Nicolas Puillandre
email: puillandre@mnhn.fr

SPECIES DELIMITATION AND DESCRIPTION From Integrative Taxonomy to Species Description: one Step Beyond

Keywords: Cryptic species, grey zone, impact factor, literature review, species complex, species delimitation, species hypotheses, taxonomic impediment

published or not. The documents may come   L'archive ouverte pluridisciplinaire

The first part of knowledge is getting the names right

Chinese proverb

Integrative taxonomy was formally introduced in 2005 as a comprehensive framework to delimit and describe taxa by integrating information from different types of data and methodologies [START_REF] Dayrat | Towards integrative taxonomy[END_REF][START_REF] Will | The perils of DNA Barcoding and the need for integrative taxonomy[END_REF]. Even if debate remains about the hierarchy of the types of characters and criteria to use for species delimitation [START_REF] Schlick-Steiner | Integrative taxonomy: a multisource approach to exploring biodiversity[END_REF][START_REF] Padial | The integrative future of taxonomy[END_REF][START_REF] Yeates | Integrative taxonomy, or iterative taxonomy?[END_REF], most, if not all taxonomists agree that objectively evaluating several lines of evidence within a formalized framework is the most efficient and theoretically-grounded approach to defining robust species hypotheses [START_REF] Samadi | The tree, the network, and the species[END_REF][START_REF] De Queiroz | Species concepts and species delimitation[END_REF].The last ten years have seen a renewal of taxonomy, illustrated by the increasing number of published articles related to species concepts, species delimitation methodology and its application.

In the early 90s, many systematists began to suspect that the majority of species would remain undescribed (Costello et al. 2013a;[START_REF] Erwin | Tropical forests: their richness in Coleoptera and other arthropod species[END_REF][START_REF] Mora | How many species are there on Earth and in the ocean?[END_REF] but see Costello et al. 2013b) and that some of them will probably go extinct before we have a chance to describe them [START_REF] Barnosky | Has the Earth's sixth mass extinction already arrived?[END_REF][START_REF] Leakey | The sixth extinction: Patterns of life and the future of humankind[END_REF][START_REF] Pimm | Human impacts on the rates of recent, present, and future bird extinctions[END_REF]. The use of molecular data, and in particular molecular barcoding [START_REF] Hebert | Biological identifications through DNA Barcodes[END_REF], was presented as one answer to this "taxonomic impediment" (as defined in [START_REF] Rodman | The Taxonomic Impediment Overcome: NSF's Partnerships for Enhancing Expertise in Taxonomy (PEET) as a Model[END_REF], and welcomed as such by taxonomists. It thus adds to the toolkit of taxonomy, which continues its development as a synergic discipline involving morphological taxonomists, field ecologists, naturalists, and statisticians [START_REF] Knapp | Taxonomy as a team sport[END_REF]. Integrative taxonomy, used for many decades by taxonomists but only recently formalized concomitantly with the molecular revolution, is organised following a three-step workflow (see also [START_REF] Evenhuis | Helping solve the "other" taxonomic impediment: completing the eight steps to total enlightenment and taxonomic Nirvana[END_REF]: first, we need to accumulate data on numerous specimens (from various types of data: DNA, morphology, ecology…); second, we need to circumscribe groups of organisms using concepts that ensure that these groups correspond to species (this second step may be coupled with the first, as biological data are continuously accumulated and species hypotheses re-discussed); and third, we need to provide a species description, i.e. a diagnosis and a name for the species recognized as new.

Naming new species is a fundamental step when describing biodiversity and is the only way to ensure that scientists are talking about the same entity, and that all the data linked to conspecific specimens but produced by different researchers (or amateurs) can be associated in a comparative analysis [START_REF] Patterson | Names are key to the big new biology[END_REF][START_REF] Satler | Multilocus species delimitation in a complex of morphologically conserved trapdoor spiders (Mygalomorphae, Antrodiaetidae, Aliatypus)[END_REF][START_REF] Schlick-Steiner | Without morphology, cryptic species stay in taxonomic crypsis following discovery[END_REF]. Not linking biological data (should they be molecular, morphological, or ecological) to a formal species name will result in these data losing tremendous value [START_REF] Goldstein | Integrating DNA barcode data and taxonomic practice: Determination, discovery, and description[END_REF]. Indeed, when authors publish data on entities that are not defined within the framework of a referencing system (e.g. solely identified by an alphanumeric label), they make it very difficult for other authors to build on these data. The best example is the need for taxa to be named to have a chance to be listed in an endangered species list and to benefit from a conservation program: no name, no surviving [START_REF] Mace | The role of taxonomy in species conservation[END_REF]).

Beyond the need for communication among scientists, names are also key to communicating with non-scientist audiences.

While it is now widely recognized that integrating several lines of evidence is the most efficient and theoretically grounded way to delimit new species (e.g. [START_REF] De Queiroz | Species concepts and species delimitation[END_REF][START_REF] Schlick-Steiner | Integrative taxonomy: a multisource approach to exploring biodiversity[END_REF][START_REF] Yeates | Integrative taxonomy, or iterative taxonomy?[END_REF], the formal naming of new entities may have become decoupled from species delimitation. Indeed, we noted that in several cases new delimited species were not accompanied by formal species description (see also [START_REF] Goldstein | Integrating DNA barcode data and taxonomic practice: Determination, discovery, and description[END_REF]. The aim of this article is therefore to test the hypothesis that integrative taxonomy, as defined in 2005 [START_REF] Dayrat | Towards integrative taxonomy[END_REF][START_REF] Will | The perils of DNA Barcoding and the need for integrative taxonomy[END_REF], and in particular the use of molecular data, helped to alleviate the taxonomic impediment by delimiting and describing new species. We reviewed part of the "integrative taxonomy" literature of the last eight years (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) and tested if authors that delimit new species also name them. We also looked at how the number and type of characters used, across different taxa, varies across articles.

MATERIALS AND METHODS

We performed a literature survey using the Web of Science research tool, limited to the scientific articles published between 2006 and 2013, and using the following keywords: "Integrative Taxonom*" in TITLE OR TOPIC OR "Species boundar*" in TITLE OR "Integrative delineation" in TITLE OR "Integrative delimitation" in TITLE OR "Species delineation" in TITLE OR "Species delimitation" in TITLE. This timespan (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013) was chosen because it follows the formal introduction of modern integrative taxonomy. We acknowledge that older articles also include integrative taxonomic approaches (e.g. [START_REF] Hogan | Systematic and Taxonomic Implications of Karyotypic, Electrophoretic, and Mitochondrial-DNA Variation in Peromyscus from the Pacific Northwest[END_REF]see Turrill, 1938), but the lower limit for the literature survey would have been chosen arbitrarily. The keywords helped limit the size of our survey while focusing on integrative taxonomy papers, as other keywords (e.g. "new species") or options (e.g." species delineation" in TOPIC and not only in TITLE) led to a much higher number of articles (several thousands).

From the resulting list of 666 articles, we removed 172 articles that did not fit the context of this review (i.e. methodological and theoretical articles, review studies that did not perform any species delimitation, studies that re-analyzed published data, and studies that focused on supra-or infra-species levels only). For the 494 remaining articles, we extracted data on the number of delimited species, the number of new species delimited, the number of new species described (and, when given, the reason(s) why new species were not described), and the studied taxon. We did not attempt to interpret published results ourselves, but recorded the number of species (delimited, new and described) as reported by the authors of each paper. We also recorded the type of data and methods used to delimit species: molecular data, morphology (including anatomy, cytology…), ecology (including phenology, niche modelling…), cross tests, behavior (e.g. call songs) and other miscellaneous methods (e.g. caryology, chemical data, presence of endosymbionts, etc…). We considered the geographical distribution to be implicitly used in all articles. The resulting table is presented in Online Appendix 1. Contingency tables were analysed using Fisher's Exact Test, given the relatively small number of observations. We investigated journal editorial policies on including formal taxonomic descriptions into articles. As a proxy for editorial policies, we recorded whether journals that published articles in which new animals species were delimited also published formal descriptions, within three time periods (1864-2004, 2005-2010, 2011-2013), using the "Systematics Controlled Terms" feature in the Zoological Records database (Online Appendix 2). We recorded the impact factor of these journals between 2005 and 2010 to investigate whether there is a link between the inclusion of formal descriptions in papers and impact factor (Online Appendix 2). Indeed, there is a strong incentive for researchers to publish in highimpact journals (e.g. [START_REF] Casadevall | Causes for the Persistence of Impact Factor Mania[END_REF][START_REF] Casadevall | Causes for the Persistence of Impact Factor Mania[END_REF]see Werner, 2006); if these journals do not welcome descriptions, authors may be tempted to submit their contributions without descriptions to high-impact journals rather than submitting their integrative work, including descriptions, to lower-impact journals. We chose these time periods as a trade-off between the number of articles published within time groups for each journal and the variance of the impact factor (the longer the time period, the larger the variance in impact factor). Also, we noted from personal experience that narrow time periods would be preferred as editorial policies may change relatively rapidly. We used a one-tail Wilcoxon test to evaluate the null hypothesis that journals including formal species descriptions do not have lower impact factors than journals that do not. All statistical tests were performed in R (R Core Team 2014).

RESULTS

The 494 articles were published in 150 different journals, over half of which published a single article from our list, and 4 of which (Molecular Phylogenetics and Evolution, Zootaxa, PLOS ONE and the Zoological Journal of the Linnean Society) published over 20 articles. The number of articles published each year steadily increased from 2006 (20 articles) to 2013 (118 articles) (Fig. 1). Most major lineages of organisms are represented, but the number of articles varies greatly among groups (Fig. 2a). Among hexapods, hymenopterans, lepidopterans, coleopterans and dipterans were the taxon of interest for 19-26 articles each (Fig. 2b); among vertebrates, amphibians (43 articles) and lepidosaurians (43) are the most studied taxa, followed by actinopterygians (22), mammals (19), birds (10), chondrichtyans (4), and crocodilians and turtles (1 each) (Fig. 2c). In all taxonomic groups represented by more than five articles, molecular data were analyzed in 100% of the articles, except for embryophytes (71.6%), vertebrates (88.8%), chelicerates (94.7%), hexapods (92.6%) and annelids (90%). One possible explanation for the lower prevalence of molecular data in these taxonomic groups is that morphological characters may generally be more easily formalized, and congruent with molecular data (compared to other groups in which there might be fewer -or more plastic-types of characters available to taxonomists, such as some cnidarians, e.g. [START_REF] Mcfadden | Molecular phylogenetic insights into the evolution of Octocorallia: A review[END_REF].

