Fenni Kang

Veronique Letort

Hugo Magaldi

Paul-Henry Cournede

Jeremie Lecoeur

SUNLAB: a Functional-Structral Model for Genotypic and Phenotypic Characterization of the Sunflower Crop

Keywords: Sunflo, Greenlab, Sunflower, Functional-structural model, Specific Leaf Area, Genotypic variability. I

A new functional-structural model SUNLAB for the crop sunflower (Helianthus annuus L.) is developed. It is dedicated to simulate the organogenesis, morphogenesis, biomass accumulation and biomass partitioning to organs in sunflower growth. It is adapted to model phenotypic response to diverse environment factors including temperature stress and water deficiency, and adapted to different genotypic variants. The model is confronted to experimental data and estimated parameter values of two genotypes "Melody" and "Prodisol" are presented. SUNLAB parameters seem to show genotypic variability, which potentially makes the model an interesting intermediate to discriminate between genotypes. Statistical tests on estimated parameter values suggest that some parameters are common between genotypes and others are genotypic specific. Since SUNLAB simulate individual leaf area and biomass as two state variables, an interesting corollary is that it also simulates dynamically the specific leaf area (SLA) variable. Further studies are performed to evaluate model performances with more genotypes and more discriminating environments to test and expand model's adaptability and usability.

INTRODUCTION

As one of the major oilseed crops worldwide, sunflower production has to face the growing social demand in a context of strong ecological and economical constraints: growers are confronted to the challenge of increasing sunflower productivity under changing climatic conditions while maintaining low-input levels and reduced costs. A partial response to this challenge could be found by breeding new genotypes and by identifying the best genotype, among a set of existing ones, for a given location and for given management practices; see for instance [START_REF] Allinne | Genetic control of physiological traits associated to low temperature growth in sunflower under early sowing conditions[END_REF].

Assessments of genotype performances in in situ experimental trials hamper the breeding process by temporal, logistic and economical difficulties. Indeed, genotypes perform differently depending on the environmental conditions (soil, climate, etc) and the management practices (sowing date, nitrogen inputs, irrigation, etc). Therefore a large number of trials are needed to explore a sufficiently diverse set of genotypes x environment x management (GxExM) combinations in order to characterize these complex interactions. An emerging approach to overcome these difficulties relies on the use of models represented as a set of biophysical functions that determine the plant phenotype in response to environmental inputs. Models can help in breeding strategies and management by dissecting physiological traits into their constitutive components and thus allow shifting from highly integrated traits to more gene-related traits that should reveal more stable under varying environmental conditions [START_REF] Yin | Role of crop physiology in predicting gene-to-phenotype relationships[END_REF] [START_REF] Hammer | Models for navigating biological complexity in breeding improved crop plants[END_REF].

