Anne-Kristel Bittebiere
email: kristel.bittebiere@univ-lyon1.fr

Hugo Saiz

Cendrine Mony

New insights from multidimensional trait space responses to competition in two clonal plant species

Keywords: Clonal growth strategy, Functional traits, Hypervolume, Intra-and Interspecific competition, Intraspecific variability, Plant-plant interactions

1. Trait intraspecific variability determines community dynamics and species coexistence. In response to competition, plants can display intraspecific variability to enhance their competitive ability or stabilize their niche differences with competitors. This response is multidimensional because it involves changes along different functional axes and inevitable trade-offs between traits. Here, we transposed the recent concept of the multidimensional trait space to the analysis of intraspecific plant response to competition. We specifically tested the following: (1) in the absence of competitors, the plant multidimensional trait space will be packed towards strategies promoting plant colonisation, and (2) with competitors, the plant multidimensional trait space will be directed towards competition with its size and shaping characteristics dependent on competitor species richness.

2. We studied trait intraspecific variability of two clonal species, Brachypodium pinnatum (L.) P. Beauv. and Elytrigia repens (L.) Gould, in response to competition. We analysed plant response in the absence of competitors and in competition. Competition treatments included intraspecific and interspecific experimental mixtures with increasing species richness. For each target species and each treatment, we built an hypervolume based on six traits involved in the three-dimensional competition (i.e. ramet and connection traits). We measured these hypervolumes for their size, similarity and the contribution of traits in their shaping.

3. In the absence of competitors and for both species, we demonstrated a multidimensional trait space packing towards a colonisation strategy. Under competition, the multidimensional trait spaces of the two target species were the widest at the extremes of the richness gradient, i.e., intraspecific and interspecific high richness competition treatments. High intraspecific variability either promoted niche differentiation from individuals of similar species or reflected the large range of competitive responses deployed when plants were faced with many different competitor identities. The multidimensional response process was based on

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. fine adjustments of various traits depending on the surrounding neighbourhood composition and more specifically, on the competitor functional similarity with the target species.

4. This study emphasises the multidimensionality of species competitive response, and also underlines the so far neglected importance of competitor species richness for trait intraspecific variability and subsequently community assembly.

Introduction

Recent studies from trait-based ecology show that trait variability within plant species is of particular importance in determining community dynamics and species coexistence [START_REF] Lichstein | Intraspecific Variation and Species Coexistence[END_REF][START_REF] Whitlock | The role of genotypic diversity in determining grassland community structure under constant environmental conditions[END_REF][START_REF] Jung | CLO-PLA: the database of clonal and bud bank traits of Central European flora[END_REF][START_REF] Messier | How do traits vary across ecological scales? A case for trait-based ecology[END_REF][START_REF] Bolnick | Why intraspecific trait variation matters in community ecology[END_REF]. Among various mechanisms responsible for this intraspecific trait variability (e.g. neutral processes, mutation, genetic local adaptation), phenotypic plasticity is the one supporting species ability to overcome abiotic and biotic filters such as competition, subsequently affecting community assembly processes [START_REF] Jung | CLO-PLA: the database of clonal and bud bank traits of Central European flora[END_REF].

The limiting similarity theory [START_REF] Macarthur | The limiting similarity, convergence, and divergence of coexisting species[END_REF] predicts that individuals can only coexist if they use resources differently i.e. display distinct functional trait [START_REF] Kraft | Plant functional traits and the multidimensional nature of species coexistence[END_REF]. Competitive plastic responses in plants relies then on a combination of traits as they compete for multiple resource, both above and belowground [START_REF] Grime | Integrated screening validates primary axes of specialization in plants[END_REF][START_REF] Westoby | Plant ecological strategies: Some leading dimensions of variation between species[END_REF][START_REF] Reich | The evolution of plant functional variation: Traits, spectra, and strategies[END_REF][START_REF] Wright | Relationships[END_REF], leading to inevitable trade-offs and interactions between traits [START_REF] Grime | Integrated screening validates primary axes of specialization in plants[END_REF]. As

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. a result, a conceptual framework that based community ecology on multiple traits was recently proposed (Blonder, Lamanna, Violle, & Enquist 2014;[START_REF] Laughlin | The intrinsic dimensionality of plant traits and its relevance to community assembly[END_REF]. By analogy to the concept of ecological niche [START_REF] Hutchinson | The multivariate niche[END_REF], this framework suggests to infer community assembly processes using the multidimensional space of species traits rather than single traits [START_REF] Bonser | Form defining function: interpreting leaf functional variability in integrated plant phenotypes[END_REF]. [START_REF] Kraft | Plant functional traits and the multidimensional nature of species coexistence[END_REF] demonstrated that for annual plants, multidimensional trait space allows a better understanding of the drivers of competition outcomes. Here, we thus suggest transposing this promising framework at the intraspecific level, to study perennial plant communities that include clonal plants. These plants are characterised by a plastic modular structure with vertically growing shoots (ramets) arranged in a branched network allowing the horizontal spread of the clone [START_REF] Harper | The concept of population in modular organisms[END_REF][START_REF] Hutchings | Clonal plants as cooperative systems: Benefits in heterogeneous environments[END_REF]. In perennial plant communities, competition is then three dimensional as it occurs in the horizontal and vertical directions following clonal plant growth. Competitive responses would then involve complex modifications of aerial traits linked with resource use (vertical traits) but also of clonal traits involved in space acquiring (horizontal traits). These competitive responses may additionally be modulated by the clonal growth strategy of the individual (space colonisation vs. space pre-emption), as it determines the individual neighbourhood characteristics [START_REF] Benot | Fine-scale spatial patterns in grassland communities depend on species clonal dispersal ability and interactions with neighbours[END_REF].

Plant intraspecific response to competition may be determined at first by the single presence of competitors. In the absence of competitors, clonal plant growth is directed toward space acquiring and limiting intra-individual competition [START_REF] Bittebiere | Structural blueprint and ontogeny determine the adaptive value of the plastic response to competition in clonal plants: a modelling approach[END_REF]. This promotes strategies to improve space exploration, notably in the horizontal dimension through internode elongation [START_REF] Bittebiere | Structural blueprint and ontogeny determine the adaptive value of the plastic response to competition in clonal plants: a modelling approach[END_REF]. The multidimensional trait space should then be packed toward a colonisation strategy based on traits mostly involved in the horizontal growth. In response to competitors' presence however, [START_REF] Novoplansky | Picking battles wisely: plant behaviour under competition[END_REF] described three strategies (avoidance, confrontation, and

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. tolerance), all possibly involving vertical and horizontal traits of clonal plants. Under competition, the multidimensional trait space should then converged toward one of these strategies or include all of them depending on the local competitive neighbourhood characteristics [START_REF] Miller | Plant uptake of inorganic and organic nitrogen: neighbor identity matters[END_REF][START_REF] Violle | Competition, traits and resource depletion in plant communities[END_REF][START_REF] Ashton | Niche complementarity due to plasticity in resource use: plant partitioning of chemical N forms[END_REF][START_REF] Bittebiere | Plant traits respond to the competitive neighbourhood at different spatial and temporal scales[END_REF].