Almost half (47.2%) of the studies based their species delimitation on two types of characters (DNA and morphology in 89.7% of them), 15.2% three types of characters and only 2.2% four types of characters. More surprisingly, 35.4% of the studies used only one type of character (molecular data for 74.9% of them). This reflects a bias in our survey (the keywords we choose also targeted non-integrative taxonomy), but also an inappropriate use of the "integrative taxonomy" terminology by some authors. Indeed, the "integrative" aspect of the approach is restricted in these articles to the use of different methods and/or criteria of species delimitation, and not to the use of different types of characters. The number of types of characters used varied significantly according to the year of publication when all studies were considered, and non-significantly when only studies with new species delimitations were considered, suggesting a weak tendency toward more integrated species delimitation over the years (Fisher's Exact Test: p=0.019 and p=0.16, respectively; Table 1). A trend toward using preferentially two types of characters in 2012-2013 was detected among papers describing at least one new species (Fisher's Exact Test: p=0.0002; Table 1). A concurrent decline in the number of studies using a single type of character was detected, the prevalence of such studies falling from 44.7% between 2006 and 2010 to 29.3% between 2011 and 2013 (Fisher's Exact Test: p=0.0005). Finally, the proportion of articles using molecular data and/or morphological data did not vary significantly from 2006 to 2013 (Fisher's Exact Test: p=0.99; Table 2).

We then focused on comparing studies that did not delimit any new species, studies that delimited new species without describing all of them, and studies that delimited new species and described at least one of them. We decided to compare the number of studies in these categories, rather than the number of delimited and described species, because the number of species delimitation and description per study was highly variable. Indeed, among the 139 studies that described at least one species, 135 described fewer than ten species, 3 described between 10 and 16 species, and one described 101 species [START_REF] Riedel | One hundred and one new species of Trigonopterus weevils from New Guinea[END_REF].

A total of 240 studies did not delimit any new species, but confirmed the current alpha taxonomy or extracted previously described species from synonymy (on the contrary, new species for which names were available in the literature but never considered as a valid, such as forms, varieties or subspecies, were counted as new). In the remaining studies, 1346 new species were delimited (for studies providing a range of putatively new species, we used the lower number reported by the authors), representing 18.7% of the total number of delimited species in the 494 studies (7205). Among the studies that delimited new species, 125 delimited but did not describe at least one new species and 139 described at least one new species (in 10 studies some new species were described and others not). The ratio of Described over Undescribed Species (hereon called the "DUS" ratio, more specifically calculated as the number of studies that delimited new species and described at least one new species divided by the number of studies that delimited new species and did not describe at least one new species) was approximately of 1.11 for the whole dataset and did not change significantly from 2006 to 2013 (Fisher's Exact Test: p=0.91). The DUS ratio varies non significantly among taxa: when considering only the taxa represented by more than five studies, the ratio varied from 0.44 for molluscs to 4 for platyhelminthes (these differences are largely driven by small sample sizes; Fisher's Exact Test: p=0.67 Table 3). Finally, the DUS ratio also varies with the number and the type of characters analyzed. The ratio is 0.29 when only one type of character is analyzed, 1.54 with two types of characters and 1.70 with three types of characters (only four studies found new species with four different types of characters; DUS = 1.33). Studies describing new species were more likely to use two types of characters or more, compared to studies that delimited new species without describing all of them (Fisher's Exact Test: p<0.001), confirming that taxonomists prefer to have multiple sources of information to describe species. The DUS ratio is 1.05 when molecular data (alone or among other types of data) are analysed, 1.87 when morphological data are analysed, and 1.22 when other types of characters are analysed, and these differences were statistically significant (Fisher's Exact Test: p=0.009).

Among the 150 journals of our sample, 84 delineated new species. Our Impact Factor analysis, using Zoological Record, focused on 73 zoological journals. Among these journals, 90.4% published descriptions from 1864 to 2013, 9.6% never published descriptions within that period, and 16.4% stopped publishing descriptions within that period (either from 2005 onward, or from 2011 onward). The average impact factor of journals with species delimitation but without descriptions was significantly higher than that of journals publishing formal descriptions during the 2005-2013 periods (one-tail Wilcoxon: n=50, W = 72, p = 0.038).

DISCUSSION

As reported previously [START_REF] Gaston | Taxonomy of taxonomists[END_REF], taxonomy studies are strongly biased towards vertebrates (here, they accounted for 29% of the articles we reviewed), even though this taxon accounts for only ~3% of the described diversity on earth [START_REF] Chapman | Numbers of Living Species in Australia and the World, 2nd Edition[END_REF][START_REF] Zhang | Animal biodiversity: an introduction to higher-level classification and taxonomic richness[END_REF]) and probably has the highest ratio of described over undescribedspecies. Most of the studies on vertebrates actually focus on groups that still encompass high levels of unknown species, such as amphibians or lepidosaurians. Integrative taxonomy and molecular taxonomy are linked in 90% of the studies, confirming that the formal definition of integrative taxonomy in 2005 is probably linked to the concomitant molecular revolution (as explained in the introduction). In the literature, both have often been associated with an inflation in the number of new species, artificial or not [START_REF] Isaac | Taxonomic inflation: its influence on macroecology and conservation[END_REF][START_REF] Knapp | Taxonomic inflation, species concepts and global species lists[END_REF][START_REF] Sangster | Increasing numbers of bird species result from taxonomic progress, not taxonomic inflation[END_REF]). Our results suggest that this is not always true: 48.7% of studies did not detect new species, and some authors actually proposed to reduce the number of valid species in their taxon of interest.

When new species are discovered, however, they are not systematically described (in 46.1% of the articles), thus leaving the new species unnamed. In these cases, several justifications for not describing have been put forth by the authors, and we propose a few more. The first reason is the lack of support for the species hypotheses (given in 72.2% of the articles that do provide a justification). In taxa for which the proportion of unknown species is greater than the number of described species, difficulties are linked to the fact that nobody has ever proposed species hypotheses. Exploratory methods are therefore needed, either based on traditional morphological characters or on molecular markers (several DNA-based methods are now available: e.g. [START_REF] Kekkonen | DNA barcode-based delineation of putative species: efficient start for taxonomic workflows[END_REF][START_REF] Pons | Sequence-based species delimitation for the DNA taxonomy of undescribed insects[END_REF][START_REF] Puillandre | ABGD, Automatic Barcode Gap Discovery for primary species delimitation[END_REF][START_REF] Ratnasingham | A DNA-based registry for all animal species: the Barcode Index Number (BIN) system[END_REF][START_REF] Zhang | A general species delimitation method with applications to phylogenetic placments[END_REF]. This exploratory step is generally efficient to detect highly divergent lineages that most probably correspond to different species. However, it is more difficult to estimate the number of species in clades with many closely-related species because many might be in "grey zones" (i.e. parts of the tree of life where the speciation process is ongoing and where different types of characters and criteria will not provide the same answer, as defined in [START_REF] De Queiroz | Species concepts and species delimitation[END_REF]. This situation is encountered in well-studied groups (e.g. some vertebrates and flowering plants), for which what was easy to recognize as species has been described, and challenging species complexes remain to be disentangled (e.g. in orchids, [START_REF] Pessoa | Integrating different tools to disentangle species complexes: A case study in Epidendrum (Orchidaceae)[END_REF]. Several multi-locus and coalescent-based methods now exist to help delimit species in the grey zone (reviewed in [START_REF] Camargo | Species delimitation: a decade after the renaissance[END_REF][START_REF] Carstens | How to fail at species delimitation[END_REF][START_REF] Fujita | Coalescentbased species delimitation in an integrative taxonomy[END_REF], and see [START_REF] Leaché | Species delimitation using genome-wide SNP data[END_REF].

In any case, species are and remain, by definition (de Queiroz 2007; [START_REF] Samadi | The tree, the network, and the species[END_REF], only hypotheses, and these hypotheses can be more or less supported. In an integrative context, the number of arguments, data and criteria (including the need for additional specimens) needed for defining new species and their hierarchy can vary depending on the taxon considered or the approach applied, and turning species hypotheses into a formally described species remains a taxonomist-dependent decision, sometimes difficult to make. It should also be noted that, even if test cross experiments are generally considered as the most robust criteria of species delimitation (following the conceptual framework established by de Queiroz 2007), it is rarely used (16 studies only), probably because of the difficulty to set up such tests for most non-model organisms.

However, in other cases, the species hypothesis is highly supported by numerous lines of evidence, but remains undescribed. Consequently, other reasons should be invoked. For example, it could be the choice of the author to not describe the species in the article where it has been delimitated, but in a forthcoming article (reason given in 24.1% of the studies providing a justification for not describing). This can be motivated by the fact that the authors wish to present additional data that are beyond the scope of the present article (e.g. [START_REF] Pante | Use of RAD sequencing for delimiting species[END_REF]. It can also be explained by the pressure of publishing more papers, driving many authors to publish in several articles what could be published in one (i.e. submitting their work as "least publishable units"). Then, taxonomists might refrain from describing a species if no morphological differences were found with its sister-species, although there is no reason to think that all "good" species will exhibit morphological differences [START_REF] Fujita | A coalescent perspective on delimiting and naming species: a reply to Bauer et al[END_REF]. Diagnosing a new species using only DNA characters is possible, but not yet widespread [START_REF] Cook | Need morphology always be required for new species descriptions?[END_REF], especially in animals, although molecular data are increasingly included in species descriptions [START_REF] Goldstein | Integrating DNA barcode data and taxonomic practice: Determination, discovery, and description[END_REF]. Actually, a substantial part (35.4%) of the articles we reviewed delimited species with only one type of character. However, even if only one type of character is used, it generally remains associated with the use of different loci, or different methods, or different criteria (pheneticgenetic distances, phylogeneticreciprocal monophyly, reproductive isolationindependent molecular markers).

