Some authors consider that any method of classification should be adapted to the group under scrutiny, and should be reconsidered if a different group is studied.

This is for example the case of Lamarck's tree, which clearly distinguishes methods for plants and methods for animals.

Theme: aim of the tree

Character No. 123: Is the tree epistemological?

Yes: 0;

No: 1;

A tree is called "epistemological" when it offers a classification of real beings, when it exhibits relationships among concrete living things, given a classificatory theory. It is the outcome of a real research investigation.

Haeckel's, Garrod's, Lankester's, Gaudry's or Lamarck's trees are epistemological ones.

Character No. 124: Is the tree theoretical?

Yes: 0;

No: 1;

A tree is called "theoretical" when it represents a theory of relationships and/or classification rather than relationships among concrete organisms.

Darwin's or Hennig's trees are examples of strictly theoretical trees. Names at the tip at the branches are letters. Lamarck's one is also a theoretical tree: it is both theoretical and epistemological, in that it offers both a model of classification of animals and an effective classification of them.

Character 125: Does the tree have a practical purpose?

No: 0;

Yes: 1;

The tree has a “practical” purpose when it aims at helping the reader in a specific task, such as identifying a specimen. Thus, determination keys, Klein’s or Gessner’s trees have such a practical purpose.

Character 126: Does the tree have a didactic purpose?

No: 0;

Yes: 1;

A tree has a "didactic" purpose when it aims at synthesizing knowledge. Haeckel's, Teilhard de Chardin's or Gregory's trees have such a didactic purpose. However, Darwin's or Lamarck's trees, published as strict scientific works, do not have such a purpose.

Character 127: Does the tree have an aesthetic purpose?

No: 0;

Yes: 1;

A tree has an "aesthetic" purpose when its design is openly intended to be aesthetic, pleasant to read. Such are the trees drawn as "real" trees (Haeckel's, Gruenberg's or Cuénot's ones), but also the trees drawn with the *OneZoom* software.

A tree can have its leaves, its trunk or its branches designed aesthetically without having on itself an aesthetic vocation. This is for example the case of the leaves of the tree made by Gregory at the p.992 of his *Evolution Emerging*, or the trunk of Trémaux's tree.

Theme: What does the tree express?

Character No. 128: The tree topology is reconstructing the tree of life

No: 0;

Yes: 1;

Topology is here understood in its sense used in Systematics: the internal organization of branches, nodes and leaves. Some authors reconstruct the topology of their trees and then consider that this topology reflects a historical phenomenon. The theoretical « tree of life » is
reconstructed by the topology. Haeckel or Hennig are reconstructing this way the « tree of life » as an underlying historical phenomenon. Other authors like Sokal & Sneath consider that there is no « tree of life » to be reconstructed by their topology.

Character 129: The tree topology is created as a result of an investigation

Yes: 0;

No: 1;

Some authors can draw trees in which nodes are considered as the classifier's creation.

Sometimes these nodes can show neither ancestors nor genealogy. This is for example the case of phenetic trees made by Sokal & Sneath or Fitch. Other authors will be aware that the nodes of their trees are a creation resulting from their investigation, study and calculations, but will later interpret this topology as a genealogical hypothesis probably reflecting the « tree of life ». These authors are, for example, Hennig and Nelson. Indeed, onto a cladogram, the node is a reconstruction of character states, which can be given afterwards the status of an ancestor. The tree drawn is the result of human investigation.

The topology of the tree can be or reconstituted or created, or both:

Both: the tree is created by the investigator, reconstructing the tree of life: Hennig, Nelson;

Created, not reconstituted (the tree is created by the investigator, not reconstructing the tree of life): Sokal & Sneath, Fitch;

Not created, reconstituted (the tree is the direct reconstruction of the tree of life): Haeckel.

If the topology is considered as created as the result of an investigation, but probably recon-
structing the « tree of life », we are in the cladistic method. If it is only created as the result of
an investigation, without reconstructing a « tree of life », we are for example in Sokal &
Sneath's way of thinking. If the topology of the « tree of life » is directly accessible, then the
reconstruction is reified. This is particularly the case of Haeckel's trees.

Character No. 130: The tree must follow genealogy

No: 0;

Yes: 1;

Trees can follow the genealogy of the species. This is for example the case for Lamarck's, Darwin's and Haeckel's trees. On the opposite, Klein's, Linnaeus', Agassiz's or Augier's trees are not genealogical ones : their authors do not think in terms of evolution. Some trees do not to follow genealogy while their authors accept the idea of evolution. This is the case for trees developed following a phenetic method, suth as those of Sokal & Sneath.