Numerous studies demonstrated that trait plastic responses (Turkington, Hamilton, & Gliddon 1991;[START_REF] Herben | Fight or flight: plastic behavior under self-generated heterogeneity[END_REF][START_REF] Bittebiere | Morphological response to competition for light in the clonal Trifolium repens (Fabaceae)[END_REF], related to processes of stabilizing niche differences or increasing competitive ability [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF][START_REF] Turcotte | Within-population variation in localized and integrated responses of Trifolium repens to biotically patchy environments[END_REF], depend on competitor identity. In particular for intraspecific competition, a niche differentiation process should limit the competition intensity through horizontal traits plasticity, allowing complementary ramet positioning [START_REF] Herben | Is a grassland community composed of coexisting species with low and high spatial mobility?[END_REF]. However, only a few studies have investigated competitive responses in more complex multispecific assemblages (i.e., more similar to real situations) (but see [START_REF] Bittebiere | Plant traits respond to the competitive neighbourhood at different spatial and temporal scales[END_REF]. In such multispecific assemblages, species richness modulates the probability of locally meeting species of varying identities and may then determine the plant response (i.e. variations in its multidimensional trait space). Under low species richness, competitive response of target plant should converge toward the most adaptive strategy in the presence of these few particular species.

Multidimensional trait space will then be of small size with only a few traits driving the competitive response. Under high species richness however, target individuals may face a large range of local neighbourhood compositions, leading to varying responses of the target plant supporting its competitive ability and subsequently increasing the size of its multidimensional trait space. These responses must rely on both vertical and horizontal traits, because the displayed responses specifically depend on each competitive interaction.

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Based on this framework of the multidimensional trait space, we tested the effects of species richness (i.e. the number of competitor species) on the intraspecific variability of multiple traits. Species richness was manipulated in a large experimental design to study individual plant responses across a no competition treatment and one intra-and three interspecific competition treatments. We assessed the individual responses of two Poaceae species with contrasted clonal growth strategies (space colonisation vs. space pre-emption) and that were sampled in these five treatments. The intraspecific variability of individual responses was assessed through hypervolumes (i.e., multidimensional trait spaces) built for each species using measurements of vertical and horizontal traits involved in the competitive response. We measured three indicators to compare the hypervolumes between competition treatments: i. hypervolume size, ii. hypervolume overlap calculated between pairs of treatments and indicating hypervolumes similarity, and iii. each individual trait contribution to the hypervolume shaping. Specifically, we used this experimental design to test the following hypotheses:

(1) In the absence of competition, the multidimensional trait space should be packed towards the strategies that promote plant colonisation. Hypervolume should then be narrow with low similarity with hypervolumes calculated for target plants in competition. The most contributing traits to hypervolume shaping are expected to be those involved in space colonisation (internode length, number of ramets and branches) to forage for free patches and prevent intra-individual competition.

(2) Under competition, the multidimensional trait space should reflect plant adjustments to competition but its size would vary with the type of competition (intra-vs. interspecific competition) and the species richness (Fig. 1). In addition, the number of traits involved in shaping the multidimensional trait space should increase with species richness.

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Materials and methods

Target species

Elytrigia repens (L.) Desv. and Brachypodium pinnatum (L.) Beauv. are two common perennial species in the grasslands of western Europe. Both species grow laterally by producing sympodial plagiotropic rhizomes of which the apexes develop into erected shoots (ramets) (CLO-PLA database, Klimešová & de Bello, 2009). Both species present intraspecific variation in their clonal and aerial traits, particularly in response to resource availability and competition (de [START_REF] De Kroon | Habitat exploration through morphological plasticity in two chalk grassland perennials[END_REF][START_REF] Van Der Werf | Evidence for optimal partitioning of biomass and nitrogen at a range of nitrogen availabilities for a fast-and slowgrowing species[END_REF][START_REF] Pottier | On the relationship between clonal traits and small-scale spatial patterns of three dominant grasses and its consequences on community diversity[END_REF][START_REF] Bittebiere | Plant traits respond to the competitive neighbourhood at different spatial and temporal scales[END_REF].

Competition and no-competition treatments

To determine whether the intraspecific variability and therefore, the multidimensional trait space of the two target species changes across treatments, we cultivated on a homogenised mixture of sand (20%) and soil (80%), four competitive mixtures planted in May 2009, and 10 ramets of each species alone (referred to as the no-competition treatment). These five treatments were settled within the experimental garden of the University of Rennes 1 (France).

The richness of the four competitive mixtures varied from one to 12 competitor species, which corresponds to the range of species richness recorded in mesophilous grassland ecosystems in France (see e.g. [START_REF] Marion | How much does grazing-induced heterogeneity impact plant diversity in wet grasslands[END_REF]. This gradient allowed us to manipulate the probabilities of meeting each competitor species (Table S1).

Specifically, the competitive mixtures were the following: (1) each target species in monoculture (only intraspecific competition); (2) each target species mixed with three other species, either E. repens with Holcus mollis L., Agrostis stolonifera L., and Ranunculus repens L. or B. pinnatum with Festuca rubra L., Agrostis tenuis Sibth., and Anthemis nobilis Accepted Article . L. (i.e., four competitor species); (3) a mixture of all eight of these species; and (4) a mixture composed of the previous eight species with four additional species (Lolium perenne L., Dactylis glomerata L., Holcus lanatus L., and Centaurea nigra L.) for a total of 12 competitor species (see [START_REF] Benot | Fine-scale spatial patterns in grassland communities depend on species clonal dispersal ability and interactions with neighbours[END_REF]Bittebiere &[START_REF] Bittebiere | Plant traits respond to the competitive neighbourhood at different spatial and temporal scales[END_REF] for more details on the design). These species were selected from a set of species that are widely distributed in temperate grasslands in western France (des Abbayes, Claustres, Corillion, & Dupont 1971).

For each target species, the four competitive mixtures were replicated eight times, while the no-competition treatment was replicated 10 times. The replicates were randomly positioned within the outdoor experimental design. For the no-competition treatments, E. repens and B. pinnatum were each cultivated in 10 large pots. In competition, species were grown in 48 mesocosms (mixtures of eight and 12 species were shared between the two target species) that were 1.30 × 1.30 × 0.25 m. Pots and mesocosm displayed similar heights to avoid constraints on the rooting depth. In each mesocosm, 48 ramets were initially transplanted and placed 16 cm apart, following a hexagonal pattern to ensure balanced competitive interactions [START_REF] Birch | Rectangular and hexagonal grids used for observation, experiment and simulation in ecology[END_REF]. All ramets were equally distributed over all the co-occurring species in the mixture, and the design then corresponded to replacement series, with the overall density of individuals within the mixture kept constant.

The species positions in the plantation pattern were randomised for each mesocosm.