Another reason for not naming new species is the unwillingness of some scientists (e.g. molecular systematists) to describe species [START_REF] Satler | Multilocus species delimitation in a complex of morphologically conserved trapdoor spiders (Mygalomorphae, Antrodiaetidae, Aliatypus)[END_REF]. A formal description should follow strict nomenclatural rules dictated by the codes of nomenclature, and writing a species description is in itself an exercise that necessitates training that is rarely proposed in modern biological classes [START_REF] Pearson | Recovery plan for the endangered taxonomy profession[END_REF][START_REF] Fonseca | Integrative taxonomy in two free-living nematode species complexes[END_REF] and [START_REF] Leliaert | DNA taxonomy in morphologically plastic taxa: Algorithmic species delimitation in the Boodlea complex (Chlorophyta: Cladophorales)[END_REF] also highlighted the need of sequencing type-specimens to correctly attribute available species names or name new species [START_REF] Puillandre | Barcoding type specimens helps to identify synonyms and an unnamed new species in Eumunida Smith, 1883 (Decapoda : Eumunididae)[END_REF]. Furthermore, proposing a new name necessitates, at the very least, a literature review of all the species-level names available [START_REF] Bertrand | Taxonomic surrogacy in biodiversity assessments, and the meaning of Linnaean ranks[END_REF][START_REF] Jansen | Integrative inventory of Bolivia's lowland anurans reveals hidden diversity[END_REF][START_REF] Minelli | The status of taxonomic literature[END_REF], including names proposed in an old and antiquated literature, sometimes not written in English [START_REF] Balakrishnan | Species concepts, species boundaries and species identification: a view from the Tropics[END_REF][START_REF] Godfray | Challenges for taxonomy[END_REF]. Naming new species also necessitates comparison with existing type material, often requiring visits to museums. Non-taxonomists are often frustrated by the over-abundance of redundant species names (i.e. species that have multiple synonymous names) as well as doubtful names [START_REF] Dayrat | Towards integrative taxonomy[END_REF], which makes the assignation of species names to welldelineated entities even more difficult. Once again, this exercise requires excellent knowledge of the group, contrary to a genetic approach which is basically the same in mammals and in plants, and can be time consuming [START_REF] Miller | DNA barcoding and the renaissance of taxonomy[END_REF]. Other systems have been proposed, some designed to replace the Linnean System [START_REF] Dayrat | Species names in the PhyloCode: the approach adopted by the international society for phylogenetic nomenclature[END_REF][START_REF] Vences | To name or not to name: Criteria to promote economy of change in Linnaean classification schemes[END_REF], others only proposing interim systems before full description following the Linnean System [START_REF] Ratnasingham | A DNA-based registry for all animal species: the Barcode Index Number (BIN) system[END_REF][START_REF] Schindel | Provisional nomenclature: the on-ramp to taxonomic names[END_REF], to, at least partly, solve the difficulties linked to describing new species and to reduce "shelf-time" [START_REF] Fontaine | 21 years of shelf life between discovery and description of new species[END_REF].

However, none of these alternate referencing systems have been as widely accepted and applied as the Linnean system.

Finally, publishing species descriptions in high impact factor journals is in general more difficult, because editors may be reluctant to publish species descriptions, especially when they are numerous and long (the number of pages is generally very limited in these journals). In this study, we showed that among the 23 journals that included at least one study in which new species were delimited but not described, 6 of them have never published species descriptions, based on Zoological Records, and 6 did not publish species descriptions after 2004; on average, journals including descriptions had a lower impact factor than the journals that do not. Because of the publication pressure, authors will almost automatically prefer to publish in high impact factor journals, even at the price of removing the species descriptions [START_REF] Agnarsson | Taxonomy in a changing world: seeking solutions for a science in crisis[END_REF][START_REF] Costello | Motivating online publication of data[END_REF]. Scientists all know the importance in the current system to have articles in journals with high-impact factors, and thus most of them do not spend their time in writing articles that will not be rewarded [START_REF] Minelli | The status of taxonomic literature[END_REF].

CONCLUSION

The increase in the number of articles recorded between 2006 and 2013, and the large range of journals represented in our review reflects the high dynamism of the taxonomic community. In addition, the increase in the proportion of papers using multiple lines of evidence underlines the success of the modern integrative taxonomy approach, as defined in 2005. The positive relationship between the number of different types of characters used for delimitation, which can be seen as a proxy of the degree of integration, and the DUS ratio also supports the idea that integrative taxonomy contributes to a better understanding of biodiversity. However, the 446 species described in the reviewed articles are only a drop in the ocean of new species described in the same period (85,000, if considering a mean of 17,000 new species described each yearhttp://www.esf.edu/species/SOS.htm).

Nevertheless, this sample reflects the fact that modern integrative taxonomy as formalized in 2005 (thus not considering the pre-2005 articles that delimited and described species using an integrative taxonomy-like approach), is, at least for the moment, not a very efficient solution to the taxonomic impediment. Most new species seem to be described without applying an integrative taxonomy approach, and most new species are still described without the help of molecular data: a screening of 200 articles published in 2013, obtained with the keywords "Taxonomy" in TOPIC AND "sp nov" in SYSTEMATICS in Zoological Records revealed that only 18 of them mentioned the use of molecular data in the abstract. This would suggest that most species are thus still described using morphological characters only. The "molecular revolution" that was announced after the renewal of the taxonomy in the early 2000s, largely associated with the emergence of the integrative taxonomy approach, has apparently not happened yet. We are convinced that integrative taxonomy, when associated with formal species description, is a good way to improve the quality of species hypotheses and associated descriptions, and should therefore be encouraged. However, and contrary to a barcoding approach that can perhaps accelerate the rate of species discovery (but not improve the quality of the species hypotheses nor the rate of species description; e.g. [START_REF] Will | The perils of DNA Barcoding and the need for integrative taxonomy[END_REF] "Other taxa:" taxa for which fewer than five articles were analysed.

  , integrative taxonomy did not accelerate the rate of species description between 2006 and 2013. Efforts must be made by authors to seek training or new collaborations to formalize their species delimitation, and to avoid delaying new species descriptions for reasons associated with impact factors. Editors may help the naming of newly delimited species by encouraging the publication of species descriptions. Editorial policies could, for instance, impose that new delimitation be either accompanied by formal descriptions or a strong justification for not describing. Research institutions and funding agencies may encourage the naming of newly delimited species by recognizing taxonomic work as a foundation of biological research, and refrain from putting too much emphasis on impact factors when evaluating scientists.

Figure 1 :

 1 Figure captions:

Figure 2 :

 2 Figure 2: Number of articles per taxa (a), with emphasis on hexapods (b) and vertebrates (c).

ACKNOWLEDGMENTS

The authors thank Jean-François Flot, organizer of the Species Delimitation Symposium, and the Society of Systematic Biologists, which funded the participation of NP to the 2013 Evolution meeting. This work beneficiated from the project CONOTAX, funded by the French ANR (ANR-13-JSV7-0013-01). Amélia Viricel, Philippe Bouchet and Sarah Samadi are also thanked for their helpful comments.

FUNDING

This work was partly supported by the project CONOTAX, funded by the French "Agence Nationale de la Recherche" (grant number ANR-13-JSV7-0013-01). Salary for E.P. was covered by a grant to the Poitou-Charentes region (Contrat de Projet-État-Région 2007-2013) and by a grant from the Fond Européen de Développement Régional.

Online Appendix 2: List of the journals in which new species were delineated. Editorial policies on including formal taxonomic descriptions to articles and impact factors were investigated before 2005, between 2005-2010, and 2011-2014. Y=Yes, N=No, NA=Not Available and IF=Impact Factor.


N Cohen

Zs Tuza

Induced decompositions of highly dense graphs

Given two graphs F and G, an induced F -decomposition of G is a partition of E(G) into induced subgraphs isomorphic to F . Bondy and Szwarcfiter [J. Graph Theory,

Introduction

Given two graphs F and G, an F -decomposition of G is a partition of the edges of G into subgraphs isomorphic to F . It is called an induced decomposition if the subgraphs are induced copies of F . Starting from Section 2 we shall only deal with the induced notion of these terms, and occasionally omit the word 'induced' hoping to not cause confusion.

In [START_REF] Bondy | Induced decompositions of graphs[END_REF], Bondy and Szwarcfiter defined the function ex * (n, F ) as the maximum number of edges in a graph on n vertices that admits an induced F -decomposition. They determined the exact value of ex * (n, F ) (with arithmetic restrictions on n in some cases) when F is one of the following graphs: C 4 (the cycle of length four), K 1 + K 2 (the graph with three vertices and one edge), 2K 1 + K 2 (the graph with four vertices and one edge), K 1 + K 1,2 (the graph with four vertices and two intersecting edges), K 1,k (a star), or a complete r-partite graph with the same number k of vertices in each part. They also proved that ex * (n, K - 4 ) ≤ n 2 -n 5 and ex * (5n, K - 4 ) ≥ 5n 2 -10n, where K - 4 = K 4e is the graph with four vertices and five edges.

Besides those graphs, the value of ex * (n, F ) is known for some values of n when F is a complete graph. Indeed, as any complete subgraph is necessarily induced, the equality ex * (n, K k ) = n 2 is equivalent to the existence of an (n, k, 1) BIBD (see [START_REF]Handbook of Combinatorial Designs[END_REF] for such values when k ≤ 9). In particular, for k = 3, the existence of Steiner Triple Systems gives ex * (n, K 3 ) = n 2 when n ≡ 1, 3 (mod 6). More generally, a theorem of Wilson [START_REF] Wilson | An existence theory for pairwise balanced designs, III: Proof of the existence conjectures[END_REF] implies that ex * (n,

K k ) = n 2 -O(n).
Theorem 1 (Wilson [START_REF] Wilson | An existence theory for pairwise balanced designs, III: Proof of the existence conjectures[END_REF]). For any integer k and sufficiently large integer n ≥ n k , the complete graph K n can be decomposed into edge-disjoint copies of K k if and only if k 2 divides n 2 and k -1 divides n -1.