Character 131: The tree must follow overall similarity

Yes: 0;

No: 1;

Trees can sometimes be non-genealogical ones, like those of Wallace, Augier or Sokal &
Sneath. Others may be genealogical but with no idea of overall similarity, such as Darwin's or
Hennig's ones. Some other trees follow both genealogy and overall similarity, such as Haeckel's
or Romer's ones. Finally, some trees will follow neither genealogy, nor overall physical similar-
ity: Gessner's, Klein's or Brisson's "keys". Combinations of considerations about genealogy
and overall similarity among authors can be listed as follows:

Trees reflect overall similarity and genealogy: Haeckel, Romer;

Trees reflect genealogy but not overall similarity: Darwin, Hennig;

Trees reflect overall similarity but not genealogy: Augier, Sokal & Sneath;

Trees reflect neither genealogy nor overall similarity: Klein, Brisson.

Theme: Trees and time

Character 132: How is time considered in the tree?

No time: 0;

The tree is temporal, but not genealogical: 1;
The tree is genealogical: 2;

Some trees do not take time into consideration. This can be explained by an absence of consideration of evolution as a phenomenon: so are, for example, Augier's or Gessner's trees. But this phenomenon can also be found in clearly evolutionist authors' trees: phenetician ones, like Sokal & Sneath. Here, the tree does not bear any notion of time because its authors are aware that the genealogy of the species can not be found with their method. Other trees are only temporal (coded 1): Agassiz's one, for example. Those trees are based on the fossil record and see a succession of species over time, but without any idea of evolution. Agassiz indeed sees a succession of creations and extinctions of species due to supernatural causes. Finally, most of our trees take into consideration the genealogy of species: Darwin's, Lamarck's or Haeckel's ones, for example.

Character 133: Can fossils be classified?

No: 0;

Yes: 1;

Some authors cannot classify fossils on their trees. This may be because they do not believe in the possibility of disappearance of species, such as, for example, Lamarck. This can also be explained by the fact that the method used is not compatible with fossil data. This is notably the case of trees derived from molecular data only.

Theme: Characters and their states

Character 134: States of characters used

Arbitrary choice: 0;

All of them: 1;

Only derived ones: 2;

Some authors will use discrete characters in order to justify their groupings. Many authors will base them on several arbitrary character states. This is particularly what do authors like Gessner or Klein. Others will instead use all character states to establish their classifications (being either primitive or derived). This justifies some groups such as "reptiles" (an amnios but neither hair nor feathers) or "fishes" (vertebrae, but no four legs). This is for example what Haeckel and Romer do. Finally, some authors, such as Hennig will classify beings only on the basis of derived character states: what is original and unique to several species will justify their grouping. This character is not redundant with the character #93: indeed, an "incomplete" group set on a tree can be based on the sharing of derived characters. Such are for example, the traditional groups of "reptiles" (the amnios appears at the root of reptiles and it is a derived feature in the context of vertebrates) or "fishes" (the cranium appears at the root of fishes and it is a derived feature in the context of deuterostomians).

Character 135: Characters used

Arbitrary choice: 0;

Several sources: 1;

Only one given kind of characters: 2;

A group is justified on the basis of sharings. These can be chosen arbitrarily, and their kind (either the shape of seeds, number of petals, etc.) possibly change depending on the group studied: such are, for example Gessner's, Klein's and Linnaeus' ones. Other authors will classify species according to multiple and heterogeneous information sources: living environment, alignment, organs. Such are, for example, Romer's and Haeckel's classifications. Other authors will finally take into account only some character type. In cladistics, for example, species are only classified on the basis of what they have, and not depending on where they live or what they do. Such authors are, for example, include Sokal & Sneath or Hennig.

Character 136: Use of an outgroup?

No: 0;
Yes: 1;

An outgroup is a set of entities thought to be close to the studied group, but outside it, not belonging to it. This outgroup is used to determine what is proper to the group under study, or proper to a part of it (then called “derived” or « apomorphic » character states) and what is not (then called « primitive » or « plesiomorphic » character states). In other words, it is made to identify what is new among the set of species to classify, and what is not. Although it is commonly used today (with authors like Nelson or Sober), the use of an outgroup is not so recent: Garrod also used it for his classification of parrots. This character is not redundant with the character #134 because of the classificatory system proposed by Buffon or Darwin. Indeed, if it seems impossible to identify derived states of characters without using an outgroup, this has not always been the case. Some authors, like Buffon, or Darwin, do not use an outgroup to do so.

Theme: tree and algorithmics

Character 137: Criterion for the choice of the tree: maximization of sharings

No: 0;

Yes: 1;

The tree that is chosen maximizes consistency of sharings across all the characters of the matrix. The maximization of sharings among objects of a classification aims at minimizing the assumptions of independent appearance of characters—that is to say, finding the shortest possible tree. This is now formalized as the "parsimony principle" and the shortest tree of all is found with the help of computers and algorithms: this is for example what do authors such as Nelson & Platnick or Sober. It is noticeable that several authors have, long before the development of the computers, tried to find by themselves the shortest tree of all. Tillyard, Lankester and Garrod are those authors. However, this is not the case for trees developed using phenetic methods: such trees do not take into consideration the sharing of explicit characters.

Character 138: Criteria for the choice of the tree based on overall similarity

No: 0;

Yes: 1;

Algorithms may aim at selecting the tree that maximizes or minimizes a metric dealing with numerized overall similarity (for instance in phenetics, the choice of a tree that best reflects the pairwise distances of the initial matrix using a least-square method). As a result, the most globally similar are the species classified, the closer they are in the tree. Saitou or Sokal & Sneath use such methods. Note that this character is not duplicating character #131. Overall similarity can be considered for the elaboration of the tree, but without algorithms nor explicit criterion for retaining one of the possible trees (like in Augier, Romer or Haeckel, for instance; especially in Haeckel there is no explicit choice among possible trees).

Character 139: Criteria for the choice of the tree: probabilistic approaches

Yes: 0;

No: 1;

The optimization of sharings according to the likelihood method consists in selecting, among all trees, the tree that maximizes the likelihood of the data at hand according to the tree and the model. The model is about probabilities of molecular evolution. Another probabilistic approach is calculating the posterior probability of a branch according to the data and the evolutionary model at hand. This is called the Bayesian approach. Hedges and Kumar use, as an example, probabilistic approaches to develop their Timetree of life. Note that this method retains characters and can infer a node reconstruction, unlike, for example distance methods.

Character 140: Use of algorithms

No: 0;

Yes: 1;
An algorithm is a sequence of operations. They may be used to construct trees. Sober, Sokal & Sneath or Nelson especially use algorithms for their trees.

Character 141: Characters formalization

No: 0;

Yes: 1;

Formalizing characters means precisely describing their states for each studied object and coding those states into a character matrix. A character matrix and an alignment of DNA sequences are two forms of formalization of characters, but other ones exist: tables, lists, etc. Garrod, Sokal & Sneath or Hennig formalize the characters of the objects they classify. Haeckel, however, does not do this.

**Supporting information**

**S1 File. Matrix-copy-raw-data.** Matrix in Word format.
(DOCX)

**S2 File. Matrice-Fisler-Lecointre.nex.** Matrix in Nexus format.
(NEX)

**S3 File. Matrix of 235 trees and 141 characters.** “?” means “unknown”; “-” means “irrelevant”. See Annex I for description of trees that are coded and Annex II for description of each of the 141 characters.
(PNG)

**Acknowledgments**

The present project has been supported by Pr. Evelyne Heyer and Pr. Philippe Grandcolas, directors of the units UMR 7206 and UMR 7205 respectively, for a successful application to the « Laboratoire d'Excellence BCDiv » led by Jean-Denis Vigne. We also thank support from the ARN project « Anthropos » led by Delphine Kolesnik, Ecole Normale Supérieure de Lyon. We warmly thank Giulio Barsanti, Pascal Charbonnat, Claude Dupuis, Pascal Duris, Sarah Franceschelli, Jean Gayon, Alice Michel-Salzat, Michel Morange, Armand de Ricqlès, Stéphane Schmitt, René Zaragüeta-y-Bagils for helpful comments and discussions. We thank Eglantine Lemense for help on the manuscript. We thank the *Société Française de Systématique* by which this work has been awarded « Prix Jacques Lebbe ».

**Author Contributions**

**Conceptualization:** Guillaume Lecointre.

**Data curation:** Marie Fisler, Cédric Crémière, Guillaume Lecointre.

**Formal analysis:** Marie Fisler, Pierre Darlu, Guillaume Lecointre.

**Funding acquisition:** Cédric Crémière, Guillaume Lecointre.

**Investigation:** Marie Fisler.

**Methodology:** Marie Fisler, Pierre Darlu, Guillaume Lecointre.

**Project administration:** Guillaume Lecointre.

**Supervision:** Cédric Crémière, Guillaume Lecointre.

**Validation:** Marie Fisler, Cédric Crémière, Pierre Darlu.

**Writing – original draft:** Marie Fisler, Pierre Darlu, Guillaume Lecointre.
**Writing – review & editing:** Cédric Crémière, Guillaume Lecointre.

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