Nevertheless, species covers changed over time due to the ongoing dynamics of the competitive mixtures and the clonal propagation of their initially planted ramets. The transplanted ramets of each species (including for E. repens and B. pinnatum) were collected from several locations in temperate grasslands near Rennes (Brittany, West France) to maximise genetic diversity among clones.

Each year, all the mature inflorescences were cut to suppress seed production, and all of the seedlings that emerged from the substrate seed bank were removed manually. The

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. aboveground biomass was mown in late September. To prevent any possible effects of drought, the mesocosms and pots were watered every two days during the dry season (July-August).

Trait measurements

In April 2012 (i.e., after three years of competitive mixtures cultivation), we sampled each target species from five points within all mesocosms (in the centre and the four mesocosm corners when target species were sufficiently abundant to make this selection process possible). In total, we sampled 40 clonal fragments of each target species in each competitive mixture, and 10 clonal fragments from the no-competition treatment. The sampled fragments resulted from the clonal propagation of the initially planted E.repens and B. pinnatum ramets.

They always began with one mature shoot to standardise sample age and were composed of five consecutive rhizome internodes and the associated shoots. We measured two types of plant traits. First, we measured vertical traits: ramet height, Specific Leaf Area (SLA), and Leaf Dry Matter Content (LDMC). These traits characterise plant photosynthetic efficiency and tissue conservation, i.e., resource use [START_REF] Cornelissen | A handbook of protocols for standardised and easy measurement of plant functional traits worldwide[END_REF]. These traits were measured on the older mature ramet of the sampled fragment to standardise the age and position of the ramet along the rhizome, following [START_REF] Cornelissen | A handbook of protocols for standardised and easy measurement of plant functional traits worldwide[END_REF]. Second, we measured horizontal traits: maximum internode length, the number of branches (i.e., the number of rhizomes that branched from the sampled fragment rhizome), and the number of ramets (i.e., potential new clonal individuals). These traits characterise space colonisation in clonal species.

Constructing six-dimensional hypervolume

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. We built the six-dimensional trait space of E. repens and B. pinnatum using a multidimensional kernel density estimation procedure [START_REF] Blonder | The n-dimensional hypervolume[END_REF]. This method allows a hypervolume to be constructed with an arbitrary number of dimensions (sensu, number of traits), which in this case, represented the multidimensional trait space of the target species. We constructed one hypervolume for each species in each treatment (i.e., the four competition treatments and the one no-competition treatment) using a kernel based on the Silverman estimator [START_REF] Silverman | Density estimation for statistics and data analysis[END_REF]. Before analysis, we checked for redundancy between traits (no correlation between traits with coefficients higher than 0.6, fig. S2), and all trait data were centred and scaled (sensu, data were standardised using the mean and standard deviation of the data from all treatments simultaneously, [START_REF] Blonder | The n-dimensional hypervolume[END_REF]. All hypervolumes were constructed using the "hypervolume" package from R 3.2.4. (Blonder et al., 2014).

Effects of treatment on the multidimensional trait space of target species

To determine treatment effects on target species hypervolumes, we first calculated their volumes in the four competition treatments and in the no-competition treatment. Volume is a measure of hypervolume size and represents the width of the multidimensional trait space of the species (sensu, the variability of all traits shaping the hypervolume simultaneously).

Because we could only calculate one hypervolume per target species and treatment (hypervolume calculation requires at least one individual per each trait involved in hypervolume shaping), we lacked variability for comparing volumes between treatments. To solve this problem, we simulated 1000 hypervolumes per target species and treatment using bootstrapping [START_REF] Gardener | Community ecology: analytical methods using R and Excel[END_REF]. Specifically, we made a random selection of sampled fragments with replacement. Because the volume depends on the number of values used to build the hypervolume (Lammana et al., 2014), we set the number of values used to build the

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. hypervolume at 10 for each simulation, which was the number of values obtained in the treatment with the least sampled fragments (i.e., no-competition). Therefore, we compared the volume of different treatments with all the hypervolumes built from the same number of values. For each competition treatment, because we used 10 ramets sampled from both similar and different mesocosms for hypervolume calculation, hypervolume simultaneously included trait variation within and among mesocosms. Thus, to evaluate the relative importance of intra-treatment and inter-treatment effects, we compared the variability of the hypervolumes built for each treatment and target species against the variability of a hypervolume built using ramets from all treatments at the same time. As the variability of intra-treatment hypervolumes was always negligible compared with inter-treatment variability (Fig. S3), we assumed that the observed hypervolume variations were actually due to effects of competition treatments.

Second, we calculated the overlap between the hypervolumes of target species for each pair of treatments (i.e., the four competition treatments and the no-competition treatment). The overlap between two hypervolumes measured the intersection of the hypervolumes in the six-dimensional volume defined by the traits and was calculated as multidimensional variation of Sorensen similarity index:

= 2 × ℎ ℎ ℎ +
In this case, hypervolume overlap represented the similarity of the two multidimensional trait spaces (sensu, the overall similarity of all trait values between the two hypervolumes), with high overlap indicating more similar spaces. Similarities between multidimensional trait spaces were then compared using a Ward's clustering method [START_REF] Murtagh | Ward's hierarchical agglomerative clustering method: Which algorithms implement ward's criterion[END_REF].

We also calculated overlap values between the hypervolumes of all species from the competitive mixtures to check that the target and all competitor species occupy different multidimensional trait spaces (Table S2).

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Effects of treatments on traits shaping the hypervolumes of target species

We calculated in each of the five treatments the contribution of the six measured traits to multidimensional trait space. The trait contribution is related to its variability, relatively to other traits. An increase in trait variability leads to an increased axis range in the hypervolume. Thus the more variable is one trait relative to the five others, the more it contributes to the hypervolume shaping i.e. is more important for the multidimensional trait space definition. Trait contribution is calculated as the ratio between the volumes of two hypervolumes: the hypervolume which considers all the traits, and the hypervolume which considers all the traits but the trait of interest. For each target species separately, we compared the measured contribution of each single trait in shaping the hypervolumes under the different treatments to an expected value. Specifically, we simulated 1000 hypervolumes for each species by resampling 40 random clonal fragments from the pool of all the treatments (similar to that presented in Lammana et al., 2014). These simulated hypervolumes represented the potential multidimensional trait spaces of species in our experiment, because they were created from the trait values extracted from all of the observed values. Then, for each treatment, we compared the contribution of each trait against a 95% confidence interval built from the simulated data (i.e., by selecting the 2.5 and 97.5

percentiles of simulated values). Thus, when the value of contribution of any trait was outside the confidence interval, the contribution of that trait in that treatment was significantly different from that expected for the species in the experiment.

Results

Influence of treatments on target species multidimensional trait space

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To determine the effect of competition on species hypervolumes (i.e., their multidimensional trait spaces), we compared the sizes (volumes) and similarity (overlap values) among the five treatments (four competition treatments and one no-competition treatment). Our results

suggest that the volumes of E. repens and B. pinnatum hypervolumes varied among treatments (Fig. 2). The smallest hypervolumes of target species were in the absence of competitors compared to the four competition treatments.