For intermediate values of n, which violate the divisibility conditions, Chee et al. [START_REF] Chee | Covering and packing for pairs[END_REF] recently proved that the number of K k subgraphs in a largest edge-disjoint packing is at most an additive constant c = c(k) away from

n k n-1 k-1 .
Another strong result of Wilson [START_REF] Wilson | Decomposition of complete graphs into subgraphs isomorphic to a given graph[END_REF] deals with the F -decomposition of large complete graphs; it is important to emphasize, however, that these decompositions are not induced decompositions.

Theorem 2 (Wilson [17]). For any graph F and sufficiently large integer n, the complete graph K n can be decomposed into edge-disjoint copies of F if and only if |E(F )| divides n 2 and n -1 is divisible by the greatest common divisor of the degree sequence of F .

In sharp contrast to the classical extremal theory of Turán-type problems, we prove that the asymptotic equality ex * (n, F ) = n 2o(n 2 ) holds for all graphs F as n → ∞ (Theorem 5). Moreover, for some small graphs F mentioned in [START_REF] Bondy | Induced decompositions of graphs[END_REF] for which the exact value of ex * (n, F ) is not settled so far, we provide explicit constructions of dense graphs admitting induced F -decompositions. Those F include 2K 2 (the perfect matching on 4 vertices -Theorem 3), K + 1,3 (the 'paw', i.e. a claw graph augmented with an edge), P 3 (the path of length two) and C 6 (the cycle of length six), the latter three given in Corollary 1.

The small graphs are treated in Section 2, while the general Theorem 5 is proved in Section 3.

It is important to note that several decades ago Frankl and Füredi [START_REF] Frankl | Colored packing of sets[END_REF] studied a very general problem on hypergraph packing, which is strongly related to the one investigated here. Given a family H of t-subsets of a k-set, they call a family F of k-subsets of a v-set a (v, k, H)-packing if for each F ∈ F there is a copy H F of H such that the t-element sets of F corresponding to H F are covered only by F . The main result of [START_REF] Frankl | Colored packing of sets[END_REF] -proved by probabilistic methods -states that, for every fixed k and H, the largest size of a (v, k, H)-packing is asymptotically v t /|H| as v → ∞.

Induced decompositions into some small graphs

In this section we give constructions of dense graphs decomposable into induced copies of the graphs 2K 2 , K + 1,3 , P 3 , and C 6 . Our constructions begin with the Kneser graphs, which are good candidates for 2K 2 -decompositions. This approach is strong enough to verify the lower bound n 2o(n 2 ) on ex * (n, 2K 2 ), nevertheless the bound obtained will be improvable by a refinement of the method. We use the standard notation [p] := {1, 2, . . . , p}.

Definition. The Kneser graph KG p k has the vertex set

V (KG p k ) = [p] k = {S : S ⊆ [p] such that |S| = k}
where two vertices S, S ′ are adjacent if and only if S ∩ S ′ = ∅.

Theorem 3. We have ex * (n, 2K 2 ) = n 2 -O(n 5
3 ).

Proof. KG 6 3 is a 1-regular graph with 10 edges, and therefore admits an induced 2K 2 -decomposition. More generally KG p 3 is a p-3 3 -regular graph with Decomposition results for other small graphs like P 3 or K + 1,3 seem to be not obtainable using this family of graphs. While there may exist an instance of KG p 3 admitting a decomposition into P 3 , what one would need is a way to ensure that all of them -or most of them -do so when p grows large; but the technique above does not work, as the copies of KG p 3 [S] would not be disjoint anymore. We now give an alternative construction achieving precisely that, e.g. when F is one of P 3 , C 6 , or K + 1,3 .

Definition. The Bipartite Kneser Graph BK p1 ,p2 is defined over the set of

p 1 p 2 vertices 1 V (BK p 1 ,p 2 ) = {v : v = {v 1 , v 2 } with v 1 ∈ [p 1 ] 1 and v 2 ∈ [p 2 ] 2 },
where

[p 1 ] 1 and [p 2 ] 2 are disjoint copies of [p 1 ] and [p 2 ], and two vertices v, v ′ are adjacent if and only if v ∩ v ′ = ∅.
Remark. The graph BK p 1 ,p 2 is isomorphic to L(K p 1 ,p 2 ), the complement of the line graph of a complete bipartite graph on p 1 + p 2 vertices.

We prove in Theorem 4 that a Bipartite Kneser Graph decomposes arbitrarily larger ones. This will be sufficient to obtain that ex * (n,

F ) = n 2 -O(n 3
2 ) holds for F = 2K 2 , P 3 , C 6 , K + 1,3 , as these graphs decompose small Bipartite Kneser Graphs. Indeed, 2K 2 ∼ = BK 2,2 , P 3 decomposes C 6 and C 6 ∼ = BK 3,2 , and K + 1,3 decomposes BK 4,3 as will be shown in Lemma 1 below.

Theorem 4. The graph BK p 1 ,p 2 admits an induced BK a 1 ,a 2 -decomposition whenever K p 1 and K p 2 respectively admit a K a 1 -decomposition and a K a 2 -decomposition.

Proof. Let S 1 and S 2 be respectively a subset of [p 1 ] 1 or cardinality a 1 and a subset of [p 2 ] 2 of cardinality a 2 , and let

BK p 1 ,p 2 [S 1 , S 2 ] denote the subgraph induced in BK p 1 ,p 2 by the vertices {v = {v 1 , v 2 } ∈ BK p 1 ,p 2 : v 1 ∈ S 1 , v 2 ∈ S 2 }. For any choice of sets S 1 and S 2 , BK p 1 ,p 2 [S 1 , S 2 ] is isomorphic to BK a 1 ,a 2 .
By assumption, there exists for i = 1, 2 a collection C i of sets of size a i such that any two elements v i , v ′ i of [p i ] i appear together in exactly one element of C i . We can produce an induced BK a 1 ,a 2 -decomposition of BK p 1 ,p 2 by considering the collection

{BK p 1 ,p 2 [S 1 , S 2 ] : S 1 ∈ C 1 , S 2 ∈ C 2 }. Indeed, for each edge between v = {v 1 , v 2 } and v ′ = {v ′ 1 , v ′ 2 } there exists exactly one set S 1 ∈ C 1 containing both v 1 and v ′ 1 , and one S 2 ∈ C 2 containing both v 2 and v ′ 2 .
Therefore, the collection is the desired induced decomposition.

In particular, 2K 2 ∼ = BK 2,2 decomposes BK p 1 ,p 2 for any choice of p 1 , p 2 ≥ 2.

Corollary 1. For every fixed p 1 and p 2 we have ex * (n,

BK p 1 ,p 2 ) = n 2 -O(n 3/2 ). Moreover, by transitivity, ex * (n, F ) = n 2 -O(n 3/2 ) for F = 2K 2 , P 3 , C 6 , K + 1,3 .
Proof. By Theorem 1, for i = 1, 2, there exists constants c i such that K c i k admits a K a i -decomposition for any integer k. Hence, BK c 1 k,c 2 k admits an induced BK a 1 ,a 2 -decomposition for any integer k. As k gets large, the number of nonedges in BK c 1 k,c 2 k grows with n 3/2 (where n = c 1 c 2 k 2 ), while the gap between

(c 1 k, c 2 k) and (c 1 (k + 1), c 2 (k + 1)) adds an error term of O(n) for intermediate values of n.
Besides, we quote from Corollary 2 of [START_REF] Bondy | Induced decompositions of graphs[END_REF] that ex * (n, 2K 2 ) ≤ n 2 -Θ(n 3/2 ). Since C 6 decomposes into induced copies of 2K 2 , this upper bound implies ex * (n, C 6 ) ≤ n 2 -Θ(n 3/2 ), too. Hence, combining these inequalities with our Corollary 1 we obtain:

Corollary 2. We have ex * (n, 2K 2 ) = n 2 -Θ(n 3/2 ) and ex * (n, C 6 ) = n 2 - Θ(n 3/2 ).
At the end of this section we prove a lemma that completes the proof of Corollary 1 for K + 1,3 .

Lemma 1. The graph BK 4,3 admits an induced K + 1,3 -decomposition.

Proof. The following decomposition was obtained with the software Sage [START_REF] Stein | Sage Mathematics Software (Version 4.6.2)[END_REF], asked to compute a maximum independent set in the graph of all induced K + 1,3

subgraphs of BK 4,3 , two of them being adjacent when they share an edge. It produced a list of 9 edge-disjoint graphs with 4 edges, each of them being isomorphic to K + 1,3 , which partitions the 36 edges of BK 4,3 . Alternatively, if we label the columns with {a, b, c, d} and the rows with {1, 2, 3} (1a being the bottom-left corner and 3d the top-right one), the decomposition is given by the graphs induced by the following sets of vertices: {1a, 2d, 3b, 3d} {1c, 2b, 3d, 2d} {2c, 1d, 3b, 3d} {2a, 1d, 3c, 3d} {1a, 2b, 3c, 2c} {3a, 1b, 2c, 1c} {1b, 2d, 3c, 3d} {2a, 1c, 3b, 1b} {3a, 1d, 2b, 2d}

Induced decomposition into general graphs

This section is devoted to the proof of the following general result.

Theorem 5. We have ex * (n, F ) = n 2o(n 2 ) for any graph F .

