing of characters by taxa = 0; A degree of divergence between taxa = 1

Analysis
Standard parsimony approach was conducted using PAUP* 4.0b10 [12]. Characters were treated as unordered and unweighted in the search of most parsimonious trees. Heuristic searches were performed with 1000 random addition sequences and TBR branch swapping. The results are shown under a 50%-majorityrule consensus tree. Characters are optimized on that tree using the ACCTRAN option, favoring reversions over convergences. Trees are rooted on Linnaeus (1758) and Adam Zaluziansky (1592) because the first elaborated classifications without trees and the second created trees without neither classificatory nor explanatory purposes.

Results
The matrix contains 41 taxa and 91 characters, all informative for parsimony ( Table 3).
The parsimony analysis provides 279 trees of 378 steps, with a C.I. of 0.24 and a R.I. of 0.61 (50% majority-rule consensus tree shown Fig. 2). In Fig. 2 it is possible to name some previously recognized groups.
Node 78: Initial tree users Initial tree users are non-evolutionist authors that are the first ones to use trees to depict life into the realm of Natural History.
The branches of their trees do not refer to purely logical links (char.9) but to gradations in value (char.10). This gradation is also carried by the hierarchical axis of the tree (char.39).
The tree graph is as theoretical as epistemological (char.46) and expresses a gradation in terms of values among beings (char.51).
A special place is assigned to a group to which mankind belongs (char.68). This last character has a C.I. of 0.5.
In terms of taxonomy, groups represent a non-arbitrary order (char.69) and are elaborated following a perfection degree or an increasing degree of complexity achieved through harmony between structures and their role in the environment (char.75). They are not perfectly circumscribed (char.78). Then, a reality is given not to all ranking categories, but at least for some of them (char.82). This character has a C.I. of 1 and strictly occurs in this group.

Node 79: tree makers
Tree-makers are authors that use trees as tools for the classification of life.
The hierarchical axis of their trees is oriented vertically from the bottom to the top (char.28) or horizontally from a side to the other (char.30). None of the axes carries properties. (char.37). There are no more well-marked discontinuities (char.42).
To elaborate the tree, the authors consider common methods to study plants and animals (char.63). There is generally one tree in each work, and even if a kinship link between animals and plants is asserted, it is not translated into the use of similar methodologies for the study of the two (char.66).
Groups are no more independent but embedded into each other (char.76). Then, reality is given to phylogenetic categories (char.81).

Node 72: evolutionists
Evolutionist authors consider not only a mere localized transformism, but a phenomenon of evolution in whole life, whatever its mechanisms are.
On the root of their trees is set an extinct object (char.4). The hierarchical axis does no more bear an idea of diversification (char.36), but a notion of time appears on it (char.38). Horizontally, discontinuities are well-marked (char.41).
With the idea of evolution comes new interpretations of fossils. Fossils are included into the tree graph (char.55). Trees take into consideration the extinctions of species (char.57). The notion of time is held into the graph (char.60). This character has a C.I. of 0.5.
Classificatory ranks express a sharing of characters by taxa, and no more a degree of divergence between them (char.79).
Finally, authors do not see an inheritance of acquired characters (char.91).

Node 63: cladists
Cladists define themselves through the use of formally coded characters and formalized procedures to find phylogenies and the rejection of grades. The main principles have been defined in Hennig's Phylogenetic Systematics (1966).
For Cladists, the entity carried by the root is neither a concrete species nor ancestral group (char.1) but initial states of characters (char.2). The cladogram's lines do not express genealogical kinship links (char.8) but purely logical links (char.9).
Classificatory ranks express a sharing of characters between taxa (char. 79).
Finally, there is no inheritance of acquired characters (char. 91).

Node 68: pheneticists
Created in 1963 by Sokal and Sneath, the phenetic school is mainly characterized by a renunciation to find the phylogeny of life. A new, mathematically based methodology is elaborated to use trees to represent degrees in global similarity. If, in node 69 (see below), including pheneticists, the classification is elaborated by global similarity (char.86), there is no redundancy with this character because of the separation made by some authors of this last group between classification and elaboration of the tree. Pheneticists group those two actions in a single one, the computation of the tree. And it is the methodology of that computation that is based on global similarity.
The entity carried on the root of the tree graph is a general states of characters (char.2) in the sense that the tree is rooted by an outgroup or on the most distant OTU to any other. The Phenogram's lines do not express genealogical kinship links (char.8) but purely logical links (char.9). The internal nodes express concepts (char.13) and no fossil is set on (char.14). Then, the hierarchical axis of the tree does not express time (char.38) (but degrees of global similarity).
With the renunciation to discover the phylogeny, the tree does not intend to illustrate the order of nature (char.47) and is not genealogical (char.49).
Phenetician authors use commons methods of study for separate trees (char.66). There is no special position assigned to mankind (char.67).
The groups elaborated are openly made as virtual (char.69) and aim at assigning a specimen (char.71).
Finally, there is a use of parsimony for phenetics (char.83). As an example, Sokal writes in his article: ''A computer program developed by Camin and the author constructs cladograms with the fewest number of evolutionary steps'' (p. 10).