Consequently, an important question to examine is how to design models that can be used in that context. The models should simulate the phenotypic traits of interest (e.g. yield) with good robustness and predictive capacity. The models should also present a trade-off between mechanistic aspect and complexity: Chapman et al [START_REF] Chapman | Evaluating plant breeding strategies by simulating gene action and dryland environment effects[END_REF] state that, for such use, a growth model should include 'principles of responses and feedbacks' to 'handle perturbations to any process and self-correct, as do plants under hormonal control when growing in the field' and to 'express complex behavior even given simple operational rules at a functional crop physiological level'. Casadebaig et al [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF] discuss that question in the case of their model SUNFLO [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF]. SUNFLO is a biophysical plant model that describes organogenesis, morphogenesis and metabolism of sunflower (Helianthus annuus L.). It has shown good performances to identify, quantify, and model phenotypic variability of sunflower at the individual level in response to the main abiotic stresses occurring at field level but also in the expression of genotypic variability [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF]. The authors mixed mechanistic and statistical approaches to deal with highly integrative variables such as harvest index (HI). HI is determined by a simple statistical relationship dependent on covariables previously simulated by the mechanistic part of the crop model throughout the growing season. Although this statistical solution and the large datasets used for its parameterization conferred good robustness to the prediction of HI and thereby crop harvest, feedback effects of biomass partitioning on other processes cannot be taken into account. Moreover, it was shown in [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF] that HI is the parameter that contributes the most to the coefficient of variation of the potential yield (14.3%). It was also shown that when ranking the processes in terms of their impact on yield variability, the first one was biomass allocation (before light interception according to plant architecture, plant phenology and far behind photosynthesis). Therefore, Lecoeur et al [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF] suggest that a better formalisation of the trophic competition between organs could be a way to improve our understanding of genotypic variation for biomass harvest index. In order to face this challenge, a new sunflower model, named SUNLAB, was derived from SUNFLO. The representation of plant topological development and allocation process at individual organ scale were inspired by the functionalstructural plant model (FSPM) GREENLAB, that has been designed as a "source-sink solver" [START_REF] Christophe | A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana[END_REF] and is accompanied with the appropriate mathematical tools for its identification [START_REF] Ph | Some parameter estimation issues in functional-structural plant modelling[END_REF]. SUNLAB thus inherits the flexible rules of sink competition for biomass partitioning at organ scale (blade, periole, internode and capitulum) from GREENLAB, together with the more detailed representation of ecophysiological processes and environmental stress effects on biomass production and yield from SUNFLO. This paper will present in detail the mechanisms of SUNLAB, its parameters and identification procedure based on field experimental data. Afterwards, we illustrate the potentials of SUNLAB for genotypic characterization by comparing the parameters obtained for two genotypes, namely "Melody" and "Prodisol". In the end, we discuss the use of SUNLAB for extracting specific leaf area (SLA, g cm - 2 ), i.e. the ratio of leaf area to dry leaf mass, which is an influent variable often associated with large uncertainty ranges [START_REF] Rawson | Sources of Variation in Specific Leaf Area in Wheat Grown at High Temperature[END_REF].

II. MATERIALS AND METHODS

A. Modeling: SUNLAB modules

SUNLAB consists of five modules: phenology, water budget, organogenesis and morphogenesis, biomass accumulation, and biomass distribution. Phenology, water budget, and biomass accumulation modules are directly inherited from SUNFLO model. Organogenesis and morphogenesis module modifies SUNFLO module by defining each organ's biomass initialization and termination thermal time. Biomass partition module is a new module. We describe here equations of these modules, briefly for those that have been inherited from SUNFLO -we refer to [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF] and [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF] for an exhaustive description -and in detail for the new contributions.

1) Phenology: Plant phenology is driven by thermal time. Cumulative thermal time since emergence on day d CTT(d) (in •C.days) was calculated in (1) as the sum of the daily mean air temperature Tm(d) (•C) above a base temperature Tb of 4.8 •C common to all sunflower genotypes. Four key physiological stages, expressed as genotype dependent thermal dates (in °C.days), were defined: flower bud appearance (Ez), beginning of flowering (F1), beginning of grain filling (early maturation, M0) and physiological maturity (M3) [START_REF] Wu | A water supply optimization problem for plant growth based on Greenlab model[END_REF]. Crop development can be accelerated by water stress, that causes overheating of the plant through the reduction of transpiration. This was modeled using a multiplicative effect on day d, FHTR (d) with thermal time accumulation. The water stress effect on plant phenology FHTR(d) is calculated as function of the fraction of transpirable soil water FTSW(d) divided by a genotypic parameter RT of response sensitivity to water deficiency, which is formulated in detail in [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF]:

 1 ( ) (( ( ) ) (1 (1 ( )))) d k CTT d Tm k Tb FHTR k          .
where Tb = 4.8 •C and α = 0.1. 2) Water budget: fraction of transpirable soil water FTSW(d) depends on the interaction of root system with the environment including soil features, soil evaporation, precipitations and irrigation. Soil features include horizontally soil particle size texture, humidity capacity, soil density. Plant transpiration decreases the available water in soil. FTSW(d) is used to compute a water stress index and has effects on three processes: leaf expansion, plant transpiration, and biomass production. For example, for biomass production, FTSW(d) acts as a constraint to effective radiation use efficiency RUE(d) (gMJ -1 ) based on crop's maximal potential use efficiency RUEp(d) (gMJ -1 ):

 () ( ) ( ) (1, ) ( ) FTSW d RUE d RUEp d min FT d PHS RT     . 
where FT(d) is thermal stress on day d, function of daily mean temperature [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF] and PHS is a genotypic parameter giving the ratio of the genotype photosynthesis capacity to that of the reference genotype "Melody".