Let us begin with a preliminary remark. Although the family of Bipartite Kneser Graphs is sufficient to obtain decomposition results for some graphs, it cannot be hoped to provide a proof for all graphs. Indeed, Bipartite Kneser Graphs are "complements of line graphs of bipartite graphs", and for this reason none of them contains e.g. the complement of the claw graph (i.e. the graph K 1 + K 3 , cf. Fig. 1) as an induced subgraph. The second drawback comes from the method itself: in order to deduce anything on the value of the ex * function, we need to prove that a graph decomposes a Bipartite Kneser Graph, an operation which we have no specific tool for. We now enlarge the graph class once more, and prove that any graph is an induced subgraph of some graph in this family (Lemma 2).

Definition. The Multipartite Kneser Graph MK p 1 ,...,p k is defined over the set of

k i=1 p i vertices 2 V (MK p 1 ,...,p k ) = [p 1 ] 1 × • • • × [p k ] k = {v = {v 1 , . . . , v k } : v i ∈ [p i ] i }.
Two vertices of MK p 1 ,...,p k are adjacent if and only if their corresponding sets of size k are disjoint. We denote by MK p×k the graph MK p,...,p on p k vertices (see Fig. 1). Remark. As a generalization of the bipartite case, the graph MK p 1 ,...,p k is isomorphic to L(K (k) p 1 ,...,p k ), the complement of the line graph (intersection graph) of a complete k-partite hypergraph whose i th vertex class has p i vertices for i = 1, 2, . . . , k.

Lemma 2. Any graph F is an induced subgraph of all MK p×k for sufficiently large p and k.

Proof. We prove that it is already sufficient to chose p = |V (F )| and k = |E(F )|. This implies that also any larger values of p and k satisfy the requirements. Let us 2 Notation here is analogous to that for bipartite Kneser graphs. The sets [p 1 ] 1 , . . . , [p k ] k are mutually disjoint copies of [p 1 ], . . . , [p k ], respectively. This allows us to view v = {v 1 , . . . , v k } as a k-element set rather than a k-tuple or a vector of length k. For instance, v ∩ v ′ then then simply means intersection and not the more complicated notion of the set of coordinates in which two k-tuples agree.

note that usually much smaller values work, too. 3Assuming that V (F ) = {1, . . . , p} and E(F ) = {e 1 , . . . , e k } (the set of nonedges of F ), we consider the set {v 1 , . . . , v p } of |V (F )| vertices of MK p×k , where

• If i is an endpoint of e j = ii ′ , we set the jth component v i j of vertex v i to min(i, i ′ ) implying that v i and v i ′ are not disjoint sets.

• If i is not an endpoint of e j , the jth component v i j of vertex v i is equal to i. In such a family, two vertices v i and v i ′ correspond to disjoint sets if and only if they are adjacent in F , ensuring that this collection of vertices induces a copy of F in MK p×k .

Considering the symmetry properties of the MK graphs, one can already expect to find many disjoints instances of F inside of large instances. It is quite unlikely, though, that for a fixed F all sufficiently large graphs MK p×k would admit an induced F -decomposition, if only because of arithmetical constraints. As it is also increasingly difficult to produce F -decompositions of MK graphs when F grows large, we change our proof's methodology.

Indeed, if trying to decompose MK p×k into induced copies of a graph F may be too ambitious, it is actually sufficient to be able to decompose a dense subgraph of MK p×k into copies of F to obtain the desired result. Hence, we could be satisfied with finding many edge-disjoint induced copies of F in MK p×k covering most of the edges. The union of these copies is a perfectly valid example of a dense graph admitting an induced F -decomposition.

In order to obtain this decomposition, we will use a powerful theorem from Pippenger and Spencer [START_REF] Pippenger | Asymptotic behavior of the chromatic index for hypergraphs[END_REF]. Their result being much more general, its content below is specialized to suit our problem, and is similar to the version appearing in [START_REF] Grable | More-than-nearly-perfect packings and partial designs[END_REF] (see also [START_REF] Frankl | Near perfect coverings in graphs and hypergraphs[END_REF][START_REF] Alon | On a hypergraph matching problem[END_REF]). As a matter of fact, the version in [START_REF] Frankl | Near perfect coverings in graphs and hypergraphs[END_REF] is already strong enough for our purpose. For a hypergraph H we introduce the notation ∆ 2 (H) := max

x,y∈V (H), x =y

|{e ∈ E(H) : x, y ∈ e}|, and call it the maximum co-degree of H.

Also, if H is regular, we denote by deg(H) the degree of regularity.

Theorem 6 (Pippenger, Spencer [START_REF] Pippenger | Asymptotic behavior of the chromatic index for hypergraphs[END_REF]). Let H be an infinite family of r-uniform regular hypergraphs. If

∆ 2 (H) ≪ deg(H)
as |V (H)| gets large (for any increasing sequence of hypergraphs H ∈ H), then there exists in H a set of mutually disjoint hyperedges missing at most o(|V (H)|) vertices.

This theorem can let us find the desired set of edge-disjoint induced copies of F in a large MK p×k if we can achieve a rephrasing of our problem in terms of a maximum hypergraph matching (a matching in an hypergraph is a set of mutually vertex-disjoint edges). What we need now is to define a hypergraph whose edges are all the induced occurrences of F in MK p×k .

Definition. Let H p×k be the hypergraph whose vertex set is the set E(MK p×k ) of all edges of MK p×k , and whose hyperedges are the edge sets of all the induced subgraphs of MK p×k isomorphic to F .

We deduce from the edge-transitivity of MK p×k that the the hypergraph H p×k is vertex-transitive, hence regular. It is also

|E(F )|-uniform. Besides, a matching of H p×k covering (1 -o(1))|V (MK p×k )| vertices corresponds to a collection of induced edge-disjoint copies of F in MK p×k covering (1 -o(1))|E(MK p×k )|
edges, i.e. a dense subgraph of MK p×k admitting an induced F -decomposition. Hence, to obtain Theorem 5 we need to ensure that the conditions of Theorem 6 are satisfied.

We will prove that ∆ 2 (H p×k ) ≪ deg(H p×k ) holds for any fixed k > |E(F )| when p grows large. To do so, we show that the number of induced copies of F in MK p×k containing two given edges is negligible compared to the number of copies containing exactly one of the two edges in question.

For the proof, let us consider two vertices of H p×k , i.e. two edges

v 1 v ′ 1 , v 2 v ′ 2 in M K p×k ,
corresponding to four sets of size k. By the definition of adjacencies in

MK p×k we have v 1 ∩ v ′ 1 = ∅ and v 2 ∩ v ′ 2 = ∅, but v 1 ∪ v ′ 1 and v 2 ∪ v ′ 2 may very well intersect. Recall that V (MK p 1 ,...,p k ) = [p 1 ] 1 × • • • × [p k ] k ;
we shall refer to the elements of the components

[p i ] i (1 ≤ i ≤ k) as 'points'. In our case p 1 = • • • = p k = p holds, that means V (MK p×k ) = [p] 1 × • • • × [p] k . When k > |E(F )|, i.e.
when the size of the sets defining the vertices v 1 , v ′ 1 , v 2 , v ′ 2 of M K p×k is large compared to the number of non-edges of F , some of their points are not necessary to encode the adjacencies of a copy of F . Let us now consider a copy

F * ⊆ MK p×k of F containing the edges v 1 v ′ 1 , v 2 v ′ 2 .
We are going to distinguish a set of necessary points and modify this copy by playing with the other points.

According to the definitions, any non-edge of F * is represented by two intersecting sets, which correspond to two vertices of MK p×k . If the intersection of those two sets is contained in

v 1 ∪ v ′ 1 ∪ v 2 ∪ v ′ 2 ,
we mark one point in it. Having marked (at most) one point for every non-edge of F * , each of our four sets contains at least k -|E(F )| unmarked points.

The unmarked points of v 1 and v ′ 1 are not actually relevant to the adjacency properties of these sets with the other sets of the copy of F . Since As a conclusion, one can associate to any copy F * containing the edges

v 1 = v ′ 1 , v 2 , v ′ 2 , we can obtain a different induced copy of F containing v 2 v ′ 2 but avoiding v 1 v ′ 1 by replacing in v
v 1 v ′ 1 and v 2 v ′ 2 a set f (F * ) of at least (p -|V (F )|) k-|E(F )| copies of F using v 2 v ′ 2 but not v 1 v ′
1 (and differing from F * only by the content of v 1 ). Furthermore, at most c F choices of F * can produce a given alternative copy of F , where c F is a constant depending on F but not on p. (To reverse the operation, it is enough to identify one set of the copy and replace it with v 1 or v ′ 1 .) We deduce that in H p×k the degree of a vertex is at least Θ(p k-|E(F )| ) ≥ Θ(p) times more than the co-degree of the pair v 1 v ′ 1 , v 2 v ′ 2 (chosen arbitrarily), yielding ∆ 2 (H p×k ) ≪ deg(H p×k ) as p grows large. Thus, Theorem 6 implies the existence of a family of edge-disjoint induced copies of F in M K p×k covering almost all edges of M K p×k as p gets large. Now the proof is completed by the observation that M K p×k has p k vertices and is regular of degree (p -1) k = p k -O(p k-1 )the number of sets disjoint from a given set in

[p] 1 × • • • × [p] k -therefore almost all vertex pairs are adjacent in M K p×k .

Conclusion

We have proved that the largest graphs of order n admitting an edge decomposition into induced copies of a given non-edgeless graph F have This question also appears as Problem 2 in [START_REF] Bondy | Induced decompositions of graphs[END_REF]. Some of our results also give a tight answer, apart from a multiplicative constant, to this formulation, exhibiting graphs F with n 2ex * (n, F ) = Θ(n 3/2 ). Some more cases are settled in the recent paper [START_REF] Halász | Asymptotically optimal induced decompositions[END_REF], solving Problem 1 of [START_REF] Bondy | Induced decompositions of graphs[END_REF] as a corollary. Substantially different examples, with linear growth, are K - 4 , the stars, C 4 and more generally the complete equipartite graphs in [START_REF] Bondy | Induced decompositions of graphs[END_REF], and further infinite families in [START_REF] Halász | Asymptotically optimal induced decompositions[END_REF] and [START_REF] Cs | Transversal designs and induced decompositions of graphs[END_REF]. It is worth noting that, although the order of magnitude of n 2ex * (n, F ) is determined in those cases, still there are very few graphs for which the exact value (as a function of n) is known.

Many problems of interest remain open. Some have been raised at the end of [START_REF] Bondy | Induced decompositions of graphs[END_REF]; here we mention further ones. Conjecture 2. For every F , with the value α defined in Conjecture 1, the sequence n 2ex * (n, F ) /n α has only finitely many limit points.

Note that more than one limit point can exist; for example if F = C 4 then there are two of them, one for n even and one for n odd.

Problem 2. What is the expected asymptotic growth f t (n) of n 2ex * (n, F ) as a function of n if F is chosen at random from the graphs on t vertices while n ≫ t but the parameter t also gets large?

An upper bound can be derived from the principles of our construction. One can observe that the value k in the multipartite Kneser graph M K p×k does not need to be larger than 1 plus the minimum k ′ such that the edge set of the complement F of F can be covered with k ′ complete subgraphs.

In the case where F is a complete graph, Problem 1 asks exactly about the smallest possible size of the leave graph of a partial Steiner system. Several related results are available for triple systems. The smallest leave of an STS(n) was determined by Schönheim [START_REF] Schönheim | On maximal systems of k-tuples[END_REF] and Spencer [START_REF] Spencer | Maximal consistent families of triples[END_REF]. Further relatively small graphs which are leave graphs of some STS(n) were described in [START_REF] Colbourn | Support sizes of sixfold triples systems[END_REF][START_REF] Milici | Coverable graphs[END_REF]. For a wealthy collection of results on leave graphs, we refer to Section 9 of [START_REF] Colbourn | Triple Systems[END_REF].

Figure 1 :

 1 Figure 1: A realization of K 1 + K 3 as an induced subgraph of MK 3×3

1

 1 these unmarked points by any other point not contained in F * , i.e. at least p -|V (F )| alternatives for each of the k -|E(F )| unmarked points.

n 2 -Problem 1 . 2 -

 212 o(n 2 ) edges for each graph F as n gets large. This result solves the problem of Bondy and Szwarcfiter completely in the asymptotic sense. Viewing it from the other side, however, it just opens the field for a new track of studies: Given a graph F , determine the exact or asymptotic value of n ex * (n, F ) as a function of n.

Conjecture 1 . 2 -

 12 For every F there exist positive reals c 1 , c 2 and a rational α(1 < α ≤ 2) such that c 1 n α ≤ n ex * (n, F ) ≤ c 2 n αholds for all n ≥ |V (F )|.

  = {u 1 , u 2 , u 3 } and v = {v 1 , v 2 , v 3 } belongs to KG p 3 [S] if and only if S = {u 1 , u 2 , u 3 , v 1 , v 2 , v 3 }. Hence, the p

	edge-disjoint, and as KG 6 3 decomposes KG p 3 we obtain by transitivity that 2K 2 decomposes KG p 3 . When p 3 ≤ n < p+1 3 , we lower-bound ex * (n, 2K 2 ) with ex * ( p 3 , 2K 2 ),
	which leads to the result.
	1 2 6 edges -an even number -and we are going to show that KG 6 10 p 3 decom-p 6 6 3 = poses KG p 3 for any p > 6, which will yield the result. For any 6-subset S ⊆ [p], the graph KG p 3 [S] induced by the vertices of KG p 3 whose representative set belongs to S is isomorphic to KG 6 3 . Besides, an edge
	between two vertices u 6 induced copies of KG 6 3 are
	3

Notation is meant to ensure that we can speak about {v 1 , v

} as a set rather than an ordered pair or a vector of two components in[p 1 ] × [p 2 ].

It is for instance possible to chose k = ∆(F ) + 1 and use Vizing's theorem, or to optimize on both of p and k, or consider coverings of the edge set of F with subgraphs which are vertex-disjoint unions of complete graphs. Finding the smallest integers is probably an interesting combinatorial problem of its own.

Acknowledgments

The authors thank Adrian Bondy for helpful discussions and Jean-Claude Bermond for his careful readings. This work has been partially supported by EA EWIN, ANRs AGAPE and GRATEL and by the ESF EUROCORES programme Eu-roGIGA, CRP ComPoSe, Fonds National de la Recherche Scientifique (F.R.S.-FNRS). Research of the second author was supported in part by the Hungarian Scientific Research Fund, OTKA grant 81493, and by the Hungarian State and the European Union under the grant TAMOP-4.2.2.A-11/1/KONV-2012-0072.


Julio Araujo

Nathann Cohen
email: nathann.cohen@gmail.com

Susanna F De Rezende
email: susanna@ime.usp.br

Frédéric Havet
email: frederic.havet@inria.fr

Phablo F S Moura

On the proper orientation number of bipartite graphs ✩

Keywords: proper orientation, graph colouring, bipartite graph, hardness

An orientation of a graph G is a digraph D obtained from G by replacing each edge by exactly one of the two possible arcs with the same endvertices. For each v ∈ V (G), the indegree of v in D, denoted by

The proper orientation number of a graph G, denoted by -→ χ (G), is the minimum of the maximum indegree over all its proper orientations. It is well-known that -→ χ (G) ≤ ∆(G), for every graph G. In this paper, we

We then prove that deciding whether -→ χ (G) ≤ ∆(G) -1 is an NP-complete problem. We also show that it is NP-complete to decide whether -→ χ (G) ≤ 2, for planar subcubic graphs G. Moreover, we prove that it is NP-complete to decide whether -→ χ (G) ≤ 3, for planar bipartite graphs G with maximum degree 5.

Introduction

In this paper, all graphs are simple, that is without loops and multiple edges. We follow standard terminology as used in [START_REF] Bondy | Graph theory[END_REF].

An orientation D of a graph G is a digraph obtained from G by replacing each edge by just one of the two possible arcs with the same endvertices. For each v ∈ V (G), the indegree of v in D, denoted by d - D (v), is the number of arcs with head v in D. We use the notation d -(v) when the orientation D is clear from the context. The orientation

D of G is proper if d -(u) = d -(v)
, for all uv ∈ E(G). An orientation with maximum indegree at most k is called a k-orientation. The proper orientation number of a graph G, denoted by -→ χ (G), is the minimum integer k such that G admits a proper k-orientation. This graph parameter was introduced by Ahadi and Dehghan [START_REF] Ahadi | The complexity of the proper orientation number[END_REF]. It is well-defined for any graph G since one can always obtain a proper ∆(G)-orientation (see [START_REF] Ahadi | The complexity of the proper orientation number[END_REF]). In other words, -→ χ (G) ≤ ∆(G). Note that every proper orientation of a graph G induces a proper vertex colouring of G. Thus, -→ χ (G) ≥ χ(G) -1. Hence, we have the following sequence of inequalities:

ω(G) -1 ≤ χ(G) -1 ≤ - → χ (G) ≤ ∆(G).
These inequalities are best possible in the sense that, for a complete graph K, ω(K) -1 = χ(K) -1 = -→ χ (K) = ∆(K). However, one might expect better upper bounds on some parameters by taking a convex combination of two others. Reed [3] showed that there exists ǫ 0 > 0 such that χ(G) ≤ ǫ 0 •ω(G)+(1-ǫ 0 )∆(G) for every graph G and conjectured the following.

Conjecture 1 (Reed [3]). For every graph G, χ(G)

≤ ∆(G)+1+ω(G) 2 .
If true, this conjecture would be tight. Johannson [START_REF] Johansson | Asymptotic choice number for triangle free graphs[END_REF] settled Conjecture 1 for ω(G) = 2 and ∆(G) sufficiently large.

Likewise, one may wonder if similar upper bounds might be derived for the proper orientation number.

Problem 1. e (a) Does there exist a positive

ǫ 1 such that - → χ (G) ≤ ǫ 1 • ω(G) + (1 -ǫ 1 )∆(G)? (b) Does there exist a positive ǫ 2 such that - → χ (G) ≤ ǫ 2 • χ(G) + (1 -ǫ 2 )∆(G)?
Observe that both questions are intimately related. Indeed if the answer to (a) is positive for ǫ 1 , then the answer to (b) is also positive for ǫ 1 . On the other hand, if the answer to (b) is positive for ǫ 2 , then the answer to (a) is also positive for ǫ 1 = ǫ 0 • ǫ 2 by the above-mentioned result of Reed.

In Section 2, we answer Problem 1 positively in the case of bipartite graphs by showing that

: if G is bipartite, then - → χ (G) ≤ ∆(G)+ √ ∆(G) 2
+ 1. We also argue that this bound is tight for ∆(G) ∈ {2, 3}.

In Section 3, we prove that -→ χ (T ) ≤ 4, for every tree T . Moreover, we show that

- → χ (T ) ≤ 3 if ∆(T ) ≤ 6,
and

- → χ (T ) ≤ 2 if ∆(T ) ≤ 3.
We also argue that all these bounds are tight.

In Section 4, we study the computational complexity of computing the proper orientation number of a bipartite graph. In their seminal paper, Ahadi and Dehghan proved that it is NP-complete to decide whether -→ χ (G) = 2 for planar graphs G. We first improve their reduction and show that it is NP-complete to decide whether -→ χ (G) ≤ 2, for planar subcubic graphs G. Moreover, we prove that deciding whether -→ χ (G) ≤ ∆(G) -1 is an NP-complete problem for general graphs G. Finally, we show that it is also NP-complete to decide whether -→ χ (G) ≤ 3 for planar bipartite graphs G with maximum degree 5.

Due to space limitation, we omit the proofs of these results.

General upper bound

Theorem 1. Let G be a bipartite graph and let k be a positive integer.

If ∆(G) > 2k + √ 1+8k+1 2 , then - → χ (G) ≤ ∆(G) -k.

Sketch of proof.

In order to prove this theorem, we describe an algorithm (see Algorithm 1) that produces a proper (∆(G) -k)-orientation. Let G = (X ∪ Y, E) be a bipartite graph as in the statement of Theorem 1. The algorithm consists of two phases.

The first phase (lines 1 to 8 in Algorithm 1) produces an orientation, not necessarily proper, of the edges of G in such a way that the indegree of each vertex in X is at most k and the indegree of each vertex in Y is at most ∆(G) -k. It proceeds as follows. We first orient all edges xy ∈ E(G) from x to y, where x ∈ X and y ∈ Y . Then we define k matchings as described subsequently.

Let G 1 = G, and let M 1 be a matching in G 1 that covers all vertices of maximum degree. For each i ∈ {2, . . . , k}, let G i be the graph obtained from G i-1 by removing the edges in

M i-1 , that is G i = G i-1 \M i-1 ,
and let M i be a matching in G i that covers all vertices of degree ∆(G i ). Such a M i exists since it is well known that every bipartite graph H has a proper ∆(H)-edge-colouring. Clearly, we have ∆(

G i ) = ∆(G i-1 ) -1, for each i ∈ {2, 3, . . . , k}. Let M := k i=1 M i . Observe that if a vertex has degree ∆(G) -k + j in G,
where j ∈ {1, 2, . . . , k}, then it is incident to at least j edges in M . Hence, for all j ∈ {1, 2, . . . , k} and for each vertex y in Y of degree ∆(G) -k + j in G, we reverse the orientation of exactly j edges in M incident to y. This ends the first phase.

The second phase reverses the orientation of some edges in E(G) \ M , step by step, in order to obtain a (∆(G) -k)-orientation. This orientation is proper under the assumption of Theorem 1.

Algorithm 1: Proper Orientation of Bipartite Graphs

Input: Bipartite graph G = (X ∪ Y, E) and k ∈ N s.t. ∆(G) > 2k + √ 1+8k+1 2 . Output: Proper (∆(G) -k)-orientation for G. 1 G 1 ←-G 2 Orient all edges in G from X to Y 3 for i = 1, . . . , k do 4 M i ←-matching of G i saturating all vertices of degree ∆(G i ) 5 G i+1 ←-G i -M i 6 M ←- k i=1 M i 7 foreach y ∈ Y do 8 reverse the orientation of max{0; d G (y) -∆(G) + k} edges of M incident to y 9 X ←-X 10 for ℓ = ∆(G) -k -1, . . . , 2 do 11 while ∃x ∈ X s.t. |N ≤ℓ (x)| ≥ ℓ -d -(x) and |N =ℓ (x)| ≤ ℓ -d -(x) do 12 Y ←-set of ℓ -d -(x) vertices of highest indegree in N ≤ℓ (x) 13 foreach y ∈ Y do 14
Reverse the orientation of xy (i.e. re-orient xy towards x)

15 X ←-X \ {x} Theorem 2. If G is a bipartite graph, then - → χ (G) ≤ ∆(G)+ √ ∆(G) 2 + 1.

Sketch of proof. By Theorem 1, for every

k ∈ N, if ∆(G) > 2k + √ 1+8k+1 2 , then - → χ (G) ≤ ∆(G) -k.
In order to obtain a good upper bound for -→ χ (G), we must find the largest positive integer k such that the condition of Theorem 1 holds for a given graph G.

Solving the inequality for k, we obtain that k <

∆(G)- √ ∆(G) 2 . Since k is integer, we conclude that - → χ (G) ≤ ∆(G) - ∆(G)- √ ∆(G) 2
+ 1, and the result follows.

Note that if G is bipartite and ∆(G) ∈ {2, 3, 4}, then the bound of Theorem 2 is equal to the trivial upper bound -→ χ (G) ≤ ∆(G). For ∆(G) = 1 and ∆(G) = 2, this bound is tight due to the paths with 2 and 4 vertices, respectively. In addition, there exists a bipartite graph G with ∆(G) = 3 and -→ χ (G) = 3.

Trees

Theorem 3. If T is a tree, then the following statements hold:

(1) if ∆(T ) ≤ 3, then - → χ (T ) ≤ 2; (2) if ∆(T ) ≤ 6, then - → χ (T ) ≤ 3; (3) - → χ (T ) ≤ 4.
Sketch of proof. We prove the three statements by using similar arguments. For i ∈ {1, 2, 3}, we consider a minimal counter-example M i to statement (i) with respect to the number of vertices, and derive a contradiction that implies that no counter-example exists. Since M i is a minimal counter-example, we have -→ χ (M i ) > i + 1, but -→ χ (T ) ≤ i + 1, for any proper subtree T of M i . We use the latter fact to derive a proper (i + 1)-orientation of M i , which contradicts -→ χ (M i ) > i + 1.

The three statements of the theorem are tight in the following sense: there is a tree with maximum degree 4 and proper orientation number 3, and a tree with maximum degree 7 and proper orientation number 4.

NP-completeness

Ahadi and Dehgan [START_REF] Ahadi | The complexity of the proper orientation number[END_REF] showed that it is NP-complete to decide whether -→ χ (G) ≤ 2 for planar graphs G by using a reduction from the Planar 3-SAT problem. We first improve this result by showing that it is NP-complete to decide whether the proper orientation number of planar subcubic graphs is at most 2.

Theorem 4. The following problem is NP-complete:

Input : A planar graph G with ∆(G) = 3 and δ(G) = 2. Question : - → χ (G) ≤ 2?
Sketch of proof. We show a reduction from the problem of deciding whether a planar 3-SAT formula is satisfiable. It is known that the Planar 3-SAT problem is NP-complete [START_REF] Lichtenstein | Planar formulae and their uses[END_REF]. Let φ = (X, be an instance of this problem, where X = {x 1 , . . . , x n } is the set of variables and C = {C 1 , . . . , C m } is the set of clauses. Using the variable and clause gadgets depicted in Figures 1(a Recall that -→ χ (G) ≤ ∆(G), for any graph G. On the other hand, the following theorem shows that, for any integer k ≥ 3, it is already NP-complete to determine whether -→ χ (G) < k, for graphs G with ∆(G) = k. Sketch of proof. We show a reduction from the problem of deciding whether a planar monotone 3-SAT formula is satisfiable. This problem was recently shown to be NP-complete [START_REF] Berg | Optimal binary space partitions for segments in the plane[END_REF]. The idea of our reduction is roughly the same as in Theorems 4 and 5.

  ) and 1(b), respectively, we construct a planar graphG ′ (φ) such that -→ χ (G ′ (φ)) ≤ 2 if,and only if, φ is satisfiable. Gadget associated to variable x i . (b) Gadget associated to clause C j .

Figure 1 :

 1 Figure 1: The variable and clause gadgets.

Theorem 5 .Theorem 6 .

 56 Let k be an integer such that k ≥ 3. The following problem is NP-complete:Input : A graph G with ∆(G) = k and δ(G) = k -1. Question : -→ χ (G) ≤ k -1?Finally, we show that it is NP-complete to decide whether -→ χ (G) ≤ 3, for planar bipartite graphs G. The following problem is NP-complete: Input : A planar bipartite graph G with ∆(G) = 5. Question : -→ χ (G) ≤ 3?

✩ Research supported by CNPq-Brazil (477203/2012-4), FUNCAP/CNRS INC-0083-00047.01.00/13, FAPESP-Brazil (Proc. 2011/16348-0, 2013/19179-0, 2013/03447-6) and ANR Blanc STINT ANR-13-BS02-0007-03.


A Miskiewicz

S Buffat

J Lorenceau

A.-L Paradis

Anne-Lise Paradis
email: anne-lise.paradis@upmc.fr

Temporal dissection of stimulus-driven and task-driven processes during perceptual decision about 3D SFM stimuli

Abstract-Analyzing the visual properties of a stimulus, such as its shape or its motion, involves a temporally constrained cascade of processes including sensory integration, attentional selection and perceptual decision. In natural conditions, these processing stages may temporally overlap. In this study, we used a time constrained paradigm designed to segregate these stages, and recorded MEG activity to characterize their cortical correlates.

The experimental sequence comprised a structure-frommotion (SFM) target flanked by pre and post masks, which limited the stimulus-driven processes in time.

The MEG responses were recorded in three perceptual tasks bearing on the presence or absence of the target SFM stimulus, on its direction of motion or on its 3D shape.

Subjects' responses were delayed to the end of the trials using a random stimulus-response mapping.

The analysis of the evoked magnetic fields reveals temporally non-overlapping responses for stimulus-driven and taskrelated processes.

Source reconstruction reveals that the occipital, dorsal and ventral stimulus-related areas follow different temporal profiles, The response in IPS slowly rising after the beginning of the activity in the lateral occipital cortex and falling back to the baseline prior the delayed motor response, may reflect accumulating evidence on the presented stimulus leading to a motor response, in line with the results from single cell studies in monkey LIP [START_REF] Huk | Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making[END_REF].

Keywords-visual motion, 3-D shape, perceptual decision, MEG, source reconstruction.

I. INTRODUCTION

Analyzing the visual properties of a stimulus, such as its shape or its motion in the 3-D environment, involves a temporally constrained cascade of processes including sensory integration, attentional selection and perceptual decision. In natural conditions, visually dynamic events require the integration of information about form and motion. Recent studies have challenged the traditional dichotomy between form-and motion-related processes in the ventral and dorsal visual pathways, and there is now evidence that form and motion processing interact in several ways. Both figural and low-level form cues guides motion perception, whereas motion cues can induce figural percept (see [START_REF] Kourtzi | Linking form and motion in the primate brain[END_REF] for a review). However, more work is needed to better understand the perceptual decision stages and the attentional modulation required by the task. The experiments described in this paper aims at investigating these issues.

To segregate the different processing stages, we used structure from motion stimuli which yield both motion and shape percepts from motion cues only, and designed a time constrained paradigm with dynamical masks. We recorded MEG activity to characterize the cortical correlates of such perception in three perceptual tasks bearing on the presence or absence of a target SFM stimulus, its direction of motion or its 3D shape. We reasoned that the masks would isolate a time window for measuring the integration of form and motion cues by interrupting the early visual processing. By carefully choosing supra-threshold stimuli, we ensured that this integration yield to a perceptual decision, the MEG correlate of which should be detectable.

We specifically tested when the attentional modulation induced by the task takes place in the cortical activity, and if this modulation could be found in the occipital and intraparietal areas that are involved in the stimulus integration. We also searched a magnetic correlate of the perceptual decision processes in IPS, a region known to be involved in the accumulation of evidence in visual task implying motion stimuli [START_REF] Huk | Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making[END_REF].

II. MATERIALS AND METHODS

A. Experimental procedure

Participants. Sixteen people (age 28.5±8.1, right-handed, normal or corrected-to-normal vision, 7 men) took part in the study after giving their informed consent. The study was approved by the Local Ethical Committee.

SFM stimuli and motion masks. Structure-from-motion (SFM) stimuli were made of 140 white dots (0.19° visual angle) randomly distributed on a black background and back-projected on a 3D virtual surface. The surface had three possible shapes and oscillated in depth with three possible motion directions. Stimuli were viewed through a 20° circular mask hiding the boundaries of the 3D surface. Overall, nothing but motion cues could be used to identify the shape.

For the masks, dots followed a random walk with instant speeds comprised between 0°/s and 7°/s to match that of the SFM stimuli. More details about the display can be found in [START_REF] Miskiewicz | Shape and motion interactions at perceptual and attentional levels during processing of structure from motion stimuli[END_REF], where identical stimuli were used.

Experimental design. During the MEG recording, participants underwent six runs of 90 trials (see Figure 1) each. Depending on the experimental run, participants had to: • identify the target shape among three (Shape task); • identify its motion direction among three (Motion task); • answer whether a 3D stimulus appeared or not among the mask (Presence task). Run order was randomized across subjects.

The target, either a 3D stimulus (56 %) or a black screen (44 %) was flanked by dynamical masks to limit the duration of its visual integration. Because the stimulus-response mapping varied across trials, participants had to wait for the response screen to give their answer, so that motor activity was delayed after the end of the second mask.

Participants fixated the center of the screen but were advised to broaden their attention on the whole viewing window to ease identification. When a null target occurred in the shape and motion tasks, they had to choose a default response, which was specified at the beginning of the experiment and was randomized across subjects.

Stimulation was projected at 90 cm from the participants, using a calibrated LCD video device (60 Hz refresh rate) located outside the shielded room.

Data acquisition. MEG was recorded continuously during the runs (sampling rate: 1250 Hz), using a 151-channel whole-head system (axial gradiometer, CTF System, Canada). We ensured that the head position relative to the sensors did not change by more than 5 mm along the whole experiment. Electro-oculogram was also measured for offline artefact rejection.

B. MEG analyses

Trials with signal artefacts (blinks, saccades, muscle sig-nal…) were rejected using semiautomatic procedures. A 300-ms baseline was defined in the fixation period.

Event-related magnetic field (ERF). Trials were averaged by task and type of target, resulting in six ERF by subject.

Source estimation. The cortical current density was estimated using overlapping spheres for the head model and a minimum-norm constraint for the solution of the inverse problem (http://neuroimage.usc.edu/brainstorm). Individual anatomy was available for half subjects; scalp tessellation was then computed using BrainVISA (http//brainvisa.info). For the other half, we used a default head model based on the same template as that used to define the cortical surface on which results were projected (MNI "Colin 27" brain).

Sensors and regions of interest (ROI). The response to the 3D target condition in the Presence task was used to delineate groups of sensors and brain areas activated by structure-from-motion perception. We selected four regions of interest (see Figure 2), the activity of which was representative of the profiles encountered in all activated regions.

ANOVA. ERF were averaged within sensor groups and analyzed time by time in a repeated-measure ANOVA with factors Task (Shape, Motion); Target (3D, Null) and Sensors (Occip, Temp, Pariet, Centr, Front). We also performed a 2 x 2 (Task, Target) ANOVA in the selected areas.

III. RESULTS

A. Temporal dissociation of task and target effects

The ANOVA performed on the sensors revealed a temporal dissociation of the task and target effects, with significant (p < 0.001 uncorrected) target x sensors and task x sensors crossed effects occurring respectively between 100 and 200 ms, and between 300 to 320 ms. These crossed effects are explained by the topographies depending on the target in the first time window, and on the task in the second time window. More precisely, the target-related effect corresponds to modulations in the occipital sensors, whereas the task-related effect better corresponds to modulations in the parietal and temporal sensors.

B. Cascade of activity from V1 to IPS

At the source level, both the time window of the target effects and the activity profiles (see Figure 3) reveal the successive involvement of the regions of interest in processing the 3D stimulus. The four areas indeed show very different time course after the 3D target, with tiered peak latencies. In V1, we observe a peak at 90 ms (M100 for target apparition) and another one at 240 ms, well accounted for by the M100 of the 2 nd mask (onset at 150 ms). In line with this, we find a target effect (with p < 0.01 uncorrected during more than 20 samples) during the first peak (85 to 190 ms). We also find a late task effect during the M100 of the 2 nd mask (230 to 250 ms). V3 also shows an early peak at 90 ms and corresponding target effects between 90 and 210 ms. LOC, with a later peak at 200ms, shows target effects between 200 and 350 ms. Neither V3 nor LOC reach significant task effect. Eventually, IPS activity rises slowly after the beginning of the activity in LOC, peaks at 170 ms, and falls back to the baseline prior the delayed motor response. It does not show any significant effect of target or task.

The activity related to the 2 nd mask, which is visible in the null target condition, reveals the same succession of activity in the different areas.

IV. DISCUSSION

We recorded activity related to structure from motion integration in a mere detection task (Presence), as well as in identification tasks (Shape and Motion) requiring selective attention to the shape or 3D motion of the stimulus.

A. Task-related modulation

The regions of interest highlighted by the processing of SFM stimuli in the detection condition did not appear to be significantly modulated by the identification tasks, which is consistent with previous fMRI results [START_REF] Paradis | Processing 3D form and 3D motion: respective contributions of attentionbased and stimulus-driven activity[END_REF] showing that the attentional selection of 3D motion and shape involve different areas from stimulus-driven activity. Rather, the task effect seems to involve more anterior visual brain regions as well as right fronto-polar areas. Further study is required to clarify whether task difficulty [START_REF] Mangina | Neural correlates of "analytical-specific visual perception" and degree of task difficulty as investigated by the Mangina-Test: a functional magnetic resonance imaging (fMRI) study in young healthy adults[END_REF] or prospective memory due to the delayed response [START_REF] Burgess | The role of the rostral frontal cortex (area 10) in prospective memory: a lateral versus medial dissociation[END_REF] might account for such frontal activity.

B. From V1 to IPS

In the regions of interest, the time window of the target effect, as well as the activity profiles, revealed the successive involvement of these areas in processing the 3D stimulus. This cascade being consistent with what has been described recently for structure from motion stimuli [START_REF] Jiang | Binding 3-D object perception in the human visual cortex[END_REF].

Note that we find the implication of the superior occipital gyrus (putative V3) at earlier latencies than LOC activation, consistent with our previous proposal that this area could be involved in an intermediate stage of gross shape extraction.

Although one can wonder to what extent spiking activity can be related to MEG signal, we find in IPS a late climbing activity similar to that described in cell studies [START_REF] Huk | Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making[END_REF]. Also, the particular timing of IPS activity relative to MT/LOC is consistent with the idea that IPS might accumulate evidence about the moving stimulus before reaching a perceptual decision, as long as information about the target is required, and available from earlier areas. Further studies modulating both the amount of information necessary to reach a decision and the possible duration of stimulus integration (between masks) would be needed to confirm the causal relation of the activity in these areas.

C. Target-related activity and masking

In this study, we used a time constrained paradigm with masks immediately preceding and following the target in order to segregate stimulus integration stages from task related-activity and hopefully perceptual decision. Our hypothesis however, was that the dynamical masks would successfully interfere with the integration of the visual cues leading to the perception of the 3D target stimulus. It is noteworthy, that contrary to [START_REF] Jiang | Binding 3-D object perception in the human visual cortex[END_REF], we neither found massive and sustained activity in the infero-temporal areas nor a rebound of activity in the early visual areas (V1 and V3) around 500 ms. This is a first hint that target visual integration is interrupted by the masks.

Another indication is given by the response to the 2 nd mask after a Null target (Figure 4.A). In this condition, the mask-related M100 clearly appears in the ERF, delimiting the moment when target-related signal may not be observable anymore. Such response to the mask can also be found for the 3D target condition in V1, and to a less extent in V3 (see figure 3). Eventually, the sources of the response to the mask (Figure 4.B) appear to overlap largely with the areas involved in the 3D target processing, suggesting that the mask effectively compete with the 3D target for access to cascade of visual processing.

V. CONCLUSIONS ERF revealed temporally non-overlapping effects of stimulus-driven and task-related processes in the perception of structure-from-motion stimuli.

Source reconstruction showed that the occipital, dorsal and ventral stimulus-related areas follow different temporal profiles and confirms a cascade of activity from V1 to IPS passing through MT/LOC for moving object perception.

The rising activity found in IPS may reflect accumulating evidence about the motion stimulus presented, in line with the results from single cell studies in monkey LIP [START_REF] Huk | Neural activity in macaque parietal cortex reflects temporal integration of visual motion signals during perceptual decision making[END_REF].

Fig. 1

 1 Fig. 1 Schematic time flow of a trial

Fig. 2

 2 Fig. 2 Activity related to the 3D target in the Presence task (left) and selected regions of interest (right). V3: superior occipital gyrus; LOC: lateral occipital cortex; IPS: intraparietal sulcus.

Fig. 3

 3 Fig. 3 Reconstructed activity in the regions of interest

Fig. 4

 4 Fig. 4 Temporal window of target integration (A) and brain areas (B) defined by the response to the masks

ACKNOWLEDGMENT

This work was supported by a doctoral grant from DGA to AM and a MRIS-DGA grant (2006.34.059) to JL.