Under competition, target species consistently tend to display larger hypervolumes in treatments with one and 12 competitor species than those in the four and eight species treatments. Overlap analyses were similar for both target species and showed that the largest dissimilarity in hypervolume was between the no-competition treatment and the four competition treatments (Fig. 3). Two pairs of competition treatments were more similar than others: those with one and 12 competitor species vs. with four and eight competitor species.

Influence of treatments on main traits shaping hypervolumes

In the absence of competitors, for both target species E. repens and B. pinnatum, we found that two of the three traits involved in space colonisation (i.e., number of ramets and branches) contributed significantly more to the hypervolume shaping than expected (Table 1).

Conversely, traits involved in resource use were overall less contributing than expected.

Under competition and for both target species, only one trait (number of ramets) did not display a response in any competition treatment (Fig. 4).

In the intraspecific competition treatment, the response depended on the target species. In B. pinnatum, no trait had higher, and only SLA had lower contribution to hypervolume shaping than expected (Fig. 4b). By contrast, in E. repens, ramet height and number of branches on the one hand, and maximum internode length on the other hand were

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. respectively significantly more and less contributing to hypervolume shaping than expected (Fig. 4a).

In interspecific competition, the number of branches was less contributing to hypervolume shaping than expected in almost all competition treatments for both E. repens and B. pinnatum (with the exception for E. repens in the 12 competitor species treatment) (Fig. 4). Except for the number of branches, patterns of trait contribution to hypervolume shaping strongly varied with the competition treatment and between target species with no apparent relationship with the gradient of species richness. In E. repens, no trait was more contributing than expected (Fig. 4a), whereas in B. pinnatum, either LDMC or ramet height and SLA were more contributing than expected in the four and the 12 competitor species treatments, respectively.

Discussion

The multidimensional trait space primarily depends on the presence of competitors

In both target species, the primary determinant of multidimensional trait space was the single presence of competitors. As expected, the multidimensional trait space tends to be packed in the absence of competition. This space was strongly dissimilar from the others, indicating a shift in plant strategy from space colonisation to varying competitive strategies. In absence of competitors, individuals mostly seek colonizing space, thereby generating environmental heterogeneity related to ramet spatial distribution and density [START_REF] Jackson | The scale of nutrient heterogeneity around individual plants and its quantification with geostatistics[END_REF][START_REF] Herben | Spatio-temporal patterns in grassland communities[END_REF]. The most important traits for shaping the multidimensional trait space were then the number of branches and ramets. In heterogeneous space, the high flexibility in the number of branches helps to reach free spaces [START_REF] Slade | The effects of light intensity on foraging in the clonal herb Glechoma hederacea[END_REF][START_REF] Sutherland | The foraging tactics of plants[END_REF] and avoid intra-clonal competition (Lovett-Doust, 1981b;[START_REF] Schmid | Spatial dynamics and integration within clones of grassland perennials with different growth form[END_REF] Optimal ramet positioning through horizontal trait plasticity may cancel the requirement of a foraging response in the vertical direction.

The multidimensional trait space under competition depends on the number of competitor species in the local neighbourhood

The multidimensional responses of both E. repens and B. pinnatum depended on the competition treatment and followed a similar pattern. The largest multidimensional trait spaces were in the intraspecific and 12 species treatments, whereas these spaces were intermediate in the four and eight species treatments. Additionally, hypervolumes were more similar between the four and eight species treatments and between the intraspecific and 12species treatments.

Under intra-and interspecific competition, trait variability is likely related to mechanisms of equalizing fitness and stabilizing niches differences [START_REF] Chesson | Mechanisms of maintenance of species diversity[END_REF]. Under intraspecific competition, the target individual and its neighbours have similar resource use.

Strong plasticity would thus result from a niche differentiation process following the limiting similarity prediction [START_REF] Macarthur | The limiting similarity, convergence, and divergence of coexisting species[END_REF][START_REF] Violle | The return of the variance: intraspecific variability in community ecology[END_REF]. Plastic individuals may then differ from their functionally similar neighbours to limit competition intensity and support coexistence. Under interspecific competition, trait variability increases while competitive responses change, from the four and eight species to the richest (12 species) community. This species richness effect was likely due to the probabilities of encountering and then locally interacting with competitors of different identities (i.e., resource acquisition strategies) and competitive abilities (Table S1). Accordingly, target species should then adopt

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. and combine multiple strategies [avoidance, confrontation, tolerance, sensu [START_REF] Novoplansky | Picking battles wisely: plant behaviour under competition[END_REF]] to adjust to these varying competitor identities [START_REF] Bittebiere | Morphological response to competition for light in the clonal Trifolium repens (Fabaceae)[END_REF][START_REF] Callaway | Phenotypic plasticity and interactions among plants: Trait plasticity and community dynamics[END_REF] and support their fitness differences [START_REF] Turcotte | Within-population variation in localized and integrated responses of Trifolium repens to biotically patchy environments[END_REF].

Our results thus underline the strong role of intra-vs. interspecific competition, and for the first time, highlight the probable role of species richness for trait intraspecific variability in the plant community. This was so far little considered, as experimental community ecology is mostly based on simplified plant species assemblages. Ultimately, considering species richness in future works dealing with plant community assembly rules should constitute a huge step forward in determining mechanisms supporting or hindering species coexistence.

Trait importance in the shaping of multidimensional trait spaces along the gradient of species richness

In contrast to our expectations, the number of traits involved in the target species multidimensional response to competition was not influenced by the gradient of species richness.

Under intraspecific competition, the niche differentiation process not only relies on horizontal traits. The characteristics of the multidimensional trait space were partially shared with the no-competition treatment. Notably, the number of branches remained highly variable relatively to other traits, in E. repens, unlike in B. pinnatum. Monocultures of guerilla individuals must, at a very local scale (a few centimetres), be similar to the no-competition treatment because of the rapid and diffuse clonal growth of guerilla species. However, the clumped clonal growth of B. pinnatum [i.e. phalanx species, (Lovett Doust, 1981;[START_REF] Benot | Fine-scale spatial patterns in grassland communities depend on species clonal dispersal ability and interactions with neighbours[END_REF]] generated more heterogeneous and far less predictable competitive environments in monocultures [START_REF] Bittebiere | Morphological response to competition for light in the clonal Trifolium repens (Fabaceae)[END_REF] than in the no-competition treatment. Thus,

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. individuals did not invest in the variability of one particular trait [START_REF] Alpert | The relative advantages of plasticity and fixity in different environments: when is it good for a plant to adjust?[END_REF].

Instead, the response of B. pinnatum in intraspecific competition relied on the local adjustment of different traits.