3) Organogenesis and morphegenesis: The number of blades increases linearly with cumulative thermal time, . The number of emergenced leaves on day d, N(d), was thus calculated as:

 ( ) ( ) 1 N d R CTT d     
where R (in leaves / (°C.days)) is the rate of leaf production. Leaf senescence occurs during the period of grain filling between M0 and M3. Consequently the number of senescent leaves NS(d) was considered to increase in proportion to the time elapsed since M0 and was calculated as follows:

 3 ( ) () 3 1 M CTT d NS d Ntotal M M     . 
where Ntotal is a genotypic parameter equal to the maximal number of leaves.

Since, in sunflower, leaf area distribution along the stem showed a bell-shape, total leaf area A(d) (m²) per plant, was calculated with a logistic equation:

 4 3 ( 2 ( )) 1 1 () 1 A A N d A A Ad e      . 
where A1 (m²)is the maximal leaf area, A2 (m²)and A3 (m²)are respectively the rank and the area of the largest leaf of the plant. The calculation of senescent leaf area AS(d) (m²) is determined by a similar logistic equation but replacing N(d) by NS(d). The photosynthetically active leaf area AA(d) (m²) was estimated as the difference between total leaf area A(d) and senescent leaf area AS(d). Leaf area growth and senescence are affected by water stress and temperature stress coefficients described in detail in [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF].

 4 3 ( 2 ( )) 1 4 3 ( 2 ( )) 1 1 1 () 1 1 A A N d A A A NS d A A A AA d e e           . 
From the emergence and senescence blades numbers, the thermal times of initiation bladeInitTT(i) and senescence bladeSeneTT(i) of each blade of rank i can be computed:

 ( ) ( 1) ( 3 1) ( ) 3 bladeInitTT i i R i M M bladeSeneTT i M Ntotal    . 
The petiole i and the internode i from the same metamer of blade i has the same value of initiation thermal time. While petiole i has the same value of senescence time as bladeSeneTT(i), senescence thermal time of internode i is the same as the accumulative thermal time in the end of the plant life. Capitulum initialization thermal time equates M0 and it grows until the end. With all the information of initialization thermal time and senescence thermal time of every organ, a general sunflower structure can be constructed. For every organ, besides their appearance and senescence thermal time, their expansion thermal time are also calculated, explained in section C: parameter identification.

4) Biomass accumulation: Daily increase in aboveground dry matter DM(d) (g m -²) was calculated from Monteith's equation (1977) linking dry matter production to incoming photosynthetically active radiation through two radiation efficiencies as follows

 ( ) ( ) ( ) 0( ) DM d RUE d RIE d PAR d    . 
where PAR0(d) (MJ m -²) is the daily incident photosynthetically active radiation. RUE(d) (gMJ -1 ) is daily radiation use efficiency and RIE(d) is daily radiation interception efficiency, estimated from Beer's law. In order to estimate the total above-ground biomass CDM(d) (g m -²) daily biomass production was cumulated from emergence

 1 ( ) ( ) d k CDM d DM k   
. 

5) Biomass distribution:

As in GREENLAB, the biomass produced by each leaf is distributed to all organs proportionally to their sink strengths and independently of their position. Blades are sources. Blades, petioles, internodes, and capitulum are sinks. The total above-ground biomass CDM(d) (g m -²) is the total biomass of all leaves, petioles, internodes and the capitulum. For each individual organ, the duration of sink activity is equal to the organ expansion duration epdTT (•C), calculated since its initialization thermal time initTT (•C). Its sink competition ability SA(d) depends on its type, its time of initiation initTT, epdTT and its age. The density function of beta distribution is chosen to model this evolution, with three organ-specific parameters; the organ sink ratio SR and two shape parameters sinkA and sinkB:

1 1 1 1 ( ) 1 ( ) ( ) ( ) 1 1 ( ) (1 )
                                
On day d, the plant total demand sumSink(d) is computed as the scalar product of the number of appeared organs to their daily sink activity SA(d) corresponding to their expansion status. The part of the dry matter production, DM(d), allocated to a single organ is proportional to its SA(d) divided by sumSink(d). For example the biomass allocated to the leaf at rank i at a day d is:

 ( ) ( ) ( ) ( ) i i DM d DM d SA d sumSink d  
.

 

In this way, the daily biomass increments and the cumulated biomass of every single organ can be simulated.

B. Field Experiments and Measurements

Experiments and measurements for designing and constructing modules and parameters directly inherited from SUNFLO are not presented in this paper, as they are described in detail in [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF]. Data used for SUNLAB parameters estimation, simulation and application comes from an field experiment conducted in 2001 at SupAgro experimental station at Lavalette (43°36' N, 3°53' E, altitude 50 m) on a sandy loam soil for five genotypes (Albena, Heliasol, Melody, Mirasol and Prodisol). Sunflowers were sown on 5 May 2001 at a density of about 6 plants m -2 and a row spacing of 0.6 m, in a randomized complete block design with four replications. Plots measured 5.5. X 13.0 m. The crop was regularly irrigated to avoid severe water deficits. It was also fertilized and showed no mineral deficiency. So its biomass production could be considered as potential.

During the experiment, meteorological data such as temperatures and radiation were recorded. FTSW representing the available water in the soil was estimated. Organogenesis is described based on the phenomenological stages that are recorded every 2-3 days [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF]. Once a week, six plants per genotype were harvested. Individual leaf areas were estimated from blade lengths and widths. All the above-ground organs (leaves, stem, capitulum and seeds) were collected and then oven-dried at 80°C for 48 h. The dry weights of these organs were measured by compartments. Daily radiation interception efficiency RIE(d) and daily radiation use efficiency RUE(d) are respectively calculated and estimated based on field measurements as in [START_REF] Lecoeur | Quantifying physiological determinants of genetic variation for yield potential in sunflower. SUNFLO: a model-based analysis[END_REF].

C. Parameter Identification

Two genotypes "Melody" and "Prodisol' are referred in this paper. They are genotypes characterized by a large study of genetic improvement of sunflower during the last 30 years, and they are two of those most widely grown varieties in France. SUNLAB parameters can be decomposed in two subsets. One subset contains the parameters inherited from SUNFLO which keep the same values in SUNLAB (Table I). The other subset contains 17 additional parameters of SUNLAB which needs parameter estimation. They include 12 parameters that drive the sink competition (SR, sinkA, sinkB for four types of organs), and 5 parameters:

initTTAdjust (•C), epdTTA (•C), epdTTB (•C), internodeEpdTT (•C), capitulumEpdTT (•C), explained
together with the model mechanism defining organs' biomass expansion.

For organs' biomass initilisation thermal time, according to the experimental criterion: leaves are recorded when lengths of their central vein are bigger than 4cm [START_REF] De La Vega | Effects of planting date, genotype, and their interactions on sunflower yield: I. Determinants of oil-corrected grain yield[END_REF], in SUNFLO blade initialization thermal time bladeInitTTi (•C) is blade appearance thermal time when leaf size could be measured, but then this leaf has already received a small amount of biomass. So in SUNLAB, an adjustment parameter initTTAdjust (•C) had to be added to bladeInitTTi (•C) for calculating the initiation thermal time of blade biomass. Petioles and internodes of the same metamers share the same initialization thermal time. Capitulum begins its sink competition at plant age M0.

The biomass expansion duration of blades and petioles can vary with their rank: the variation is linear and depends on two parameters, epdTTA (•C) and epdTTB (•C). For example, blade rank i has expansion duration, expressed in thermal time, bladeEpdTT(i) (•C):

 ( ) ( ) ( ) bladeEpdTT i bladeSeneTT i epdTTB epdTTA i     .
where bladeSeneTT (•C) is the thermal time of leaf of senescence. Internodes and capitulum have respective parameter internodeEpdTT (•C) and capitulumEpdTT (•C) to define its expansion.