New groups
Along with previously recognized groups of tree-thinkers, it is possible to point out in Fig. 2 some groups to which names can be given.
Node 44: ''buffonians''. The two first identified ''evolutionist'' trees have been elaborated during the XVIII th century. The first one has been written by Buffon and the other by his disciple, Duchesne. The ''buffonians'' school is a novel one. It is epistemologically characterized by a theory of transformism by ''degeneration''.
Buffon considers two kinds of change along bloodlines, both used to create ''monophyletic'' groups. The first one is due to a reversible differentiation and the second one is the consequence of the phenomenon of degeneration. Reversible modifications are the consequence of changes in climate or in living conditions. They can be superimposed with one another, as for dogs, and they bring their current varieties. But when a dog returns to its ''natural state'', he returns then to his primary characteristics. This type of change is represented by linking the initial state of a dog with its different biogeographical modifications.
''The Great Dane, the Mastiff and the Greyhound, although different at the first glance, are, however, the same dog: The Great Dane is no more than a Mastiff [with a hair] thicker, more enriched; the Mastiff a Greyhound slenderer, more tapering, and both neater; and there is no more difference between a Great Dane dog, a Mastiff and a a Greyhound, than between a Dutchman, a Frenchman and an Italian. Supposing therefore that the Mastiff is originated or rather natural to France, he will have produced the Great Dane in a colder climate, and the Greyhound in a warmer climate: and this is also verified by facts, as Great Danes comes us from the north, and Greyhounds come from Constantinople and the Levant'' (Histoire Naturelle, Générale et Particulière, Tome 5, p. 205) The phenomenon of degeneration, mutationist and nonreversible, is itself associated with a high requirement of monophyly. The successive degenerations of a species will be represented on the same tree than the parent one. This is what is described in Buffon's famous tree of horses, donkeys and zebras: ''From this point of view, the horse, the zebra and the donkey belong all three to the same family, if the horse is the strain/root or the main trunk, the zebra and the donkey will be the collateral stems/branches: because the number of their similarities (/the similarities between them) is infinitely greater than their differences, we can consider them as making only one genera, from which the main characters are clearly defined and common to all three: they are the only ones really solipeds, that means, who have the horn of their feet in a single piece without any appearance of fingers or nails; and although three species are distinct, they are however not absolute nor clearly separated, since the donkey product with the mare, the horse with the jenny, and it is probable that if one overcomes to domesticate zebra, and ease its wild and recalcitrant nature, it would also occur with the horse and the donkey, as they produce together''.(Histoire Naturelle, Générale et Particulière, Tome 14, pp. 335-336).
This consideration of monophyly is not isolated: there are numerous other examples in this chapter: ''Those animals who have antlers, although they are ruminants and shaped inside such as those who bear horns, seem to make a genera, a separated family, in which the moose is the main stem and the reindeer, the deer, the cheetal, the fallow deer and the roe are the minor and collateral branches; because there are only those six species of animals that have the head armed with a branching antler which falls and is renewed every year; and independently of this generic and common character, they resemble each other a lot in the conformation and natural habits: so we would rather obtain hybrids of the deer or of the fallow deer mixed with the reindeer and the cheetal than hybrids of the deer and the cow'' (p. 349).
The monophyly exhibited in Buffon's groups is more than a mere intuition. The author sees the ability of interbreeding as a Table 3. Cont.  6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9  Mayr could read Aristotle [10]. Transmission of ideas is not constrained by a physical process that imposes its temporality. If two authors are sister-groups, this could perfectly be because an author has learnt directly from his master, or one picked up the idea from one of his contemporary colleague, or because one of both has read writings of the other dating back to centuries. This makes no difference: the fact is that one has read someone else's ideas and adopted them. The distinction between adopting someone else's idea (synapomorphy) and having the same idea twice by convergence (homoplasy) is maintained here. The fact that networks are not useful at the present step of the study does not mean that the cladogram is not useful. The cladogram is used here to maximize consistency among sharings of ideas about trees, whatever the ways employed in ideas circulation. It functions as a test for common origin (it also has potentially the power of revealing convergences), and provides test for categories.
If the transmission of ideas was really constrained through times, with a generation of authors linearly transmitting their ideas to their intellectual offspring, we would have obtained a comb with the earliest author as the most basal branch and the branches at the top being the most recent authors. It cannot be the reverse because an author can read his predecessors but cannot read future authors. The situation here is obviously more complicated: readings have been anachronistic in the sense that a given author could read any author of the past, whatever its ancientness.