In interspecific competition, the number of branches converged to low values in both target species (Figs. S4,S5). In these growing conditions, competitive ability is indeed supported by a switch of plant growth toward a caespitose form (consolidated plant positions). Nevertheless, with the exception of the number of branches, the two target species displayed different multidimensional responses to interspecific competition. In E. repens, no particular trait was more plastic than expected. Individual responses to the local neighbourhood involved different traits, to specifically adjust to each local competitor identity, resulting in a wide multidimensional trait space but with no particular trait characteristics. By contrast, in B. pinnatum, we overall found (with four and 12 competitor species) that traits involved in resource use were the most plastic. Because of its phalanx growth strategy, B. pinnatum displays low dispersal ability [START_REF] Benot | Fine-scale spatial patterns in grassland communities depend on species clonal dispersal ability and interactions with neighbours[END_REF], which highly conditions its neighbourhood composition. In our system, B. pinnatum individuals more often met competitors from the most abundant species (see Table S1, although abundances at the mesocosm scale are a proxy of the individual neighbourhood). Some of the most abundant species in the four and 12 competitor species treatments are functionally similar to B. pinnatum: A. tenuis shared close LDMC values, while E. repens and D. glomerata both displayed similar SLA and ramet height values (Table S3). Functional differentiation from these species might explain the importance of traits involved in resource use in shaping the multidimensional trait space of B. pinnatum. Besides, investment in the plasticity of B.

pinnatum ramet height relatively to other traits, increases with competitor species richness, likely because of an asymmetric exploitation of light resource [START_REF] Demalach | Size asymmetry of resource competition and the structure of plant communities[END_REF]. This trait would support B. pinnatum fitness differences with neighbours.

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Manipulating species richness resulted in nonlinear variations of competitor meeting probabilities across competitive treatments (Table S1), which subsequently led to complex multidimensional responses in relationship with competitor relative abundances and functional similarity with the target species. Competitive responses under interspecific competition eventually relied on fine adjustments of multiple traits involved in either space exploration or resource exploitation depending on the local neighbourhood.

The determining role of trait intraspecific variability in competitive environments

This study is the first to determine the intraspecific variability of the multidimensional trait space notably in response to competition. We demonstrated that the competitive neighbourhood structured this space, mostly by the presence of competitors alone, and to a lesser extent by their species richness. The multidimensional trait space is determined by species richness likely because it influences the probability of meeting competitors of different identities. The amplitude of the overall trait variability followed a curved relationship with the highest values at both extremes of the gradient characterizing two main processes of competitive response: niche differentiation from functionally similar neighbours (variations in resource use) and specific plastic adjustments to the various competitor species supporting competitive abilities (variations in resource acquisition strategies). In our experimental design, we used the same competitor species in all the replicates at each level of our species richness gradient; thus, the effects of richness and competitor species identities on the multidimensional response to competition were partially confounded. Therefore, we recommend that further studies in community ecology based on species richness gradients use different species at similar levels of richness to solve this problem.

The shaping of the multidimensional trait space under intraspecific competition, i.e., with functionally similar competitors, depended on the clonal growth strategy shared by the

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. target plant and its neighbours. Under interspecific competition, the competitive response relied on fine adjustments of multiple traits involved in environmental exploration and exploitation depending on the local neighbourhood. These fine adjustments suggested that the competitive response was integrated at the scale of the individual. Overall, highlighted by the results, we argue that to assess with accuracy the evolutionary and ecological processes that determine plant resource acquisition strategies and support species coexistence within communities, a large range of traits and their fine variations must be considered.

This work demonstrates the importance of trait intraspecific variability in plant responses in a competitive environment. Beyond contributing to the current debate on the relative importance of intraversus interspecific trait variation in plant community assembly, we provide new insights on the underlying mechanisms generating this variability. Our results suggest that trait intraspecific variability is selected for a particular target plant species relative to the composition (species richness) of its plant neighbourhood. Nevertheless, its consequences for the whole plant community dynamics remain to be determined as phenotypic plasticity in response to competition can either hinder or favour species coexistence [START_REF] Turcotte | Within-population variation in localized and integrated responses of Trifolium repens to biotically patchy environments[END_REF].

Accepted Article

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among ecologically important dimensions of plant trait variation in seven neotropical forests.

Annals of Botany, 99, 1003-1015. 2.88 -Notes: Sim 0.025 , 2.5 percentile of the simulated data; Sim 0.975 , 97.5 percentile of the simulated data. When comparing the observed value with the simulated data, trait contribution was significantly higher (+), lower (-), or not different (ns).

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  , whereas changes in the number of ramets indicate different degrees of spatial Accepted Article . aggregation depending on free-patch size. By contrast, values of the traits involved in resource use converged. Individual plants constantly displayed low SLA and ramet height or LDMC, suggesting they invested less in light acquiring organs variability (Figs. S4, S5).

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Distributions of volumes of target species hypervolumes depending on treatment:

TableTable 1 .

 1 Trait contributions to hypervolume shaping for the target species in the no-

	competition treatment.
	Target species	Traits	Observed value	Sim 0.025 Sim 0.975	Result
	E. repens	Maximum internode length	2.64	1.96	2.94	ns
		Number of branches	4.07	1.91	2.91	+
		Number of ramets	4.56	1.70	3.13	+
		Ramet height	0.96	1.90	2.98	-
		LDMC	2.79	1.66	3.19	ns
		SLA	1.08	1.88	2.89	-
	B. pinnatum Maximum internode length	2.69	1.84	2.99	ns
		Number of branches	2.87	2.12	2.85	+
		Number of ramets	3.34	1.82	2.99	+
		Ramet height	2.38	2.06	2.94	ns
		LDMC	1.35	1.77	2.91	-
		SLA	1.13	2.16

Acknowledgements

This project benefited from two grants from the French National Agency for Research ANR-08-SYSC-012 and the Systerra call ANR-10-STRA-002 for data collection. The Diversify FP7 FET Project, the ERC Grant agreement 647038 [BIODESERT], and the Juan de la Cierva-Formación fellowship from the Spanish Ministry of Economy and Competitiveness (FJCI-2015-26782) financed the postdoctoral position of H. Saiz. We are very grateful to T. Fontaine, V. Gouesbet, and F. Nassur for providing technical assistance with the maintenance of the experimental design and to P. Boulard for providing assistance with the experiment and data collection. We also thank American Journal Experts for editing the English.

Accepted Article

.

Data availability

All

data are available in figshare (DOI: 10.6084/m9.figshare.6860138; https://figshare.com/s/b0a0e77f4416af93776c).

Accepted Article

.

Authors' contributions

AKB and CM conceived the ideas and designed the methodology; AKB collected the data; HS analysed the data; AKB, HS and CM wrote the manuscript.

Accepted Article


Sandra Devin

Aurélie Clodic

Rachid Alami

About Decisions During Human-Robot Shared Plan Achievement: Who Should Act and How?

It has been shown that, when a human and a robot have to perform a joint activity together, they need to structure their activity based on a so-called "shared plan". In this work, we present a scheme and an implemented system which allow the robot to elaborate and execute shared plans that are flexible enough to be achieved in collaboration with a human in a smooth and non-intrusive manner. We identify and analyze the decisions that should preferably be taken at planning time and those that should be better postponed. We also show in which conditions the robot can determine when it has to take the decision by itself or leave it to its human partner. As a consequence, the robot avoids useless communication by smoothly adapting its behavior to the human.