Regarding the target data for parameter estimation, only blade areas were measured at organ scale. All other organs were only weighted at compartment scale. In particular, independent blade mass data was not available, while these data are needed for a better estimation of SUNLAB parameters. Therefore, profiles of individual blade mass were estimated as follows: at each date where total blade mass and total blade areas were measured at compartment level, a virtual SLA value was computed and was used to generate a set of individual blade mass. The model can thus be viewed as a dynamic interpolation solver that generates both blade areas and mass between those fixed measurement dates. This will be detailed in the SLA study.

The non-linear generalized least squares method with Gauss-Newton method for optimization [START_REF] Ph | Some parameter estimation issues in functional-structural plant modelling[END_REF] was used for fitting these parameters to field data including total blade biomass, total petiole biomass, total internodes biomass, capitulum biomass and individual blade biomass. The estimation and the simulation for parameter verification were performed with a plant modeling assistant platform PYGMALION developed in Digiplante in Ecole Centrale Paris, France.

III. RESULTS AND ANALYSIS

A. Model Performances for Gentoype Melody

Estimated values of SUNLAB subset of parameters for genotype Melody are shown in Table 2. Since the sink competition model is chosen to be proportional (all the daily produced biomass is allocated, no reserves), a reference sink value has to be set: conventionally, the sink of blades SRblade is set to 1.

Simulations of total leaf area, radiation interception efficiency, total dry above-ground biomass, and individual blade area expansion are the same as in SUNFLO. Total blade biomass, individual blade biomasses, total petiole biomass, total internode biomass, and capitulum biomass are simulated by SUNLAB after parameter identification. Their comparisons with experimental data are shown in

B. Genotypic Variance in Model Performances

Simulation and field data comparisons of genotype Melody and Prodisol are shown in Fig. 2. SUNLAB is able to reproduce the genotypic diversity in biomass partitioning.

In Table 2, significant parameters and their standard errors are compared between the genotype "Melody" and "Prodisol". With a Student's t-test, parameters of internode sink ratio SR and the parameter sinkB in the sink variation function of internodes (SRinternode and sinkBintern) proved significantly difference between the two genotypes, while no clear evidence of genotypic variability was found for other parameters. According to those parameter features, internodes of Prodisol show an earlier peak of biomass competition but a general low competition capacity than Melody (Fig. 2). More rigorous parameter variance analyses and corresponding parameter estimation on more genotypes are to be carried out.

C. Model Application: an Exploratory Study of Specific leaf Area (SLA)

SLA is an important variable in plant growth modeling. For example, it determines blade surface area values based on blade biomass for further simulatio n loops in GREENLAB [START_REF] Christophe | A model-based analysis of the dynamics of carbon balance at the whole-plant level in Arabidopsis thaliana[END_REF]. SLA is usually considered constant in those models. In reality SLA varies according to genotypes, leaf ranks and leaf growing periods, as it has been observed for instance for the SLA variations of wheat [START_REF] Rawson | Sources of Variation in Specific Leaf Area in Wheat Grown at High Temperature[END_REF]. Last graph displays comparison of sink capacity of internode. Its x axis represents the ratio of internode age to its expansion duration.

TABLE II. SUNFLO INHERITED PARAMETER VALUE SUNLAB PARAMETERS VALUES AND THEIR VARIANCES

For sunflowers, the variations of SLA and the factors influencing them are still poorly known. Accurate estimation of SLA is mentioned as a major source of error in models and implies difficulties in obtaining a reliable computation of leaf area index, which is the main component of biomass production modules [START_REF] Heuvelink | Evaluation of a dynamic simulation model for tomato crop growth and development[END_REF] [START_REF] Marcelis | Modelling of biomass production and yield of horticultural crops: a review[END_REF]. As SUNLAB simulation outputs include individual blade masses and blade areas, a preliminary study of SLA characteristics based on simulation is carried out. Figure 3.A shows the SLA evolution with time (day 40 to 100) for leaves ranking from 6 to 10. These leaf ranks and time windows were chosen as at that time both their simulated blade biomasses and surfaces were in very good agreement with experimental data. In the selected time period, their SLA curves show a quick increase and afterwards a decline towards a stable value. Figure 3B shows the variation of SLA value among leaves at different positions (ranking 1 to 25) for the two genotypes "Melody" and "Prodisol". The SLA for each blade in this graph is the value at the time when this blade has its maximum leaf surface and biomass. Blades at the top of the sunflower crop which rank higher in the graph have bigger SLA than those at the bottom. "Melody" blades have slightly bigger SLA than "Prodisol". Some phenomena coincide with the reported results for SLA of wheat [START_REF] Rawson | Sources of Variation in Specific Leaf Area in Wheat Grown at High Temperature[END_REF]: the genotype with the longer longevity of leaves had smaller SLA, and that SLAs of leaves on top of sunflower crop were bigger. Since the current SUNLAB parameters come from the reconstructed individual blade masses, the simulated SLA results can be improved with better experimental data and corresponding estimations in the future. SUNLAB is a pioneer crop model for detailed study on SLA variable. SUNLAB could assist studying SLA variation response to environment and genotypes. Further studies are planned.

Figure3A: Time evolution of average SLA for "Melody"; Figure3B: SLA for ranked leaves of genotypes "Melody" and "Prodisol".

IV. DISCUSSION AND CONCLUSION

A functional-structural model, SUNLAB was developed. It describes the sunflower topology and morphogenesis at organ level with blades, petioles, internodes, and capitulum. Coordination of the expansion dynamics of these organs are ruled by their initiation and senescence times, expressed with respect to thermal time. Because of the simple sunflower architecture, organogenesis and morphogenesis modules could be implemented in SUNFLO without adding too many supplementary parameters. Eco-physiological processes work together with plant structural dynamics to affect biomass accumulation and partitioning to organs.

In the present study, we have then evaluated the ability of this newly-developed model to reproduce observed data of sunflower growth. It was applied on data of two different genotypes, Melody and Prodisol. It was observed that Prodisol had a higher capitulum mass accumulation, thus better yield, than Melody after around 80 days (see Fig. 2). Identifying the processes that most contributed to that difference was difficult. Our results suggest several potential factors: Prodisol has slightly larger SLA values, which implies a larger photosynthetically active blade area than Melody for the same leaf biomass. The internode sink variation is different and may also contribute to explain the difference, since less biomass is allocated to the stem compartment of Prodisol. The later peak of internode sink of Melody results in a later internode completion of biomass at the important periods of capitulum biomass accumulation, which may be detrimental to the yield of Melody. Apart from internodes, no significant differences were found for the sink parameters, which suggests that functional balance is similar for the two genotypes and that the difference observed in yield for these two genotypes is also explained by differences in their SUNFLO subset of parameters, such as differences in their phenology.

As a joint concept of SUNFLO and GREENLAB, SUNLAB has better structural features than SUNFLO and it succeeds to deal with the biomass distribution at organ level.

Compared to GREENLAB, SUNLAB inherits the ecophysiological functions of SUNFLO that have been validated in different environmental conditions for 26 genotypes [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF][6] and possesses SUNFLO's following merits. Firstly, SUNFLO contains more genotype-specific parameters. It could predict well large phenotypic variability of complex genotypic traits [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF]. These genotypic traits, represented as genotypic parameters in the model, have enough genotypic variability to discriminate between genotypes. In the construction process of SUNFLO, the authors used the approach of linking a complex phenotype to a set of accessible genotypic traits. Each genotype is defined by chosen traits which were transcribed into a set of genotype-specific parameters. These genotypic parameters are thus under certain genetic control. With the reason of improving the model parameters update ability for yearly cultivar releases, parameters number is limited while a useful predictive capacity is maintained. Meanwhile, as most SUNFLO parameters could be estimated by direct measures, it allows parameter values to be more representative of crop physiology than those that are estimated indirectly with optimization algorithms [START_REF] Casadebaig | SUNFLO, a model to simulate genotype-specific performance of the sunflower crop in contrasting environment[END_REF]. Secondly, SUNFLO and SUNLAB have better ecophysiological functions. GREENLAB over-simplifies a number of processes, such as photosynthesis and assimilate conversion to biomass [START_REF] Guo | Modeling of biomass acquisition and partitioning in the architecture of sunflower[END_REF], and it is still in its preliminary stage to include water source influence and root system [START_REF] Wu | A water supply optimization problem for plant growth based on Greenlab model[END_REF]. In SUNFLO and SUNLAB, the radiation use efficiency is taken into account for photosynthesis. Many environmental stresses to phenotypic plasticity are considered, such as temperature and water. The included root sub-model induces water stress, which affects crop processes such as leaf expansion, plant transpiration, and biomass production. This consideration enriches environment discrimination by taking into account the effects of soil texture, apparent soil density and stone content.

Modeling crop growth and breeding through empirical experimental analysis and direct parameter measurements, such as SUNFLO model, has outstanding ecophysiological advantage such as parameters have good genotypic variability, as explained in the previous paragraph. Alternative modeling methods relying on optimization algorithms are less ecophysiologically representative, but they have their advantages of saving cost and producing more information. For example GREENLAB model produces far more details of organs structure and biomass partitioning than SUNFLO. While it is hard to find a balance for a model design, SUNLAB model is an interesting trial. It models ecophysilogical functions of photosynthesis and morphogenesis to ensure a more accurate and a better representative of crop physiology for biomass production. But biomass partitioning that was not modeled in SUNFLO cannot be directly measured and can hardly be handled because of the heavy experiments and the difficulty to understand the organs interaction. Then parameter estimation by model inversion from experimental data is necessary, as done in this study for biomass partitioning to all organs. SUNLAB proves that this combination of concepts is effective because it manages to explain the competition of biomass by simulating organ biomass distribution, while it preserves genotypic discrimination (as shown for the internode sink ratio and the parameter β in the sink variation function of internodes).

SUNLAB could simulate water deficiency effect on the crop sunflower, but in this paper it is only tested with an environmental input data without strong water deficiency. The upcoming research involves model evaluation in strong water deficiency case with many more genotypes.

Fig. 1 .

 1 The simulated and observed values for individual blade areas and masses are displayed for each rank and seven different growth stages. The dynamics of compartment mass variations, as well as individual blade mass profiles, are satisfactorily reproduced by the model.

Figure 1 .

 1 Figure 1. Experimental data (dot) and simulation (line) comparisons for the genotype "Melody". The last two graphs have blade rank for x-axis. Others have crop growth time as x-axis

Figure 2 .

 2 Figure 2. Biomass partitioning comparisons between genotypes "Melody" and "Prodisol". Experimental data is represented by dot and simulation by line.Last graph displays comparison of sink capacity of internode. Its x axis represents the ratio of internode age to its expansion duration.

TABLE I .

 I SUNFLO INHERITED PARAMETER VALUES


Gwendoline Fox

Juliette Thuilier

Predicting the Position of Attributive Adjectives in the French NP

Introduction

French displays the possibility of both pre-nominal and post-nominal ordering of adjectives within the noun phrase (NP).

(1) un a magnifique magnificent tableau painting / / un a tableau painting magnifique magnificient "a magnificient painting" While all adjectives may alternate in position, the choice between both orders is not as free as suggested in (1): The examples in [START_REF] Forsgren | La place de l'adjectif épithète en français contemporain, étude quantitative et sémantique[END_REF] show that the positionning of attributive adjectives is a complex phenomenon: unlike magnifique, the adjective beau cannot be placed freely when it is the only element of the adjectival phrase (AP). It is strongly preferred in anteposition (2-a). The addition of the pre-adjectival adverb très gives more flexibility and equally allows both orders (2-b) whereas the use of a post-adjectival modifier constrains the placement to postposition (2-c).

The phenomenon of adjective alternation has been widely studied in French linguistics ( [START_REF] Waugh | A semantic analysis of word order : Position of the Adjective in French[END_REF], [START_REF] Forsgren | La place de l'adjectif épithète en français contemporain, étude quantitative et sémantique[END_REF], [START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF], [START_REF] Delbecque | Word order as a reflexion of alternate conceptual construals in french and spanish. similarities and divergences in adjective position[END_REF], [START_REF] Nølke | Où placer l'adjectif épithète? focalisation et modularité[END_REF], [START_REF] Abeillé | La position de l'adjectif èpithète en français : le poids des mots[END_REF], [START_REF] Noailly | L'adjectif en français[END_REF] among others). Many constraints were proposed on different dimensions of the language: phonology, morphology, syntax, semantics 3 , discourse and pragmatics. Only one of them is categorical in the sense that it imposes a specific position to any attributive adjective: the presence of a post-adjectival complement [START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF] or modifier (2-c) only allows postposition of the adjective. The other constraints participating in the alternation between anteposition and postposition are not categorical. For instance, as noted in the corpus studies of [START_REF] Forsgren | La place de l'adjectif épithète en français contemporain, étude quantitative et sémantique[END_REF] and [START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF], length is a preferential constraint: short adjectives tend to be anteposed to the noun. The sequence "un magnifique tableau" in [START_REF] Waugh | A semantic analysis of word order : Position of the Adjective in French[END_REF] illustrates that this rule can be violated whether one considers the length of the adjective alone: magnifique has 3 syllables, or the relative length between the adjective and the noun (3 > 2).

Although the above-mentioned works have enabled to identify the constraints playing a role in the placement of adjectives, most are based on introspection and only examine a few of these constraints. It is thus very difficult to evaluate the actual impact of each of them in usage, and therefore to estimate their respective weight in the speaker's choice for one position over the other. This paper aims to get a better grasp of the general picture of the phenomenon. To do so, we present along the same lines as [START_REF] Arnold | Heaviness vs. newness: the effects of structural complexity and discourse status on constituent ordering[END_REF], [START_REF] Rosenbach | Animacy versus weight as determinants of grammatical variation in english[END_REF] and [START_REF] Bresnan | Predicting the dative alternation[END_REF], a quantitative study, based on two corpora: the French Tree Bank (henceforth FTB) and the Est-Républicain corpus (henceforth ER). We propose a regression model based on interpretable constraints and compare the prediction capacities of different subsets in order to determine what kind of informations are the most reliable to account for the placement of adjectives.

The paper is organised as follows. We present in section 2 the methodological aspects of our study : constitution of the datatable and presentation of the statistical model. In section 3, we describe the variables derived from the constraints found in the literature. Section 4 is dedicated to the comparison of the models based on the different subsets of variables and to the interpretation of the results.

Methodology

Building the Datatable The first step of this work is to collect the data concerning adjectives and capture the constraints found in the literature. The study is based on the functionally annotated subset of the FTB corpus [START_REF] Abeillé | Enriching a french treebank[END_REF] 4 , which contains 12,351 sentences, 24,098 word types and 385,458 tokens. It is, for the moment, the only existing treebank for French. We extracted all the occurrences of attributive adjectives from this corpus5 , and filtered out numeral adjectives 6 , adjectives appearing in dates 7 , abbreviations 8 and incorrectly annotated occurrences. We also discarded the 438 adjectives occurring with a post-adjectival dependent since postposition is obligatory in this case, regardless of the values of other constraints that we consider (see (2-c) and ( 3)). The remaining adjectives constitute the basis of the datatable, to which we have added information on the position of each adjective with respect to the noun it modifies, and 10 other variables that we describe in section 3.

Three variables of our study are based on frequency counts: freq, Collo-cAnt and CollocPost. They were extracted from the ER corpus for more reliable counts. The raw corpus contains 147,934,722 tokens, and is available on the ATILF website 9 . It was tagged and lemmatized with the Morfette system [START_REF] Grzegorz Chrupala | Learning morphology with morfette[END_REF] adapted for French. We used ER for these constraints because it is around 380 times larger than FTB. We therefore consider that frequency in ER is a better estimator of the probability of use of an adjective. