Adrien Barton
email: adrien.barton@irit.fr

Cédric Tarbouriech

Laure Vieu

Jean-François Ethier
email: ethierj@gmail.com

A Mereological System for Informational Templates

Keywords: Mereology, Information content entity, Informational template

We propose an axiomatic ontological framework for informational templates based on former works on slot-mereology. Templates and their parts can be filled by information content entities, but can exist even if unfilled. Thus, we represent templates as slots that can themselves have slots, where the "slot of" relation between slots can be interpreted as a parthood relation. Some slots of a slot are mandatory and need to be filled for the parent slot to be filled, whereas others are optional and do not have this restriction. The structure of a filler is also described by slots of a different nature. We discuss how parthood between slots can be connected with parthood between their fillers.

Introduction

The ontology of informational entities has been investigated from a variety of perspectives and general ontological frameworks [START_REF] Sanfilippo | Ontologies for information entities: State of the art and open challenges[END_REF]. The kinds of informational entities that have been typically scrutinized are what we might call "substantial" informational entities, such as words, sentences or figures. For example, the Informational Artifact Ontology (IAO [START_REF] Smith | Aboutness: Towards foundations for the information artifact ontology[END_REF]) focuses explicitly on "information content entities". There is however another kind of informational entities that deserves a closer analysis, namely templates. Templates are typically filled by information content entities. But a template can exist even if unfilled: think for example of a Latex template, which is an entity in its own right.

Templates are of prime importance to characterize documents, especially documents that have a normative dimension. Consider a diploma. It typically encompasses a first name and a last name. However, we would want to be able to represent the fact that such a diploma could encompass a middle name. In open world systems, such facts are typically represented by closure axioms: for example, we could formally state that a diploma has as direct parts only the following: first name, middle name, last name, title of the grade, etc. However, such a formalization assumes that we know exactly all direct parts a diploma can have. By contrast, there might be cases where we know that a diploma must include a first name and a last name, could include a middle name in some cases, but might also include other unknown parts. In such situations, a closure axiom would not be adapted anymore.

An alternative, more expressive way would thus be to characterize a template for diplomas (rather than the diplomas themselves), stating that it has fields for last name and first name that must be filled in any diploma based on this template, and a field for middle names that may be filled or not. In such a representation, we can leave it open whether the template encompasses other unknown fields or not in an open world formalization. Thus, it is desirable to be able to represent not only filled documents but also templates, and the relations between both.

A former work [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF][START_REF] Barton | Clinical Documents and Their Parts[END_REF] proposed a first mereology of informational entities that accounts for the fact that the very same informational entity can be part several times of another informational entity, by filling several of its "slots" -inspired by Bennett's foundational work [START_REF] Bennett | Having a part twice over[END_REF]. For example, the very same word "cat" is part twice of the sentence "A cat is a cat.". This theory left room to templates in the form of unfilled "informational slots" which can themselves own informational slots. Thus, a "full name" slot could have three subslots for respectively a first name, a middle name and a last name. However, in this theory, the slots of a slot are identical to the slots of its filler. This is a strong restriction (cf. [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF], Section 5.1) that implies that informational templates could not keep their slot structure independently on whether they are filled or not. In such a system, as soon as the full name slot is filled by a full name encompassing a first name and a last name but no middle name, it loses its middle name slot. Thus, it does not fit with a common pre-formal notion of templates: a questionnaire would for example keep its unfilled space for middle name (concretizing a middle name slot) even if the spaces for the first name and for the last name (concretizing the first name slot and the last name slot) have been filled.

To account for the fact that a document of a certain type must encompass some fields and can encompass other fields, we can introduce a distinction between slots in a template that are mandatory and others that are optional. For example, a full name slot would have as mandatory slots a first name slot and a last name slot, and as optional slot a middle name slot. It could be filled by a full name filler that would have as slots only a first name slot and a last name slot.

Therefore, we will propose an ontology of slots and fillers where the slot structure of a slot does not need to be identical to the slot structure of its filler, and where a slot can have both optional and mandatory slots. The next section will specify the methods used. A third section will propose an axiomatic representation of templates, independently of their fillers. A fourth section will axiomatize parthood between fillers. A fifth section will propose theoretical and realistic models based on clinical documents. A sixth section will discuss how this system could be extended in various directions. A conclusion will follow.

Methods and first axioms

Methods

In this paper, we will work in transitive closure logic, that is, FOL enriched with the operation of transitive closure TC, where the transitive closure of a predicate X will be written " C X" [START_REF] Jackson | Software Abstractions: logic, language, and analysis[END_REF][START_REF] Van Eijck | Defining (reflexive) transitive closure on finite models[END_REF][START_REF] Claessen | Expressing transitive closure for finite domains in pure first-order logic[END_REF]. We will also assume all free variables are universally quantified when writing axioms and theorems. The variable symbols "s", "t", "u", "v", "w" will be used for slots, "x", "y", "z" for fillers, and "a", "b" for entities that can be either slots or fillers.

Taxonomy and domain/range axioms

All the axioms reflecting the taxonomic structure in Figure 1 will be accepted, that is, if A is a subclass of B, we accept Aa → Ba. We will introduce the following classes (unary predicates), that will be explained below: We consider templates as "unattached slots" or U-slots (IS U ), that are not slots of anything -that is, they do not belong to anything (we leave open here the question of whether all U-slots are templates, as well as whether all documents follow a template, at least an implicit one). Such slots can themselves have slots, which can themselves have slots, etc. This latter kind of slots is called "slot of slots" or S-slots (IS S ). Fillers also can have slots (called "slots of filler", IS F ) and can themselves fill slots (U-slots, S-slots or F-slots).

Informational slot [IS] Slot of filler [IS F ] Slot of slot [IS S ] Unattached slot [IS U ] Informational filler [IF]
We also introduce the relations on those classes as pictured on Table 1.

Fillers and slots

We accept an axiom of disjointness between fillers and slots: Five of the above-mentioned unary and binary predicates are primitive: IS ("is a slot"), S ("slot of"), MS ("mandatory slot of"), OS ("optional slot of") and F ("fills"). All the others will be derived from those five predicates. In particular, the four derived classes in the above taxonomy depicted in Figure 1 can be defined as follows:

-Fillers are entities filling a slot: Note that fillers can only exist in slots, but slots can exist independently of fillers, as argued for in former work [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF]. We want to add two constraints about the owners of S-slots and F-slots. First, S-slots belong only to S-slots or U-slots: (A3) S-slots owner IS S s & Sst → IS S t ∨ IS U t Second, F-slots belong only to fillers: (A4) F-slot owner IS F s & Ssx → IFx We can then deduce that slots are exactly S-slots, F-slots and U-slots:

(T1) Covering of IS ISs ↔ [IS S s ∨ IS F s ∨ IS U s]
Proof: The right-to-left inference is trivial. For the left-to-right inference, suppose that ISs. If there is no a such that Ssa, then IS U s. If there is some a such that Ssa, then a is either a slot or a filler by A2. If a is a filler, then IS F s. If a is a slot, then IS S s. QED We can also show that the three kinds of slots are disjoint: (T2) S-slots, F-slots and U-slots are disjoint

¬(IS S s & IS F s) & ¬(IS S s & IS U s) & ¬(IS F s & IS U s) Proof:
Consider s such that IS F s, thus there is some filler x such that Ssx. By definition D2 of IS U , ¬IS U s. Thus, ¬(IS F s & IS U s). If IS S s, there is some slot t such that Sst. Since IS F s, by A4, t is a filler. Thus t is both a slot and a filler: absurd by A1. Thus ¬(IS S s & IS F s). Consider now s such that IS S s. By definition D2 of IS U , we have ¬IS U s, thus ¬(IS S s & IS U s). QED Thus, S-slots, F-slots and U-slots form a partition of slots. We will now turn in the next part to the analysis of mere slot structures, independently of their fillers.

Templates as slot structures

"Slot of" and its transitive closure

As mentioned above, slots can themselves have slots, as represented by the relation S. Consider for example a template "complete name" that is an unattached slot 'cn0[]', which has as slots 'fn0[]' (for "first name") and 'ln0[]' (for "last name"), and can exist even if it is not filled.

We define the transitive closure of the S relation: C S. (D5) Slot_of transitive closure C S :=def TC(S) We will say that s is a "C-slot" of t when C Sst. As we will see, C S will be interpreted as a relation of proper parthood between slots, and thus we want S to be irreflexive (nothing is a slot of itself). Indeed, we do not want to have cycles by the S relation such as represented on

Mandatory and optional slots

We can now turn to relational properties of slots of slots, namely being mandatory or optional relatively to their owner. First, slots of slots (and only those) are either mandatory or optional relatively to their owners: (A6) Slots of slots are mandatory or optional

(ISt & Sst) ↔ (MSst ∨ OSst)
(in the models graphically represented in this paper, either S or MS/OS relations will be pictured, keeping in mind that if S holds between two slots, then either MS or OS holds, and vice versa; also, C S relations will not be pictured but can easily be inferred from S relations) Second, no slot is both optional and mandatory relatively to the same owner: (A7) Optional and mandatory slots are disjoint ¬(OSst & MSst) Note however that a slot can be optional relatively to a slot, and mandatory relatively to another slot: the mandatory or optional characters of a slot are relational properties. On Figure 2.b, for example, u is a mandatory slot for t, but an optional slot for s. A realist model would consist of t being a slot for a name that must encompass a last name slot (v) and can -but must not -encompass a first name slot (u); and s being a slot for a name that must encompass both a first name slot and a last name slot.

Unwanted properties: Transitivity, Anti-transitivity and Functionality

Contrarily to what was assumed in former work [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF], S is not a strict order relation: it is not transitive. Instead, what corresponds to the transitive "slot_of" relation in this former work is here the transitive closure C S (for reasons that will be discussed in Section 6). Thus, the model pictured on Figure 2.c is intended. Note that in this model, u' is a slot of t and v is a slot of u', but v is not a slot of t (we do not have Svt): however, v is a C-slot of t (that is, C Svt). This means intuitively that the template t does not have v as a direct part, but as an indirect part (we will indeed justify later that C S can be interpreted as a parthood relation).

To take a clinical example inspired by an ontology of drug prescriptions [START_REF] Ethier | An ontological analysis of drug prescriptions[END_REF], t could be a drug prescription template, u' a posology slot (the posology is the part of the drug prescription that explains when and under which condition to take a dose) and v a dose specification slot (where the dose specification states which quantity of which drug to take): the dose specification is not a direct part of the drug prescription template, but only indirectly through the posology slot.

Note that we do not want to impose the functionality of S here, that is, that slots would have only one owner. Indeed, it would exclude slot-overlap as presented on Figure 3.a, which might be acceptable. A realistic model of Figure 3.a would be e.g. having u being a slot for a day number (between 1 and 31, e.g. 24), v a slot for a month (e.g. October), and w a slot for a year (e.g. 1981) (t being a slot for a day in a month without specifying the year, e.g. October 24, t' a slot for a month of a specific year, e.g. October 1981, and s a slot for a specific day of a specific month of a specific year, e.g. October 24 1981). Another example of slot-overlap, this time in the clinical domain, would be a template for a drug prescription of several drugs (suppose here there are only two) made by the same prescriber: such a document is composed by two slots t and t' that should each be filled by the information about the prescriber and the prescription of a single drug, and where t and t' overlap on the prescriber slot v (u being the slot for the prescription of the first drug, and w the slot for the prescription of the second drug).

Supplementation

C

S can be seen as a proper parthood relation on the domain IS U ∨ IS S . It already satisfies axioms of strict partial order: it is irreflexive, asymmetric and transitive. Arguably, for it to be an authentic proper parthood relation, it must also satisfy some supplementation axiom [START_REF] Simons | Parts: A study in ontology[END_REF]. For this, we can define C-slotoverlap C SO as follows: two slots C-slot-overlap if they have a C-slot in common, if one is a C-slot of the other, or if they are identical: (D6) C-slot overlap

C SOst:=def (ISs & ISt) & (s=t ∨ C Sst ∨ C Sts ∨ ∃u ( C Sus & C Sut))
-An axiom of C-slot weak supplementation would be the following: if t is a C-slot of s, there is a Cslot of s that does not C-slot-overlap t: (A8) C-slot weak supplementation

C Sts → ∃u ( C Sus & ¬ C SOut)
Note that we do not want a stronger axiom of slot weak supplementation on S as follows (where SO would be defined like C SO, replacing C S by S): Sts → ∃u (Sus & ¬SOut). Indeed, the model presented above in Figure 3.a is intended, but does not satisfy the slot weak supplementation. As a matter of fact, in this model, Sts holds, but there is no slot a such that Sas and ¬SOta (since the two only slots of s do S-overlap). However, the model does satisfy the C-slot weak supplementation.

Do we also want an axiom of strong supplementation by C S as follows:

¬ C Sst → ∃u ( C Sus & ¬ C SOut)?
The answer is negative, as this would imply extensionality, and thus prohibit models such as the one presented on Figure 2.b. Note that we could even accept a model like on Figure 2.b but where u and v would be mandatory slots of both s and t. Indeed, templates might have the exact same slots but with different additional relations holding between those slots. For example, we might want to accept two templates for complete names 'cn[]1' and 'cn[]2' which would have the same two mandatory slots 'first_name[]' and 'last_name[]', but in different orders (where such order relations would be ternary:

'first_name[]' is before 'last_name[]' in 'cn[]1', and 'last_name[]' is before 'first_name[]' in 'cn[]2').

Fillers

The slot structure of fillers is typically different from the slot structure of slots. Indeed, since a slot of a filler cannot itself have slots (by A3 and T2), on fillers, C S collapses to S. On F-slots, S and C S never apply and C SO collapses to identity. This implies that on fillers, C-slot weak supplementation collapses to the following theorem of "company" (reusing the vocabulary of Varzi [START_REF] Varzi | Mereology[END_REF]): (T4) Company on fillers

IFx & Stx → ∃u (Sux & ¬u=t) Also, on F-slots, C-slot weak supplementation is vacuously true, since its premise never applies (as Fslots do not have slots).

However, a slot of a filler can be filled by another filler that has itself slots: this is how a filler can have a mereological structure spanning several levels, and how the slot structure of a template can be mirrored in a filler of this template (as will be discussed in Section 6). Let us now turn to more substantial statements on fillers.

First axiom

We adapt a first axiom former works [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF][START_REF] Bennett | Having a part twice over[END_REF]: there is at most one filler in a given slot: (A9) Maximum one occupant

Fyt & Fzt → y=z This implies that when we informally say that the "same" template is used for several documents constituted by different fillers, according to this theory, we are actually referring to different U-slots that are similar by being instances of a same class of templates. Indeed, a slot can have at most one filler. On the other hand, a filler can occupy several slots: an entity can "have a part twice over", as Bennett claims.

Definition of parthood

Like in traditional slot mereology [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF][START_REF] Bennett | Having a part twice over[END_REF][START_REF] Tarbouriech | The Counting Problem of Slot Mereology[END_REF][START_REF] Garbacz | Slot Mereology Revised[END_REF][START_REF] Masolo | Graph-Based Approaches to Structural Universals and Complex States of Affairs[END_REF], parthood is linked with filling a slot. But instead of defining parthood or proper parthood as filling a slot of a filler, it is the notion of direct proper parthood that is defined as such:

Parthood as a partial order

Former work [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF] endorsed an axiom (named AX8) that identified the slots of fillers with the slots of the filled slot: Fxt → (Sux ↔ As explained in Section 1, we reject such an axiom, as we want slots to have their own intrinsic slot structure, independently of their fillers. In the former theory, AX8 was used to show slot inheritance (from which could be derived proper parthood asymmetry): Stx & Pxy → Sty. Here, we also reject slot inheritance that created a counting problem (see [START_REF] Tarbouriech | The Counting Problem of Slot Mereology[END_REF] and Section 6.2 of this paper). We must thus adapt the axioms.

Since we defined proper parthood as the transitive closure of direct proper parthood, proper parthood is trivially transitive: (T5) Proper parthood transitivity

PPxy & PPyz → PPxz From this, we derive trivially parthood transitivity: (T6) Parthood transitivity

Pxy & Pyz → Pxz Former works [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF][START_REF] Bennett | Having a part twice over[END_REF] introduced an axiom stating that no filler occupies any of its slot (¬(Stx & Fxt); that is, there is no improper slot) -which translates here as ¬PP D xx (the irreflexivity of direct proper parthood). However, we need here a stronger axiom, namely the irreflexivity of proper parthood:

Filling axioms

Like in [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF], we accept that a slot of a filler is filled.

(A11) Slot of a filler is filled

IFx & Stx → ∃y Fyt We can deduce trivially from this axiom that a slot of a filler is always filled by a proper part of the filler: (T10) Slot of a filler is filled by a proper part

IFx & Stx → ∃y (Fyt & PPyx) For example, the filler 'John Doe' has a slot for the first name 'fnJD[]' filled by 'John'. As in former work [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF], we accept an "ascending" filling axiom: if all slots of a slot that has slots are filled, then this slot is also filled. (A12) A slot with filled slots is filled

ISt & (∃s Sst) & [∀u (Sut → ∃x Fxu)] → ∃y Fyt Note that we need the condition "(∃s Sst)" in A12, otherwise the condition ∀u (Sut → ∃xFxu) would be trivially true for any slot that does not have any slot, and thus such slots would always be filled. This axiom excludes models such as represented on Figure 3.b, where t is not filled, despite all its sub-slots u and v being filled. However, the reciprocal is not true: a filled slot does not need to have all its slots filled. Indeed, a slot can be filled while some of its optional slots are not filled -this is, as a matter of fact, the motivation for introducing optional slots. Moreover, a slot that has all its mandatory slots filled is not always filled. For example, if someone named 'John D. Brown' fills the mandatory slots for the first name and for the last name of a full name slot, but does not fill the optional slot for the middle name -that is, if he writes only 'John Brown', then he has not filled the full name slot.

However, we claim that if a slot is filled, then all its mandatory slots are also filled2 : (A13) Mandatory slots of a filled slot are also filled ∃y Fyt → ∀u (MSut → ∃x Fxu) We also impose that if a slot that has slots is filled, then at least one of its slots is filled. (A14) Some slot of a filled slot with slots is filled (∃t Sts) & Fxs → ∃u,y (Sus & Fyu) (note the importance of the proviso ∃s Sts, as otherwise a slot that has no slot could never be filled)

This excludes models in which a slot that would have only optional slots could be filled without any of its slots being filled, such as pictured on Figure 3.c. For example, in an informal registry of a small classroom, there could be a slot "name" with two optional slots "first name" and "last name" (that is, people could be referred either by their first name or by their last name). However, it is not possible in such a registry that a name would be indicated without indicating either the first name or the last name. A14 ensures that this constraint is satisfied.

It enables also to represent a situation where either a first name and last name (or both) must be specified, and a middle name can (but must not) be specified: this can be represented with the templates having a first mandatory slot that has two optional slots, one for the first name and one for the last name, and a second optional slot for the middle name.

Models and applications

Theoretical models

The theory was implemented in Alloy4 [START_REF] Jackson | Software Abstractions: logic, language, and analysis[END_REF] and the model presented on Figure 4 was found, proving its consistency. In this model, s is a template (U-slot) with two S-slots (one optional and one mandatory), where s is filled by x, which has itself two F-slots filled by y. Thus, y is a proper part of x twice. We will discuss in 6.1 below how models should be further constrained.

Clinical information models

Such a system might be applied to clinical documents. For example, every drug prescription specifies a drug product; however, some drug prescription specify a route of administration, but other do not [START_REF] Ethier | An ontological analysis of drug prescriptions[END_REF]. This would translate by stating that a drug prescription template has a mandatory slot for a drug product specification, and an optional slot for a route of administration specification.

Another example would concern stays at a healthcare institution. A (simplistic) template t for such documents could have three slots: s1 for the unit of care, s2 for the starting date and s3 for the end date. One could have t owning s1 and s2 as mandatory slots and s3 as optional slot, such that s3 would be filled for terminated stays and would be left unfilled for ongoing stays. An alternative template structure would be to introduce two intermediate optional slots of t, t1 for terminated stays and t2 for ongoing stays, such that t1 has as mandatory slots s1, s2 and s3 (as described above) and t2 has as mandatory slots s1' (also for the unit of care) and s2' (also for the starting date). The second template might be more desirable to make sure that no user would leave an end date slot unfilled when entering the information for a terminated stay.

Discussion

This work can be completed in several directions that will be described now.

How a template structure constrains the structure of its filler

This theory would need to be further developed to avoid all unwanted models. In particular, this work would need to be completed with an analysis of how the intrinsic structure of a slot constrains the structure of its filler. For example, if a template has as mandatory slots a first name slot and a last name slot, then any filler of this template must encompass two parts that respectively fill those slots. On the other hand, a filler can have some slot structure that is not reflected in the template. For example, in a document template, there could be a slot for names that has no slot itself; it could be completed by a filler "John Brown" which has itself one F-slot for the first name "John" and one F-slot for the last name "Brown", even if there is no equivalent in the template.

We could for this introduce a relation of mirroring between the slots of a slot and the slots of a filler. For example, if s is a slot filled by f, and s has two mandatory slots, then f would have two mirrored slot that are filled. A slot and its mirror slot would be always filled by the same filler. Thus, the mandatory structure of the slot would be found in its filler. This is one motivation for focusing the formal system on a non-transitive "slot of" relation rather than on its transitive closure (as was done in [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF]), even if both systems are equivalent, as a first investigation showed us that the former would lead to mirroring axioms whose expression is more complex.

Solving the counting problem

In this framework, we can propose a solution to the counting problem different from the one proposed by Tarbouriech et al. [START_REF] Tarbouriech | The Counting Problem of Slot Mereology[END_REF] (this paper actually presented two counting problems, but the first one does not apply here, as it relied on the existence of improper slots, which are excluded here). In the present theory, being a part is not equivalent to filling a slot: rather, being a direct proper part is equivalent to filling a slot. As for being a proper part (simpliciter), it amounts to either filling a slot of a filler, or filling a slot of a filler of a slot of a filler, etc.

Thus, if x is part of y, we cannot count the number of times that x is part of y by counting the number of slots of y that x fills. Instead, we propose the following: the mereological structure of a filler can be represented by a directed acyclic graph (whose edges are constituted by the relations S and F), and to know how many times y is part of x, we count the number of paths that link y to x.

For example, in Figure 5, y is part of x twice as it fills two slots (s and t) of x. y has as parts z and w, each of which is part of x twice, as there are two chains by S and F that link z to x and w to x. In Bennett's mereology, y would also be part of x twice as it fills two slots of x; however, z (respectively w) would be (incorrectly) part of x only once, as the slot u (respectively v) would be inherited only once by x (as explained by Tarbouriech et al. [START_REF] Tarbouriech | The Counting Problem of Slot Mereology[END_REF]). This is another motivation for focusing on a non-transitive "slot of" relation and counting parts by the number of S/F paths rather than by the number of slots filled.

Text Encoding Initiative

The topic at hand can be related with the work on documents and their structures in the digital document traditions, among which the most well-known is the Text-Encoding Initiative standards. The Text-Encoding Initiative offers a variety of slot-like tags such as <speaker> (to tag the mention of the speaker in a theater play), <quote> or <note>. However, the TEI is geared mostly at the analysis of texts, whereas our formalism aims first and foremost at representing templates that might be filled or not. Also, our focus here was on the mereological axiomatization of such a system, something which is, as far as we know, absent from the TEI; and indeed, inside a tag, not all parts of a texts need to be further tagged (whereas all parts of a text need to fill a slot in our system). There is thus a potential to strengthen the foundations of TEI thanks to the theory proposed above.

The semantic of slots

Slot could also enable to add a semantic layer to fillers. For example, the same filler "diabetes" could be used in several clinical documents: a first time as a diagnostic for a given patient, another time as a diagnosis of a family member of the patient, and a third time as a possible diagnosis that should be ruled out by a test. The filler "diabetes" refers to the disease in all the situations, but the slots in which it can be found can add this semantic layer to each occurrence of the term.

Conclusion

We have proposed a mereological system for informational templates. The relation S (slot of) defines a mereology on templates. It also applies on fillers and enables to define direct proper parthood between fillers as filling a slot. This system eschews the limit of a former system [START_REF] Barton | The Mereological Structure of Informational Entities[END_REF] by enabling a template and its filler to have different structures. It also avoids a problem in Bennett's mereology, namely the counting problem [START_REF] Tarbouriech | The Counting Problem of Slot Mereology[END_REF]. Future work is required to introduce axioms constraining the structure of a filler by the structure of the templates it fills, as well as how mereological sums can be defined on slots and fillers. The analysis of the structure of a filler presented here might be contrasted with Koslicki's account of "formal part" [START_REF] Koslicki | The structure of objects[END_REF]. Other properties of the current theory, such as the functionality of S, should be discussed in more details. The existential conditions of templates and their connection with document acts [START_REF] Brochhausen | Towards a formal representation of document acts and resulting legal entities[END_REF] should be investigated, as well as how this theory can account for sentence structure. Finally, some fringe cases of "filling" a template would need to be analyzed: for example, when a user enters a piece of information of the requested kind in a template, but does not know that he did so, did he indeed fill the template? Answering such questions in detail will require articulating an ontology of mental states with the ontology of informational entities.

Figure 1 :

 1 Figure 1: Taxonomy of entities and associated unary predicates

  slots and fillers form a partition of the domain of quantification considered in this paper.

-( D1 )

 D1 Filler definition IFx:=def ∃t Fxt --U-slots are slots belonging to nothing: -(D2) U-slot definition IS U s:=def ISs & ∀a ¬Ssa --S-slots are slots belonging to a slot: -(D3) S-slot definition IS S s:=def ∃t Sst & ISt --F-slots are slots belonging to a filler: -(D4) F-slot definition IS F s:=def ∃x Ssx & IFx

  Figure 2.a. (A5) Slot_of closure irreflexivity ¬ C Stt That is, slots are structured in directed acyclic graphs by the relation S. This implies trivially that S is irreflexive. It also implies that S is asymmetric (two slots s and t cannot own each other): (T3) Slot_of asymmetry Stu → ¬Sut Proof: If Stu and Sut, then C Stt by definition D5: absurd by A5. QED

Figure 2 :

 2 Figure 2: Models (a) Unwanted (b) Intended (c) Intended (2.b and 2.c discussed below)

Figure 3 :

 3 Figure 3: Models (a) Intended (b) Unwanted (c) Unwanted (3.b and 3.c discussed below)

  (D7) Direct proper parthood PP D xy:=def IFy & ∃t (Sty & Fxt) We then define proper parthood as the transitive closure of direct proper parthood: (D8) Proper parthood PP:=def TC(PP D ) We can define regular parthood on fillers as usual, on the basis of proper parthood: (D9) Parthood Pxy:=def PPxy ∨ (IFx & x=y)

  (A10) Proper parthood irreflexivity ¬PPxx Finally, parthood reflexivity is a trivial consequence of the definition of parthood: (T7) Parthood reflexivity IFx → Pxx This implies proper parthood asymmetry: (T8) Proper parthood asymmetry PPxy → ¬PPyx Proof: If PPxy and PPyx, then PPxx by transitivity of PP: absurd by A10. QED From this, we derive parthood anti-symmetry trivially as usual: (T9) Parthood anti-symmetry Pxy & Pyx → x=y Proof: Suppose that Pxy and Pyx. By T8, either ¬PPxy or ¬PPyx. Thus, we have x=y. QED

Figure 4 :

 4 Figure 4: Model of the theory (P and PP relations omitted)

Figure 5 :

 5 Figure 5: Counting parts (only S and F relations pictured)

Table 1

 1 Binary relations

	Name	Predicate	Domain	Range
	slot of	S	IS	IS or IF
	mandatory slot of	MS	IS S	IS S or IS U
	optional slot of	OS	IS S	IS S or IS U
	fills	F	IF	IS
	slot of closure (C-slot of)	C S	IS	IS or IF
	C-slot-overlap	C SO	IS	IS
	direct proper part of	PP D	IF	IF
	proper part of	PP	IF	IF
	part of	P	IF	IF
	We accept the binary relations summarized in Table 1, where R has domain X and range Y is
	translated as: Rab → Xa & Yb.

An alternative formalization would be to introduce a neutral element ∅ such that all slots of a filled slot are filled, but its optional slot can be filled by this neutral element. However, the ontological status of such a neutral element would raise complex issues. For example, we might not want to endorse that optional slots are pre-filled with the neutral element, since we want slots to be able to exist even if unfilled. But then, does it imply that when someone fills a template, she fills each optional slot with a filler (either the neutral element or something else)? Then, how do we account for situations where the author of the filler did not realize the existence of such slots?

Acknowledgments

We thank two anonymous reviewers for their very useful feedback.


Ameline Bardo
email: abardo@mnhn.fr

Raphaël Cornette

Antony Borel

Emmanuelle Pouydebat

Manual function and performance in humans, gorillas and orangutans during the same tool use task

Keywords: grasping, hominids, manipulation, maze task, performance, 4 figures, 3 tables, and 2 supplementary materials

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Manual function and performance in humans, gorillas, and orangutans during the same tool use task

Ameline Bardo, Raphaël Cornette, Antony Borel, Emmanuelle

INTRODUCTION

For decades, the evolution of human manipulative abilities has been of great interest and researchers have developed hypotheses that these abilities coevolved with bipedalism, toolmaking and -use, brain enlargement and laterality, and/or language in humans [START_REF] Wilson | The hand: how its use shapes the brain, language, and human culture[END_REF].

Humans are known for their enhanced dexterity compared to other primates. It has been largely assumed that this dexterity of the human hand is linked to specific morphological features, such as a long, mobile, and powerful thumb, which are considered to be associated with stone toolmaking [START_REF] Napier | Studies of the hands of living primates[END_REF][START_REF] Marzke | Precision grips, hand morphology, and tools[END_REF][START_REF] Susman | Hand function and tool behavior in early hominids[END_REF][START_REF] Tocheri | The evolutionary history of the hominin hand since the last common ancestor of Pan and Homo[END_REF][START_REF] Kivell | Evidence in hand: recent discoveries and the early evolution of human manual manipulation[END_REF]. These morphological features are considered beneficial to our ability to use more forceful precision grips (i.e. between the pads of the thumb and fingers) than the other primates [START_REF] Marzke | Precision grips, hand morphology, and tools[END_REF][START_REF] Marzke | Evolution of the power (''squeeze'') grip and its morphological correlates in hominids[END_REF]. However, other primates, such as great apes [START_REF] Christel | Grasping techniques and hand preferences in hominoidea[END_REF][START_REF] Jones-Engels | Precision grips in young chimpanzees[END_REF][START_REF] Marzke | Chimpanzee and human grips: a new classification with a focus on evolutionary morphology[END_REF][START_REF] Christel | How precisely do bonobos (Pan paniscus) grasp small objects[END_REF][START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF][START_REF] Pouydebat | Biomechanical study of grasping according to the volume of the object: human versus non-human primates[END_REF][START_REF] Pouydebat | Diversity of grip in adults and young humans and chimpanzees (Pan troglodytes)[END_REF], capuchin monkeys [START_REF] Costello | Prehension in Cebus and Saimiri: I. Grip type and hand preference[END_REF][START_REF] Christel | Manual function in Cebus apella. Digital mobility, preshaping, and endurance in repetitive grasping[END_REF][START_REF] Spinozzi | Grasping behavior in tufted capuchin monkeys (Cebus apella): grip types and manual laterality for picking up a small food item[END_REF][START_REF] Pouydebat | Biomechanical study of grasping according to the volume of the object: human versus non-human primates[END_REF], and macaques [START_REF] Christel | Grasping techniques and hand preferences in hominoidea[END_REF][START_REF] Tanaka | Social diffusion of modified louse egg-handling techniques during grooming in free-ranging Japanese macaques[END_REF][START_REF] Macfarlane | Diversity of grip in Macaca mulatta[END_REF][START_REF] Pouydebat | Biomechanical study of grasping according to the volume of the object: human versus non-human primates[END_REF] use a diversity of grasping postures that are comparable to those used by humans, including precision grips. In addition, an orangutan and a bonobo were trained to strike stones to produce flakes during experiment in captivity [START_REF] Wright | Imitative learning of a flaked stone technology-the case of an orangutan[END_REF][START_REF] Schick | Making Silent Stones Speak[END_REF][START_REF] Schick | Continuing investigations into the stone tool-making and tool-using capabilities of a bonobo (Pan paniscus)[END_REF], and even though this was not a natural behavior for them. Regardless, these subjects showed the morphofunctional capability required to perform the task. The manipulative abilities of some primates (primarily great apes, capuchin monkeys and macaques) have been studied for decades (e.g. [START_REF] Parker | Object manipulation, tool use and sensorimotor intelligence as feeding adaptations in cebus monkeys and great apes[END_REF][START_REF] Torigoe | Comparison of object manipulation among 74 species of non-human primates[END_REF][START_REF] Torigoe | Further report on object manipulation in non-human primates: A comparison within 13 species of the genus Macaca[END_REF][START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF][START_REF] Corp | Leaf processing of wild chimpanzees: physically defended leaves reveal complex manual skills[END_REF][START_REF] Macfarlane | Diversity of grip in Macaca mulatta[END_REF]) and compared directly with humans performing both simple tasks like reaching [START_REF] Christel | Grasping techniques and hand preferences in hominoidea[END_REF][START_REF] Lacreuse | Manual exploratory procedures and asymmetries for a haptic searching task: a comparison between capuchins (Cebus apella) and humans[END_REF][START_REF] Pouydebat | Biomechanical study of grasping according to the volume of the object: human versus non-human primates[END_REF][START_REF] Pouydebat | Diversity of grip in adults and young humans and chimpanzees (Pan troglodytes)[END_REF] and more complex routine tasks [START_REF] Heldstab | Manipulation complexity in primates coevolved with brain size and terrestriality[END_REF]. However, as far as we know, no experiment in captivity has compared manual abilities during the same complex tool use task.

Thus, the questions about humans' enhanced dexterity and how manipulation abilities evolved in hominids are still unresolved.

One recent study suggests that humans, having the most complex foraging niche, have developed complex manual abilities as a result, and that manipulation complexity would have coevolved with brain size and terrestriality in primates [START_REF] Heldstab | Manipulation complexity in primates coevolved with brain size and terrestriality[END_REF]. However, inhand manipulation was not taken into account when classifying manipulation complexity, despite a recent paper showing that a complex tool use task or complex object manipulation can require in-hand movements depending on the number of steps needed to perform the task [START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF]. In-hand movements were characterized by finger movements that involved object movement on the surface of the palm and the fingers. Thus, it appears necessary to take in-hand movements into detailed account to classify manipulation complexity and to draw conclusions about humans' specialization. Dynamic aspects of manual function have been described in humans [START_REF] Exner | In-hand manipulation skills[END_REF][START_REF] Santello | Postural hand synergies for tool use[END_REF][START_REF] Braido | Quantitative analysis of finger motion coordination in hand manipulative and gestic acts[END_REF]Bullock and Dollars, 2011) and a detailed taxonomy of the various forms of in-hand movements is available (Elliot and Connolly, 1984). In contrast, in-hand manipulation studies among nonhuman primates are scarce and have been investigated mainly in chimpanzees [START_REF] Boesch | Different hand postures for pounding nuts with natural hammers by wild chimpanzees[END_REF][START_REF] Marzke | Chimpanzee and human grips: a new classification with a focus on evolutionary morphology[END_REF][START_REF] Corp | Leaf processing of wild chimpanzees: physically defended leaves reveal complex manual skills[END_REF][START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF][START_REF] Marzke | Grips and hand movements of chimpanzees during feeding in Mahale Mountains National Park, Tanzania[END_REF]. Other primates such as gorillas (Gorilla sp.; [START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF], bonobos (Pan paniscus; [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF], and capuchin monkeys [START_REF] Crast | A comparison of dynamic hand movements in chimpanzees (Pan troglodytes) and capuchin monkeys (Cebus apella)[END_REF] have been the focus of even fewer studies, and orangutans' (Pongo sp.) in-hand movements have been almost entirely ignored. Although chimpanzees are our closest relatives (such as bonobos), and show the most complex tool use behavior among great apes in the wild, it is important to observe, measure, and analyze the other great apes in the effort to recount the evolution of complex manipulation in hominids. Studying the manual abilities of gorillas and orangutans is very important because they show strong manipulative abilities when processing food in the wild (e.g. orangutans: van [START_REF] Van Schaik | Manufacture and use of tools in wild Sumatran orangutans[END_REF][START_REF] Russon | The nature and evolution of orangutan intelligence[END_REF]gorillas: Byrne and Byrne, 1991;[START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF], have different lifestyles (arboreal for orangutans and terrestrial for gorillas), and differ in hand morphology [START_REF] Schultz | The skeleton of the trunk and limbs of higher primates[END_REF]. Finally, it is valuable to compare manual abilities between humans and great apes to better understand the conditions and restrictions underlying the occurrence of complex manipulative abilities, and the potential factors that may have bolstered humans into our position as the most eminently tool-using primates.

The objective of this study is to experimentally compare three different species of hominids in the same tool use task to determine the manual function and manual performance of each species. We use a novel quantification for the manual function (grip techniques, grasping postures, tool repositioning) and manual performance of humans compared to the most terrestrial (gorillas, Gorilla gorillas) and the most arboreal (orangutans, Pongo sp.) of the great apes during the same tool use tasks (i.e. the maze task used in [START_REF] Bardo | Do bimanual coordination, tool use, and body posture contribute equally to hand preferences in bonobos[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF]. Some previous studies quantified performance according to the time humans needed to accomplish one bout of actions [START_REF] Sollerman | Sollerman hand function test. A standardized method and its use in tetraplegic patients[END_REF][START_REF] Turgeon | Reliability of the NK dexterity test[END_REF][START_REF] Aaron | Development of the Functional Dexterity Test (FDT): construction, validity, reliability, and normative data[END_REF][START_REF] Schoneveld | Clinimetric evaluation of measurement tools used in hand therapy to assess activity and participation[END_REF], and the time non-human primates also needed to perform bouts of actions [START_REF] Fragaszy | Hand preference and performance on unimanual and bimanual tasks in capuchin monkeys (Cebus apella)[END_REF][START_REF] Albiach-Serrano | Apes (Gorilla gorilla, Pan paniscus, P. troglodytes, Pongo abelii) versus corvids (Corvus corax, C. corone) in a support task: The effect of pattern and functionality[END_REF]). However, we suggest that time needed to perform an action could be influenced by a diversity of factors (e.g. effect of social rank in species studied in their social group; [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF], and that quantifying manual performance with other motor skill parameters could allow us a better comparison between species. We chose to compare the manual abilities and performance of these species using the maze task because it required complex tool manipulation for bonobos [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF] navigating obstructions (i.e. obstacles placed inside the maze, and also the wire netting placed between the maze and the subject) to collect a walnut. This task involved several constraints (i.e. forelimb coordination, body posture adjustments, manual abilities, and vision) and allowed us to quantify other parameters of performance (e.g. number of wooden obstacles touched, tool repositioning in the grid). We expected that the variability these of constraints could influence the manual techniques and the manual performance among species. Moreover, this experimental task was easy to implement using identical conditions for all the species. Such an approach provides a comparative functional analysis of the manual abilities and performance in great apes and humans, allowing us to test if humans are unique in an experimental context.

METHODS

Subjects and housing

Thirty-three subjects participated in the present study between 2014 and 2015: 20 Homo sapiens, 6 gorillas (Gorilla gorilla) and 7 orangutans (4 Pongo Pygmaeus and 3 Pongo abelii) (Table 1). The gorilla group consisted of 5 males (mean age = 18.6 years old, age range: 10-31 years) and 1 female (31 years old); the orangutan group consisted of 3 males (mean age = 16.3 years old, age range: 12-20 years) and 4 females (mean age = 20.5 years old, age range: 9-38 years). Non-human subjects were housed in different zoos (Table 1) and were naïve to the maze task when we presented it, as were the humans. The human sample was constituted of students and researchers from the National Museum of Natural History of Paris (NMNH; France), and were not selected according to their handedness or personal habits or activities (we selected the first people who agreed to participate in the study). The groups of great apes were housed in indoor and outdoor enclosures with regular feedings, daily enrichment (e.g. food extraction) and water ad lib. The great ape portion of the study was conducted in the main cage in the indoor enclosure and subjects spontaneously participated. Humans were tested with the presence of one observer in a closed room at the NMNH of Paris.

Insert Table 1 about here

Apparatus and procedure

The maze task was an experimental task which consisted of using a tool to collect walnuts positioned on a wooden maze (45 cm wide by 60 cm long). The mazes were the same for all the species and were composed of 10 wooden obstacles of different shapes and sizes (Figure 1ab). For great apes, the mazes were attached outside the cage on the wire mesh (size = 5x5 cm) and were positioned between 40 and 60 cm from the ground. To avoid competition and social tension for great apes, we simultaneously placed around the cages the same number of mazes as the number of tested subjects. Moreover, we offered the task after feeding to avoid social tension and to avoid subjects' appetites having an effect on the results. For humans, the maze was placed on a table 70 cm from the ground, with a piece of wire mesh (100x100 cm) placed in front of the maze (Figure 1b). The position of the maze was related to the size of each species and placed at an average height, allowing subjects to perform the task using any body postures they wished. For humans, a chair (45 cm height) was positioned just in front of the maze. The walnuts were placed at the end of the maze (60cm away from the subject). We provided standardized tools made of bamboo branches for all species (length between 45cm and 1m depending on subject hand size); the tools for humans had smaller diameters (between 0.5 and 1cm) than the tools for gorillas and orangutans (between 1 and 1.5 cm) to account for different hand sizes among species. The tools were provided directly in the cages for great apes and placed beside the maze for humans. The only instruction for humans was to collect the walnut placed at the end of the maze through the wire netting, to extract a naïve behavior comparable to great apes.

We recorded six sessions per individual, one session corresponding to one walnut collected. The aim was to capture the variation among species and individuals, in three sessions per day and per individual over two days. A sequence began when a subject started to put the tool through the wire mesh and ended when he/she could collect the walnut. One fixed camera (CANON 600D©) was used during experiments with humans. For great apes, one camera (SONY Handycam HDR-CX240) was placed in front of each maze. Videos were recorded at 50 frames/second. For all sessions, humans used exclusively a bipedal posture and gorillas used exclusively a seated posture. For orangutans, we observed that during one session they changed their body posture 2.98 times (± 0.93). They spent more time to perform the task in seated posture (45.6 % of the time) and hanging on the wire netting (40.9 % of the time) than in bipedal posture (13.5 % of the time), but without significant differences (Friedman rank sum tests, Q = 2, df = 6, p > .05). These differences suggested a possible effect of the body postures on the manual function, but in the present study the number of sessions for each individual was insufficient to test this effect. Thus, we decided not to take into account the different body postures used by the species in the analyses, but we discuss the potential effects in later sections.

Insert Figure 1 about here

Data scoring and classification system

Manual techniques. We classified six categories of different grip techniques used to hold and use the tool: unimanual grip involved one hand; symmetrical bimanual grip involved both hands simultaneously on one tool; asymmetrical bimanual grip involved both hands simultaneously on two tools (see for example Figure 1b); mouth grip; foot grip; and other grip with combinations of two grips (e.g. one foot and one hand).

The grasping postures were recorded, including quantification of hand contact areas with the tool, following the same method and anatomical terminology of [START_REF] Borel | Sequence analysis of grip and manipulation during tool using tasks: a new method to analyze hand use strategies and examine human specificities[END_REF] and [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF]. This method allowed also us to quantify the number of different combinations of contact areas used for each individual (for more details see [START_REF] Borel | Sequence analysis of grip and manipulation during tool using tasks: a new method to analyze hand use strategies and examine human specificities[END_REF] and [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF]. To name the grasping postures we used existing typology for humans and great apes (see Table 2 footnote) and we classified them into five main categories as done previously [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF].

We recorded the different techniques used to reposition the tool in the hand, such as the use of in-hand movements, the hand that was not holding the tool, the mouth, and/or the feet.

In-hand movements were classified in two categories: simple movements and complex movements. This classification was created by observing the subject's movements and by adapting the classification system of Elliot and Connolly (1984) and [START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF]. In this study, we included movement of individual digits as in [START_REF] Bardo | Do bimanual coordination, tool use, and body posture contribute equally to hand preferences in bonobos[END_REF] unlike the two previous studies. Simple movements are movements of one finger (e.g. flexion/extension of the thumb), and movements of two fingers with simple and reciprocal synergies (Elliot and Connolly, 1984). Simple synergies are defined as convergent flexor synergies between the digits (e.g. flexion/extension of the thumb and the index finger), and reciprocal synergies are defined as dissimilar or reciprocating movements of the digits (e.g. flexion of the fingers with adduction of the thumb). Complex movements are defined as independent and uncoordinated movements of the fingers which grasp and regrasp the object using a characteristic sequence of grasps and simple movements [START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF].

Finally, our sample size and the number of sessions are too small to address population bias in manual preference, but for potential future use in meta-analysis, individual hand biases are presented in Supplementary Material 1.

Manual performance. We investigated the manual performance for each session and individual by quantifying the time needed (in seconds) to collect the walnut, adding other motors skill parameters such as the number of wrist movements used to finally collect the walnut (defined by the sum of wrist flexion/extension and abduction/adduction movements), the number of touched wooden obstacles (placed inside the maze), and the number of times the tool was repositioned in the grid. We considered that an obstacle was touched when the obstacle stopped the advancement of the walnut in the maze. We considered touching an obstacle to be due to a lack of control of the walnut's movement, and thus this parameter allowed us to quantify the control of the movement.

Insert Table 2 about here

Video Coding and Reliability Assessment

Videos were played with VLC media player and analyzed frame by frame using a focal sampling protocol [START_REF] Altmann | Observational study of behavior: sampling methods[END_REF]. We recorded events each time a subject moved his/her fingers (e.g. displacements), stopped moving the tool for more than 20s, and when a subject changed the position of the tool in the grid and recorded the time for each event. We started to collect data when the tool was within the wire mesh. Including all subjects and all sessions, we recorded 1158 events: 502 events for humans, 268 events for gorillas, and 388 events for orangutans. The duration (in seconds) was used as a measure to quantify grip techniques and grasping postures, and number of events was used as a measure to quantify the techniques to reposition the tool and the performance parameters.

Twenty percent of sessions were also coded by a second observer to assess interobserver reliability, which was excellent for all the parameters quantified (Pearson's correlation coefficient = 0.98, N = 660) and good for the combinations of contact areas (Cohen's kappa к = 0.63, N = 216). Therefore, only the data from the first observer were used for analysis.

Data analysis

The mean percentage of total time of the use of each grip technique and grasping posture were calculated relative to the time needed to perform the task for each individual. For the other parameters, we used mean values for each individual. Because some of our data did not meet the normality and homogeneity assumptions for parametric tests, we used nonparametric statistics. The comparisons between species were performed by using Mann-Whitney tests (U) for two species, and the three-species comparison by using Kruskal-Wallis rank sum tests (H).

If the latter tests were significant, we used Dunn's tests for multiple comparisons of independent samples (Z). The comparisons among individuals of each species were performed by using Friedman rank sum tests (Q) and, if the tests were significant, we performed pairwise comparisons using the Wilcoxon signed rank test (W) with continuity correction. Tests were two-tailed with a significance level set at 0.05. Bonferroni correction was applied in the case of multiple comparisons (corrected p values are marked as p'). All the tests were performed using R (R Core Team 2016).

In order to characterize the performance among all the individuals (N = 33) according to their techniques used, a Principal Component Analysis (PCA) was performed on six variables during the best session of each individual. The six variables were the four performance parameters (time needed to perform the task, number of wrist movements, number of touched obstacles, number of tool repositionings in the grid), the number of tool repositionings in the hand, and the number of changes of combinations of contact areas. The best session was defined as the session with the least time needed to collect the walnut. If several sessions had the same time needed, we used the one with the least wrist movement involved. The PCA was performed using R (R Core Team 2016), with the data normed for all the variables of all individuals.

RESULTS

Grip techniques

Unimanual grip was the preferred technique, but more used at 100 % of the time by gorillas and 90.6 % by orangutans, than 46.9 % by humans (Z = 3.962, N = 26, p' < .001; Z = 2.738, N = 27, p' < .05, respectively). Humans also used symmetrical bimanual grip at 46.2 % and asymmetrical bimanual grip at 6.9 %. No particular grip was preferred in the human group (Q = 5.0586, df = 19, p > .05), indicating inter-individual differences and also intra-individual variations for sixteen individuals. Orangutans additionally used mouth grip (7.7 %) and other grip techniques, such as mouth with one foot (0.1 %; used by one individual), symmetrical bimanual grip (0.3 %; used by 2 individuals), and foot grip (1.3 %, used by 2 individuals).

Grasping postures

Unimanual grip technique results are presented in Figure 2 as the mean percentage of different grasping posture categories used by each species. "Precision grips" were not used by gorillas and were used more by humans than orangutans (U = 109, N = 27, p < .01). "Thumb lateral" was not used by gorillas, and we did not observe differences in usage of this grip between humans and orangutans (U= 69, N = 27, p > .05). "Without thumb" was not used by humans, and we did not observe differences between gorillas and orangutans (U = 18, N = 13, p > .05). "Palm grips" showed differences among species (H = 11.793, df = 2, p < .01) -gorillas and orangutans used more palm grips than humans (respectively, Z = 2.431, N = 26, p' < .05; Z = 3.002, N = 27, p' < .01). "Other grips" also showed differences among species (H = 8.127, df = 2, p < .05) -gorillas used more grasping postures classified in this category than did humans (Z = 2.72, N = 23, p' < .05).

The detail of all the grasping postures observed for each species is presented in Table 2.

We recorded ten grasping postures used by humans (mean by individual = 2.65 ± SD 0.4) without preference within the group (Q =13.299, df = 16, p > .05). Humans seemed to use more "Lateral tripod grasp" (34.7 %), "Four-finger grasp" (30.5 %) and "Dynamic tripod grip" (13.8 %) as primary grasping postures. We recorded eight grasping postures used by gorillas (mean by individual = 3.16 ± 0.9) without preference (Q = 6.8041, df = 5, p > .05). Gorillas seemed to use mainly interdigital finger brace grasping postures, such as "Interdigital 2/3 brace" (33.6 %), "Interdigital 3/4 brace" (28.2 %) and "Power grip" (19.6 %). We recorded 16 grasping postures for orangutans (6.14 ± 1.3), who used mainly "Power grip" (33.4 %) and "V pocket" (33.8 %).

In the two bimanual grip techniques for humans, we observed no categorical differences in grasping posture between the dominant hand and the support hand (p > .05). We only observed the use of "Without thumb" grasping postures in the support hand during symmetrical bimanual grip technique (M2 in the Table 2).

Concerning changes in contact area combinations, orangutans altered their contact area on average 3.8 times (± 0.7) per session, while gorillas changed 2.9 times (± 0.6) per session, and humans 2.3 times (± 0.1) per session. We observed no significant differences in mean number of contact area combinations used among species (H = 3.0842, df = 2, p > .05).

Insert Figure 2 about here

Tool repositioning

Tool repositioning frequency differed by species (H = 14.884, df = 2, p < .001), with orangutans' mean incidence of tool repositioning being higher than humans' (Z = 3.603, N = 27, p' < .001). We recorded four distinct techniques used to move and reposition the tool in the hand, with some differences among species (Figure 3). The hand that did not hold the tool was used in a similar manner by all the species (H = 0.1811, df = 2, p > .05). The mouth was used by gorillas and orangutans, while the foot was used only by orangutans. Orangutans used their mouths more than gorillas did (U = 37, N = 13, p < .05). In-hand movements were mainly recorded in humans and gorillas, without species differences (W = 76.5, N = 26, p > .05) (Figure 3 and Table 3). Only one Sumatran orangutan (Kawan) was observed to use in-hand movements. We recorded 11 types of in-hand movements by humans, three types by gorillas and two by orangutans. Also, these types of movements were not used by every individual (Table 3) or during every session. Humans used simple and complex movements involving fingertips whereas gorillas and orangutans used simple movements involving the palm (Table 3).

Gorillas and orangutans did not significantly prefer any one strategy for repositioning the tool in their hand (p > .05), but orangutans appeared to use their mouths for repositioning the tool more often (83 %). Humans showed no difference in the number of in-hand movements used in the dominant hand, regardless of each grip technique used (unimanual, symmetrical bimanual or asymmetrical bimanual; Q = 26.708, df = 19, p > .05).

Insert Figure 3 about here Insert Table 3 about here

Performance

We found significant differences between humans and great apes according to our measured performance parameters (reported as mean values; Supplementary Material 2). On average, gorillas and orangutans needed more time to collect the walnut than humans (p' < .001), they used more wrist movements than humans (p' < .001), they touched more obstacles than humans (respectively, p' < .001 and p' < .01), and they changed the position of the tool in the grid more often than humans (respectively, p' < .01 and p' < .001).

The PCA in figure 4 shows three axes that explain 87 % of the total variance on six variables (see Methods) quantified during the best session for each individual. The first axis (40 %) was determined by the time needed to collect the walnut (loading = 0.59), the number of touched obstacles (loading = 0.53), the number of tool repositionings in the grid (loading = 0.41), and the number of wrist movements used to collect the walnut (loading = 0.34). The second axis (26 %) was determined by the number of tool repositionings in the hand (loading = -0.84) and the number of tool repositionings in the grid (loading = 0.49). The third axis (21%) was determined by the number of touched obstacles (loading = 0.72), the number of tool repositionings in the grid (loading = -0.43), the number of tool repositionings in the hand (loading = -0.41), and the total number of combinations of contact areas used (loading = -0.32).

The PCA distinguished the performance and techniques used by humans from some great apes (PC1, Fig. 4a) and also distinguished individuals within each species (PC2 and PC3, Fig. 4b-5c). Humans were almost all situated along the negative side of PC1; orangutans and gorillas were almost all situated along the positive side of PC1; in the center there was overlap among some individuals of all three species. The majority of the great apes and the few humans along the positive side of PC1 needed more time to collect the walnut, touched more wooden obstacles, changed the place of the tool in the grid more often, and used more wrist movements to collect the walnut in comparison to the other humans and the two great apes (one gorilla and one orangutan) situated along the negative side of this axis. PC1 indicates better performance in humans according to these four parameters, but also displayed inter-species variation by placing one gorilla and one orangutan within the humans' range of variability. PC2 illustrates inter-species performance in respect to two different techniques. Individuals situated along the negative side of PC2 repositioned the tool in their hand more often compared to individuals situated along the positive side of PC2, who instead more often repositioned the tool in the grid.

Humans who used bimanual coordination grip are found principally along the positive side of PC2, and thus more often repositioned the tool in the grid than in their hands. PC3 also shows inter-species performance and describes two different techniques. The individuals situated along the negative side of PC3 repositioned the tool more often in the grid and in their hand and used greater combinations of contact areas, but also touched fewer obstacles than individuals situated along the positive side of PC3. We suggest that each individual performed the task differently due to their different grip techniques and grasping postures.

Insert Figure 4 about here

DISCUSSION

In the present study, the same complex tool use task was tested on three species of hominids to compare their manual function and manual performance. The results clearly showed that each species used different techniques. Humans used bimanual grip techniques, pad-to-pad precision grasping postures, and in-hand movements involving fingertips. Gorillas used a unimanual grip technique and simple in-hand movements, while orangutans used a variety of strategies (e.g. hand, mouth or feet). Humans performed the task better than gorillas and orangutans (e.g. by being quicker and using less wrist movements to collect the food), but these inter-species differences seemed less apparent during their best performance sessions.

More detailed results are discussed below.

Specific grip techniques according to species

In the present study, bimanual coordination grips were employed half of the time and nearly exclusively by humans, while the ability to perform many two-handed tasks has been well documented in both humans [START_REF] Corbetta | The developmental origins of bimanual coordination: A dynamic perspective[END_REF] and great apes (e.g. chimpanzees: [START_REF] Marzke | Grips and hand movements of chimpanzees during feeding in Mahale Mountains National Park, Tanzania[END_REF]gorillas: Byrne et al., 2001;orangutans: Peters and Rogers, 2008). In our study, humans displayed both symmetrical bimanual coordination (both hands grasp the same tool) and asymmetrical bimanual coordination (each hand grasps separate tools). These bimanual coordination grips increase the complexity of manipulation [START_REF] Macneilage | Primate handedness reconsidered[END_REF][START_REF] Hopkins | Hand preferences for a coordinated bimanual task in 110 chimpanzees (Pan troglodytes): cross-sectional analysis[END_REF][START_REF] Heldstab | Manipulation complexity in primates coevolved with brain size and terrestriality[END_REF]. Indeed, asymmetrical bimanual coordination appears to be a more difficult task and requires eye coordination with both distant hands. The complexity of the maze task, which involves several constraints such as forelimb coordination, manual abilities and vision, could lead to expression of different grip techniques among species according to their muscular control and their morphology [START_REF] Wainwright | Stereotypy, flexibility and coordination: key concepts in behavioral functional morphology[END_REF].

We observed the use of symmetrical bimanual coordination only once in each of two different orangutans. This result could be explained by the fact that one hand was employed in hanging from the wiring most of the time. It has been shown that wild orangutans use unimanual feeding more than feeding involving two limbs (hand-hand or hand-foot) [START_REF] Peters | Limb use and preferences in wild orang-utans during feeding and locomotor behavior[END_REF]. Orangutans likely used specific grip techniques including the mouth and the foot due to their high arboreal lifestyle. Orangutans showed a strong preference for oral tool use over manual tool use in a previous study [START_REF] O'malley | Oral tool use by captive orangutans (Pongo pygmaeus)[END_REF], yet in the present study oral tool use occurred less than 10 % of the time. This could be due to the cage wiring used in the current study, which is not similar to the arboreal substrate where orangutans use tools in the wild. As orangutans are able to adopt many body postures [START_REF] Thorpe | Orangutan positional behavior and the nature of arboreal locomotion in Hominoidea[END_REF], the prevalence of non-oral manipulation could be linked to the task itself requiring both force and precision that the mouth might not provide. Gorillas exclusively used a unimanual grip technique, which is consistent with recent reports on tool use in wild gorillas [START_REF] Breuer | First observation of tool use in wild gorillas[END_REF][START_REF] Kinani | Tool use for food acquisition in a wild mountain gorilla (Gorilla beringei beringei)[END_REF].

Specific grasping postures and in-hand movements to species

We already know that great apes can use precision grips [START_REF] Christel | Grasping techniques and hand preferences in hominoidea[END_REF][START_REF] Jones-Engels | Precision grips in young chimpanzees[END_REF][START_REF] Marzke | Chimpanzee and human grips: a new classification with a focus on evolutionary morphology[END_REF][START_REF] Christel | How precisely do bonobos (Pan paniscus) grasp small objects[END_REF][START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF][START_REF] Pouydebat | Biomechanical study of grasping according to the volume of the object: human versus non-human primates[END_REF][START_REF] Pouydebat | Diversity of grip in adults and young humans and chimpanzees (Pan troglodytes)[END_REF] and in-hand movements [START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF] like humans. The human subjects in this study used pad-to-pad precision grip and in handmovements with fingertips, while gorillas and orangutans used more grasping postures in which the tool is blocked into the hand (e.g. power grip) and in-hand movements which engage the palm. First, the fact that humans used "pencil grip" (called also dynamic tripod grip) as their preferred grasping posture as well as variants of this grasping posture like the four finger grasp [START_REF] Schneck | Descriptive analysis of the developmental progression of grip position for pencil and crayon control in nondysfunctional children[END_REF]) is certainly influenced by the way human children are taught to grasp a pen or pencil for writing. Gorillas better preferred "interdigital finger brace", which was similarly observed in chimpanzees and bonobos during tool use [START_REF] Lesnik | The interdigital brace and other grips for termite nest perforation by chimpanzees of the Goualougo Triangle, Republic of Congo[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF]. Orangutans, however, used their palms more than the other species, favoring the "power grip," and were the only ones to use the grasping posture called "V pocket", also observed in chimpanzees and bonobos during tool use [START_REF] Marzke | Grips and hand movements of chimpanzees during feeding in Mahale Mountains National Park, Tanzania[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF].

The differences between humans and great apes could be also explained by the different muscular anatomy and morphology of their hands. Indeed, gorillas (and gibbons) have the highest thumb-forefinger index among apes, while orangutans have the lowest [START_REF] Schultz | The skeleton of the trunk and limbs of higher primates[END_REF].

Thus, the gorillas could more handily have involved their thumbs than orangutans could during in-hand movements, which is consistent with our results. The differences between humans and great apes could be due to the absence of several anatomical features in the latter. It appears that some human hand muscles, such as flexor pollicis longus (FPL) and extensor pollicis brevis (EPB) which are related to the movement of the thumb, are not present or not independent in the hands of great apes, except hylobatids [START_REF] Diogo | Soft-tissue anatomy of the primates: phylogenetic analyses based on the muscles of the head, neck, pectoral region and upper limb, with notes on the evolution of these muscles[END_REF][START_REF] Diogo | Evolution and homologies of primate and modern human hand and forearm muscles, with notes on thumb movements and tool use[END_REF][START_REF] Myatt | Functional adaptations in the forelimb muscles of non-human great apes[END_REF]. Nevertheless, gorillas and orangutans have a tendon of the flexor digitorum profundus running to the thumb, so it is questionable if the lack of the FPL and EPB could be linked to differences in manipulation. Moreover, in contrast to humans [START_REF] Vigouroux | Effect of object width on muscle and joint forces during thumb/index fingers grasping[END_REF][START_REF] Goislard De Monsabert | Quantification of hand and forearm muscle forces during a maximal power grip task[END_REF], the muscle activities and muscular coordination required to grasp an object for great apes are not known. Liu and collaborators (2016) recently used a virtual kinematic model to demonstrate that the different hand proportion in anthropoid hands results in a large disparity of manipulative potential among their hands. Consequently, the rare use of fingertips for both great apes could be the result of a choice based on biomechanical loadings, which cannot be balanced by their musculature when grasping with the thumb. For example, a shorter thumb would generate a different finger joint angle, corresponding to different moment arms, and probably would engage different joint and muscle loadings.

However, since the model of Liu and collaborators did not take muscles into account, questions remain about how the loading of the hand, and thus the biomechanical constraints, affect interdigital mobility in object manipulation. To better understand this point, it would be very useful to develop a musculoskeletal model based on ape morphological (e.g. size of the hand segments) and biomechanical data (e.g. force, kinematics, muscle activities) as has been done for humans (see [START_REF] Fernandez | Multiscale musculoskeletal modelling, data-model fusion and electromyography-informed modelling[END_REF]. Another interesting perspective would be to investigate the influence of grip strength on hand bone micro-architecture in great apes to access these biomechanical constraints, as is studied in humans [START_REF] Reina | Laterality and grip strength influence hand bone micro-architecture in modern humans, an HRpQCT study[END_REF].

Specifics techniques according to individuals

Inter-individual variability was present in humans, high for orangutans and low for gorillas. Because the tasks in this study were not habitual, individuals adapted their techniques according to their individual experiences. For example, human children learn to write using the pencil grip between four and six years old, and there is variation in the development of this grasping posture [START_REF] Schneck | Descriptive analysis of the developmental progression of grip position for pencil and crayon control in nondysfunctional children[END_REF]. Moreover, some individuals may be athletes and/or musicians, and previous studies show that these activities have an effect on fine motor abilities (e.g. for music [START_REF] Costa-Giomi | Does Music Instruction Improve Fine Motor Abilities?[END_REF] and on prehensile capabilities (e.g. for sports [START_REF] Cutts | Grip strength and endurance in rock climbers[END_REF][START_REF] Shea | Manual demands and consequences of rock climbing[END_REF]. In other words, learning and practising certain activities could influence manipulative abilities in human adults, which could explain the different techniques used by humans. We cannot draw conclusions on the influence of experience in gorillas' and orangutans' manipulative abilities since we do not know when they began to manipulate tools, and in what context (e.g. social, non-social). We know only that all individuals had previous access to various enrichments, such as food extraction with a tool. A longitudinal study could make it possible to deal with this unknown factor.

We found orangutans showed more inter-variability in their techniques than humans and gorillas. The fact that orangutans frequently changed their body posture could have generated changes in their grasping postures and also could have necessitated more frequent repositioning of the tool, especially with the mouth. Interestingly, despite our small sample size and even though it was not a focus of the study, we observed differences between Bornean orangutans and their Sumatran relatives. We know that Sumatran forests tend to be more productive and less seasonal than Bornean forests, and these differences could potentially have generated different behavioral responses such as foraging strategies and sociality [START_REF] Wich | Orangutans: geographic variation in behavioral ecology and conservation[END_REF][START_REF] Van Schaik | The costs and benefits of flexibility as an expression of behavioural plasticity: a primate perspective[END_REF]. There is also a difference in general morphology between the two orangutan species [START_REF] Courtenay | Inter-or intra-island variation? An assessment of the differences between Bornean and Sumatran Orang-utans[END_REF][START_REF] Groves | Unfinished business: Mahalanobis and a clockwork orang[END_REF] and we do not know if their hand morphology differs. These differences between species could explain different manipulative abilities and should be explored in future studies.

Gorillas showed less inter-individual variability in their techniques, using the same techniques repeatedly to perform the task. Even if our sample did not allow us to test the effect of body posture on manual abilities, we can suggest that compared to orangutans, gorillas are more terrestrial and are less constrained by high body posture variability compared to arboreal behaviors. They may be free to develop specific manipulative abilities including tool use and complex bimanual coordination (e.g. [START_REF] Meulman | The role of terrestriality in promoting primate technology[END_REF]. Strong inter-individual variability was also demonstrated in the techniques used by bonobos [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF] which seems to be intermediate between gorillas and orangutans. Thus, gorillas, with their more terrestrial lifestyle, could have developed different manual techniques and more specific ones than arboreal species such as orangutans. Moreover, these specific techniques could be shared among individuals. The cognitive and manual abilities of gorillas are poorly understood, and should be explored because gorillas display high manipulative ability in the wild [START_REF] Byrne | Manual dexterity in the gorilla: bimanual and digit role differentiation in a natural task[END_REF] including recently-observed tool use [START_REF] Breuer | First observation of tool use in wild gorillas[END_REF][START_REF] Kinani | Tool use for food acquisition in a wild mountain gorilla (Gorilla beringei beringei)[END_REF].

Performance

Our results showed that performance for the six sessions differed according to species, with better overall performance in humans. However, an interesting result was that when we compared performance during the best session across all individuals, we observed a less marked difference in manual performance among species. Humans collected the walnut faster than gorillas and orangutans during the six sessions. Time needed to perform the task has been previously considered as an important measure of performance [START_REF] Sollerman | Sollerman hand function test. A standardized method and its use in tetraplegic patients[END_REF][START_REF] Schoneveld | Clinimetric evaluation of measurement tools used in hand therapy to assess activity and participation[END_REF][START_REF] Albiach-Serrano | Apes (Gorilla gorilla, Pan paniscus, P. troglodytes, Pongo abelii) versus corvids (Corvus corax, C. corone) in a support task: The effect of pattern and functionality[END_REF], however, during their best session, some gorillas and orangutans succeeded in collecting the walnut in a similar period to the humans'.

For gorillas and orangutans, social pressure may have influenced task duration and their performance, as was observed in bonobos performing the same task [START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF].

Subordinate individuals tested in groups would act more quickly than high ranking individuals.

During the six sessions humans, used fewer wrist movements to collect the walnut, touched fewer obstacles, and used less tool repositioning in their hand and in the grid. These results could demonstrate a lack of efficiency and precision of wrist movements for both great apes. Moreover, the precision grasping postures used by humans could represent a good compromise between the mobility allowed by these grips for the object grasp and the relative stability produced by the pulp surfaces of the fingers [START_REF] Marzke | Precision grips, hand morphology, and tools[END_REF]. Interestingly, the two gorillas who had better performances used on average more in-hand movements and used exclusively a preferential grasping posture that was the "interdigital 2/3 brace" grasping posture. This grasping posture was also observed in chimpanzees and bonobos, who also used in-hand movements [START_REF] Crast | Dynamic in-hand movements in adult and young juvenile chimpanzees (Pan troglodytes)[END_REF][START_REF] Bardo | Behavioral and functional strategies during tool use in bonobos (Pan paniscus)[END_REF], and was defined as an inefficient variant of pencil grasp in humans [START_REF] Selin | Pencil grip. A descriptive model and four empirical studies[END_REF]. This grasping posture could allow more inhand movement compared to the other grasping postures and so would favour in-hand manipulation.

CONCLUSION

Our results indicated that all the species in this study were able to perform the task using different manual specificities and showing different performance. Historically, attention has focused on the movements of the thumb (e.g. [START_REF] Napier | The prehensile movements of the human hand[END_REF][START_REF] Lewis | Functional Morphology of the Evolving Hand and Foot[END_REF][START_REF] Rafferty | The functional and phylogenetic significance of the carpometacarpal joint of the thumb in anthropoid primates[END_REF][START_REF] Marzke | Evolution of the power (''squeeze'') grip and its morphological correlates in hominids[END_REF][START_REF] Rose | Kinematics of the trapezium-1st metacarpal joint in extant anthropoids and Miocene hominoids[END_REF]. This study provides novel information on the manual function of hominids, highlights other ways in which humans' manual dexterity differs from other species' dexterity (i.e. bimanual grip technique, pad-to-pad precision grasping postures and in hand-movements involving fingertips) and emphasizes the distinct manipulative function in orangutans. Our results supported the theory of [START_REF] Heldstab | Manipulation complexity in primates coevolved with brain size and terrestriality[END_REF] that primates may have developed complex manual abilities in respect to their foraging niche, and that manipulation complexity would have coevolved with brain size and terrestriality. Moreover, our results support the hypothesis that a terrestrial lifestyle plays a role in facilitating the development of complex tool use [START_REF] Meulman | The role of terrestriality in promoting primate technology[END_REF]. Extensive, but time-consuming, studies in the wild could help improve our knowledge about interactions between environment, body posture, natural manual tasks and manipulative techniques. Moreover, we can investigate if the different manual abilities of great apes might also be due to different brain networks and access to cognitive skills that are needed to complete tool use tasks. Indeed, we know little about sensorimotor control in the hand of great apes. An interesting recent study by [START_REF] Putt | The functional brain networks that underlie Early Stone Age tool manufacture[END_REF] investigated the brain activity during Oldowan and Acheulian stone tools learning in modern human participants. These authors suggested that a homologous cognitive network can be found in other species who use stone tools such as chimpanzees (e.g. [START_REF] Matsuzawa | Field experiments on use of stone tools by chimpanzees in the wild[END_REF][START_REF] Inoue-Nakamura | Development of stone tool use by wild chimpanzees (Pan troglodytes)[END_REF] or capuchin monkeys [START_REF] Proffitt | Wild monkeys flake stone tools[END_REF]. Investigations about the brain network during tool use in great apes, macaques [START_REF] Malaivijitnond | Stone-tool usage by Thai long-tailed macaques (Macaca fascicularis)[END_REF] and capuchin monkeys could be very useful to better understand humans' enhanced dexterity and how complex manipulative abilities evolved in primates. Crast et al., 2009; b Elliot and Connolly, 1984; c Pont et al., 2009. See these references for more functional details and illustrations of these in-hand movements.

Supplementary Material 1 Hand preferences were presented as a percentage of the duration the dominant hand was used relative to the total time needed to perform the task for each individual. The dominant hand was defined as the hand that directed movements of the tool and walnut during symmetrical bimanual grip or the hand that directed movements of the walnut during asymmetrical bimanual grip. Twelve humans used exclusively the right hand and two used exclusively the left hand (out of 20 individuals). No hand preference was observed for the group of gorillas (W = 7, N = 6, p > .05): four used exclusively the left hand and two used exclusively the right hand. For orangutans we did not observe a preferred hand (W = 7, N = 7, p > .05). Five individuals were ambidextrous and two individuals (Putri and Kawan) used exclusively the left hand.

The table shows the individual hand bias for each session. For humans, the percentages are presented according to the grip techniques used: U = unimanual grip; BiS = symmetrical bimanual grip involved both hands simultaneously on one tool; BiA = asymmetrical bimanual grip involved both hands simultaneously on two tools. Percentages in bold are for the best session of each individual. All orangutans have <100 % hand preference percentages because they used other grip techniques (mouth, foot, and mouth with one foot).

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Mean percentage of total time of the use of the five different grip categories by each

Figure 3 .

 3 Figure 3. Mean number of techniques used by session for tool reposition in the hand by each

Table footnotes :

 footnotes a-c In-hand movements describe in: a

ACKNOWLEDGMENTS

We thank the general directors of the Palmyre Zoo (P. Caillé), Ménagerie of Paris (M. Saint-Jalme), Amnéville (M. Louis) and La Vallée des Singes (E. Le Grelle) for their hospitality and for allowing us to conduct our experiments in their parks. We also thank all of the zoos' staff, the zoological director, the great apes headkeeper and the animal keepers of these zooswithout them we could not work with animals in these ideal conditions. Thanks to H. Clamouze for manufacturing the mazes. We also thank the Action Transversale of National Museum of Natural History (Paris, France, E.P.). We thank K.S. Boyle, B.A. Wehrle and N.J. Gold for the correction of the English language and their very useful comments. We also thank T. Kivell, D.M. Fragaszy for their very useful comments. A. Bardo thanks the doctoral school FdV, the Fundation Bettencourt-Schueller and Paris Descartes University for PhD funding. Finally, thanks to the Société Francophone De Primatologie (SFDP) for their financial help with the Bourse Tremplin 2014. Finally, we thank the two anonymous reviewers for their comments which greatly improved this article. This research adhered to the legal requirements of France and all the experiments were carried out following the principles of laboratory animal care in accordance with the CNRS guidelines and comply with the American Association of Physical Anthropologists Code of Ethics as it pertains to living human and nonhuman subjects.

AUTHOR CONTRIBUTION

Conceived and designed the experiments: AmB EP. Performed the experiments: AmB.

Analyzed the data: AmB RC AnB. Contributed reagents/materials/analysis tools: AmB RC AnB EP. Wrote the manuscript: AmB RC AnB EP. Variability of the grasping postures used to hold a tool and the percentage of uses by species. For humans, M1 corresponds to the dominant hand during unimanual grip technique and during asymmetrical bimanual grip technique (defined as the hand that directed movements of the tool and walnut), and M2 corresponds to the support hand during asymmetrical bimanual grip technique. Illustration examples of the grasping postures were realized with a human hand and so the position of the fingers could be changed according to the morphometric of the hand of the species. Humans used more "precision grips", gorillas used more "other grips", and orangutans used as much "other grips" as "palm grips". 3.9 ------

Table footnote:

a-h Named and described in a [START_REF] Marzke | Chimpanzee and human grips: a new classification with a focus on evolutionary morphology[END_REF]b Wynn-Parry, 1966;[START_REF] Schneck | Descriptive analysis of the developmental progression of grip position for pencil and crayon control in nondysfunctional children[END_REF]d Schneck, 1987, as cited in [START_REF] Schneck | Descriptive analysis of the developmental progression of grip position for pencil and crayon control in nondysfunctional children[END_REF]e Gesell, 1940, as cited in Schneck and[START_REF] Schneck | Descriptive analysis of the developmental progression of grip position for pencil and crayon control in nondysfunctional children[END_REF]f Marzke et al., 2015;g Benbow, 1997;h Lesnik et al., 2015. Table 3. Description of the in-hand movements observed and number of individuals who used each kind of movement (N). For humans, M1 corresponds to the dominant hand during unimanual grip technique and during asymmetrical bimanual grip technique, and M2 corresponds to the support hand during asymmetrical bimanual grip technique. Humans used simple and complex movements whereas gorillas and one orangutan, used only simple movements. Supplementary Material 2 Statistical results from the comparison of performance parameters among species. Significant results are in red. We found differences between humans and the great ape species, but no differences between gorillas and orangutans.

Humans