INTRODUCTION

One of the challenges in human-robot interaction is to devise robots able to work with humans to perform what is called Joint Action in social sciences [START_REF] Sebanz | Joint action: bodies and minds moving together[END_REF]. In this context, robots first need to establish a joint goal with their human partners. Once the joint goal has been agreed upon, the participants need to agree on a way to achieve this goal: they need to have a shared plan [START_REF] Grosz | Collaborative plans for complex group action[END_REF]. Shared plans can be based on known procedures or can be elaborated on-line. In robotics, several planners allow to take into account the human [START_REF] Cirillo | Human-aware task planning: an application to mobile robots[END_REF][START_REF] Lallement | HATP: an HTN planner for robotics[END_REF]. They allow the robot to reduce resource conflicts [START_REF] Chakraborti | Planning with resource conflicts in human-robot cohabitation[END_REF] or take divergent beliefs into account [START_REF] Warnier | When the robot puts itself in your shoes. managing and exploiting human and robot beliefs[END_REF][START_REF] Talamadupula | Coordination in human-robot teams using mental modeling and plan recognition[END_REF]. To communicate about the shared plan, several possibilities have been studied: the robot computes a plan for both agents and shares/negotiates it [START_REF] Allen | Human-machine collaborative planning[END_REF][START_REF] Milliez | Using human knowledge awareness to adapt collaborative plan generation, explanation and monitoring[END_REF], the human imposes the shared plan to the robot [START_REF] Petit | The coordinating role of language in real-time multimodal learning of cooperative tasks[END_REF][START_REF] Mohseni-Kabir | Interactive hierarchical task learning from a single demonstration[END_REF], or the robot adapts its actions to the human ones [START_REF] Levine | Concurrent plan recognition and execution for humanrobot teams[END_REF][START_REF] Fiore | On planning and task achievement modalities for human-robot collaboration[END_REF]. In [START_REF] Gombolay | Decisionmaking authority, team efficiency and human worker satisfaction in mixed humanrobot teams[END_REF], it is shown that subjects prefer letting the robot plan when the task is too complex, prioritizing efficiency. In more simple tasks, it has been shown in [START_REF] Baraglia | Initiative in robot assistance during collaborative task execution[END_REF] that a robot proactively helping the human is preferred to one waiting before proposing help. On another hand, the relevance of using a shared plan in HRI has been studied by [START_REF] Lallée | Cooperative human robot interaction systems: Iv. communication of shared plans with naïve humans using gaze and speech[END_REF]. They suggest that the shared plan should be fully communicated in order to sustain effective collaboration. However, when two humans share a plan, they usually do not communicate every detail at every step of the plan, but only the parts of their individual plans which interact in space, time and/or resources [START_REF] Bratman | Shared intention[END_REF]. In this work, we try to get rid of the entire shared plan verbalization by taking the right decision at the right time in order to come up with a robot which communicates only when necessary in order to promote efficiency, fluency and acceptability.

Then, when it comes to execute the shared plan, several contributions have been done to allow more flexibility. [START_REF] Chien | Using iterative repair to improve the responsiveness of planning and scheduling[END_REF] proposes a method to plan only a few steps in advance and plan the actions further in an iterative way. Chaski, a tasklevel executive [START_REF] Shah | Improved human-robot team performance using chaski, a human-inspired plan execution system[END_REF], allows to choose when to execute the robot actions adapting to a human partner. A system that mixes plan recognition and adaptation is described in [START_REF] Levine | Concurrent plan recognition and execution for humanrobot teams[END_REF]. It computes all possibilities for the plan and chooses an action based on the choice of the human and causal links. [START_REF] Hoffman | Effects of anticipatory action on human-robot teamwork efficiency, fluency, and perception of team[END_REF] proposes an adaptive action selection mechanism for a robotic teammate, making anticipatory decisions based on the confidence of their validity and their relative risk. [START_REF] Karpas | Robust execution of plans for human-robot teams[END_REF] presents Pike, an online executive that unifies intent recognition and plan adaptation for temporally flexible plans with choices. Turn-taking abilities have also been studied, mainly to take a turn during a conversation [START_REF] Johansson | Opportunities and obligations to take turns in collaborative multi-party human-robot interaction[END_REF] but also during physical interaction [START_REF] Chao | Timed petri nets for fluent turn-taking over multimodal interaction resources in human-robot collaboration[END_REF]. Finally, the HRI domain also took inspiration from cooperative multi-robot literature where task allocation and cooperative activity achievement have been thoroughly investigated [START_REF] Tambe | Agent architectures for flexible, practical teamwork[END_REF][START_REF] Botelho | M+: a scheme for multi-robot cooperation through negotiated task allocation and achievement[END_REF][START_REF] Gerkey | A formal analysis and taxonomy of task allocation in multi-robot systems[END_REF]. However, the two domains are very differents, since the human and the robot are not equal in any aspect and communication in HRI is essentially multi-modal, while most often robots communicate with each other through wireless network.

The work presented here is an extension of previous work in elaboration and achievement of human-robot shared plans [START_REF] Fiore | On planning and task achievement modalities for human-robot collaboration[END_REF][START_REF] Devin | An implemented theory of mind to improve human-robot shared plans execution[END_REF]. The contribution aims at improving flexibility and fluency during shared plan achievement by allowing the robot to identify which are the needed decisions and to choose the most pertinent moment to take them while smoothly adapting to the human behavior.

THE CONTEXT AND THE PROBLEM

We place ourselves in a context where a team-mate robot has to work jointly with a human. They share an environment and mutually observe each other. In order to focus on the paper contribution, we consider here that the joint goal has already been established; the robot and its human partner have a commitment to achieve the task [START_REF] Devin | An implemented theory of mind to improve human-robot shared plans execution[END_REF] and none of them will abort it unless they know that it is not achievable any more. We also consider that the robot is working with only one human, even if the proposed scheme can be easily adaptable to several humans. The question now is to achieve the task.

The blocks building scenario: To illustrate the overall process, we use a task inspired from [START_REF] Clodic | Key elements for human-robot joint action[END_REF]: a human and a robot have to build a blocks construction (Fig. 1). At the beginning of the task, the robot and the human have several colored blocks they can access.

The problem: We identify three types of decisions to be taken during shared plans elaboration and execution: Which action to perform in which order? This is done through an adaptation of HATP, a human-aware planner which has been demonstrated to be well suited to human-robot joint action [START_REF] Lallement | HATP: an HTN planner for robotics[END_REF].

Who will perform which action? We endow the robot with the ability to detect whenever the choice is trivial (only one agent can perform an action, or the efforts to perform it clearly point ton one particular agent) or whenever a decision is needed. Only then, the robot communicates concerning the choices to be made and/or simply adapts its behavior to the human one, avoiding useless communication.

With which object? when an action has been allocated, some conflicts may remain concerning the action instantiation (which object, tool or placement to use). We endow the robot with the ability to postpone this action refinement and adapt to the human choices.

This work has been fully integrated into a human-aware architecture [START_REF] Lemaignan | Artificial cognition for social human-robot interaction: An implementation[END_REF][START_REF] Devin | Some essential skills and their combination in an architecture for a cognitive and interactive robot[END_REF] that is presented in Fig. 2. Two key components will be discussed: the planner and the supervisor. In section Sec. 3, we present the adaptation of HATP in order to elaborate more flexible shared plans and to promote decisions that can be better taken at the last moment. In section Sec. 4, we present the essential mechanisms that have been designed to build a supervisor that is able to control and refine on-line the shared plan in order to promote fluency and pertinence of robot decisions and actions including verbal interactions. In section Sec. 5, we present experiments we have ran with the system and exhibit quantitative and qualitative results that validate the approach.

AN IMPROVED SHARED PLAN ELABORATION

HATP is a Human-Aware Task Planner based on Hierarchical Task Network which has been specifically designed to integrate a number of features that are meant to promote the synthesis of shared plans that are acceptable by humans and easily if not trivially understandable by them, taking into account a number of social rules [START_REF] Lallement | HATP: an HTN planner for robotics[END_REF]. The resulting shared plans contain the actions of all agents involved in the task. In previous work, all the actions of the computed plans were Fig. 2: The architecture. A Situation Assessment module [START_REF] Milliez | A framework for endowing an interactive robot with reasoning capabilities about perspective-taking and belief management[END_REF] maintains the world state from the point of view of all agents based on perspective-taking. HATP [START_REF] Lallement | HATP: an HTN planner for robotics[END_REF] allows to compute a symbolic shared plan for the robot and its human partners. The plan is executed by the Supervisor with the help of the Dialogue Manager and a Geometric Planner [START_REF] Waldhart | A novel software combining task and motion planning for human-robot interaction[END_REF] that computes trajectories as well as objects placements and grasps while taking into account human safety and comfort. The work presented here concerns HATP and the Supervisor (in red). allocated and completely instantiated during plan elaboration. For example; the first action of the shared plan for the blocks building task could be: [ROBOT PICK AND PLACE RED CUBE1 PLACEMENT 1]. In a collaborative setting, taking in advance all these decisions could be counter intuitive and it can be interesting to let the agents decide at execution time who will do what and how. To do so, we made some changes to the use of HATP resulting to the plan Fig. 3(a):

Similar objects: In order to allow to postpone the decisions of which exact objects to use, we use the notion of objects similarity: two similar objects will have the same role in the task. With this modification, the first action of the shared plan becomes [ROBOT PICK AND PLACE RED CUBE PLACEMENT].

The X agent: In order to postpone the decision of who should perform an action, we define an X agent whose capabilities correspond to the intersection of capabilities of the human and the robot (with a lower cost). It allows the planner to identify for which action the decision is trivial and for which action a decision is needed. With this modification, our action becomes [X-AGENT PICK AND PLACE RED CUBE PLACEMENT].

SHARED PLAN EXECUTION

We will now explain how the supervisor contributes to smooth the plan execution. Based on previous work [START_REF] Devin | An implemented theory of mind to improve human-robot shared plans execution[END_REF], the supervisor is able to maintain the current shared plan and compute the set of feasible actions which need to be performed at each time, using causal links and actions preconditions. This previous work also allows the robot to elaborate a new plan whenever an unexpected event leads to a plan not valid anymore (and if no plan is found, the robot will abort the goal). We describe below the main steps of the plan execution.

1) Action selection: When, according to the plan, there are actions to perform by the robot or the X agent, the robot selects an action based on priorities. In our case, a higher priority is given to the actions allocated to the robot compared to those allocated to the X agent. Then, the priorities of the robot's actions are the same, so the robot will simply select one. However, it would be possible to integrate costs, e.g. to enable to select the action the farthest of what the human is currently doing. Finally, concerning the priorities of the actions allocated to the X agent, we choose to put a higher priority on what we call analogous actions. Two actions are analogous when they have exactly the same decomposition (same action name and same parameters). For example, in the blocks building scenario, the two first actions allocated to the X agent in Fig 3(a) are analogous: the first selected action will be [X-AGENT PICK AND PLACE RED CUBE PLACEMENT]. All these choices are made with the idea to postpone as much as possible robot's decisions whenever it's possible, in order to leave the human the ability to take the initiative until the last moment.

2) Action allocation: If the action selected is attributed to X agent, the robot needs to decide whether it will execute it or let the human do it. To do so, the robot first looks for the possible actors of this action: agents which verify the preconditions of the action and which are not already performing another action. For example, if the human is currently doing something else and there is an action of the X agent to perform, the robot will be assigned to this action. Then, if there are still several possible actors for the action, the robot will compare the action cost for itself and the human and assign it to itself if it is less costly. In the current implementation, the only cost used concerns the analogous actions which will have lower cost for the robot (the robot can execute one and let to the human the possibility to perform the other(s)). Finally, as a last resort, we have developed two possible modes for action selection. In the negotation mode, the robot directly asks its human partner if he wants to perform the action and then allocated the action according to this answer. In the adaptation mode, the robot waits a certain amount of time, and if the human does not take the initiative to perform the action, the robot does it. Allocating an action to an agent can lead to other actions being automatically allocated. For example, in our scenario, the choice of who places the first blue cube automatically leads to the other agent placing the second one. For this reason, after each allocation of an action of the X agent, HATP is called to get a new plan.

3) Actions Instantiation:

Once the robot has decided to execute an action e.g. [Robot PICK AND PLACE RED CUBE PLACEMENT], it needs to be able to deal with the similar objects. This choice will be instantiated as close as possible to the execution, i.e. in a PICK AND PLACE action which will be decomposed by a PICK(object) and then a PLACE(object, placement), the choice for the destination (PLACEMENT 1 or PLACEMENT 2) will be made when it comes to do the PLACE (leaving the time to the human to choose a placement for his red cube). Then, concerning the choice of the object, the robot will choose the less costly one. We choose to put a lower cost on objects accessible only by the robot. Then we use a simple cost based on distance between the agents right-hands and objects that leads the robot to choose the object that are the closest to itself on one side and the farthest from the human on the other side. With these choices, we still want to let the maximum choices to the human while minimizing his effort.

4) Adaptation to human initiative:

The robot needs to be able to properly react to human behavior. The robot is, in parallel to the others steps described previously, constantly monitoring the human actions (it detects all actions performed by the human which involve objects from the task). If the action was previously allocated to the X agent, the robot asks to HATP a new plan to evaluate the possible allocations of the remaining actions. If the human performs an unexpected action with respect to the shared plan, the robot re-plan from the new situation induced by the human action. Moreover, if the unexpected human action is analogous to the one the robot is currently performing, the robot also stops its action (its actions may not be needed anymore). Finally, if the human approaches an object which is involved in the current robot action (e.g. in the blocks building scenario, the human places his red cube in the placement the robot has chosen), the robot first halts its action. Then, the robot looks if it can find another similar object. If it finds one, it continues its action with this object. If not, it waits the human to retreat from the object, and if the human actions did not lead to a new plan it continues its action if possible.

RESULTS

Illustrative examples on a real robot We ran experiments with several setups of the blocks building task described in Sec. 2 and with different kinds of human behaviors. Due to space constraint, we will present here only one execution which includes several interesting points. However more scenarios are available in the attached video 1 .

The presented scenario starts with the setup in Fig. 1(a). The plan produced can be found in Fig. 3(a). It starts with two analogous actions for the X agent (place a red cube), the supervisor selects one and starts to execute it. So, the robot picks the red cube and, at the same time, evaluates the consequences of its choice. Since each agent owns only one red cube, the new plan computed (Fig. 3(d)) states that the human needs to place the second red cube. After picking its red cube the robot starts to place it on the placement the farthest to the human. However, the human picks his red cube and places it in the very same placement (Fig. 3(b)). So, the robot halts and adapts by placing its cube in the other placement (Fig. 3(c)). Then, the human places the stick on the red cubes. In this scenario, we have chosen the negotiation mode. Since the next action is allocated to the X agent, the robot asks the human if he wants to do it ("Do you want to place the blue cube?"). The human answers yes, leading the robot to compute a new plan in Fig. 3(e) where the human have to place the first blue cube and the robot the second one. Finally, the human and the robot perform their last actions and achieve the goal. Fig. 3: A situation where the robot adapts smoothly its behavior to the human actions. In (b), the human places his cube in the very same placement chosen by the robot. In (c), the robot adapts by placing its cube in the other placement

Quantitative results

In order to evaluate our system, we ran it in simulation using the same scenario. Different set-ups were used as initial states and the robot was confronted to a simulated human. This simulated human performs all actions that are feasible only by him and answers robot questions. When confronted to an X agent action, he either chooses to perform it with 50% chance (50%-case), systematically chooses to perform it (hurry-case) or systematically chooses not to perform it (lazy-case). Then, we settled two different human behaviors:

the "kind" human (case=K) who adapts his behavior to what the robot verbalizes (ie does an action if the robot asks him and stops an action if the robot says it will perform it) -the "stubborn" human (case=S) who does not react nor comply to robot verbalization (he will not change his decision whatever the robot says).

A second independent variable corresponds to the 4 different modes: -using the original system, called Reference System (RS), with all decisions and instantiations performed at planning time:

• RS-none mode: the robot verbalizes nothing (unless it is strictly necessary) • RS-all mode: the robot informs the human when he has to perform an action and when it will act, -using the proposed system, called New System (NS):

• NS-N: the robot uses the Negotiation mode previously defined when a decision need to be made concerning X agent action, • NS-A: the robot uses the Adaptation mode.

Results can be found in Tab. 1. The dependent variables we measured are:

the number of verbal interactions between the human and the robot (either an information given by the robot or question asked).

the number of human/robot incompatible decisions: either both decide to perform the same action (and the robot stops its own action to avoid the conflict) or both decide not to perform the action (the robot first asks the human to

Verbal interactions

Incompatible decisions RS-none RS-all NS-N NS-A RS-none RS-all NS-N NS-A 50%-K 0.4 (0.52) 0.6 (0.52) hurry-K 0.0 6.0 (0.0) 0.3 (0.48) 0.0 lazy-K 0.9 (0.32) 0.9 (0.32) 50%-S 0.4 (0.52) 6.4 (0.52) 1.2 (0.63) 0.0 0.5(0.53) 0.6 (0.52) 0.02 0.0 hurry-S 0.0 6.0 (0.0) 0.3 (0.48) 0.3 (0.48) lazy-S 0.9 (0.32) 6.9 (0.32) 0.9 (0.32) 0.9 (0.32)

Table 1: Results for the Reference System (RS) and the proposed New System (NS): NS-N for the Negotiation mode and NS-A for the Adaptation mode. The measures are the average number of verbal interactions and the average number of incompatible decisions between the human and the robot. The numbers correspond to means in 10 runs and their associated standard deviations.

perform the action after a predefined time and, if after another period the human has still not executed the action, the robot looks for a new plan where it can proceed).

Reference System performance: The verbalizations in the RS-none mode corresponds to the case where the human and the robot both choose not to execute the action: the robot tries to solve the conflict by asking the human to execute the action. Because the robot does not inform about its decisions, the number of verbal interactions is low in this mode. However, due to the same reason, there is several incompatible decisions in each conditions. The RS-all mode avoids incompatible decisions with the "kind" human. However, the number of verbal interaction is high (6 as the number of actions to execute in the task and so to verbalize). With the "stubborn" human, even if the robot informs the human, incompatible decisions remains. The number of verbal interaction also increases as, when the human does not want to perform the action, as it is stubborn, the robot needs to compute a new plan where it executes the action, and so inform about the new action.

New System performance: We can see that the robot is able to avoid conflicts in all cases without being too talkative (or without being talkative at all for the adaptation mode). Moreover, the efficiency of the system is not degraded with the "stubborn" human: the system allows the human to execute the actions he wants without an increase of verbal interaction. Finally, here the adaptation mode performs better than the negotiation one since the human is simulated and always performs his actions in time. However, in a real context, the negotiation mode would certainly have the benefit to ensure the absence of conflicts even if the robot is a little more talkative. Moreover, a human would surely be more comfortable with a robot which directly asks when (and only when) there is a decision to take compared to a robot which has unnecessary waiting time. Such measure of "satisfaction" cannot be easily simulated and further experiments will be done with real humans.

CONCLUSION

In this paper we have presented a system which allows the robot to adapt its behavior and let the maximum latitude and initiative to the human thanks to its ability to determine the decisions that should better be postponed. This also helps to reduce communication avoiding to have a too talkative robot while still avoiding conflicts. Furthermore, this work has been implemented in a complete architecture and is based on algorithms which are generic enough to be used for other tasks and contexts. A recent user study with real subjects has been performed. The first results of this study suggest that the proposed system is better perceived by the users and that the negotiation mode is preferred to the adaptation one for naive users. Finally, number of the mechanisms described in the paper involve cost estimation in order to decide between options. In the current system, simple costs are used but could be easily replaced by more elaborate ones. For instance, a finer estimation of action costs based on geometric reasoning and human efforts or an estimation of accumulated costs of all actions remaining in the plan.

  (a) Final stack and one possible initial set-up (b) PR2 and its human partner

Fig. 1 :

 1 Fig.1: Blocks building task needing collaboration between the robot and the human. There are two identical placements where to put the two red cubes.

Video available at https://youtu.be/MZFG9GV3OD8

These results have been obtained with a simulated human which always takes his decision in a time shorter than the time the robot waits. Consequentlyn there are 0 incompatible decisions. In a more realistic context, there can be incompatible decisions if the robot waiting time is not well configured, or if the human changes his mind. However, there will always be less incompatible decisions than in the case where the robot does not inform at all.

0 This work has been partly supported by the French National Research Agency (ANR) under grant agreement ANR-16-CE33-0017-01 (JointAction4HRI Project)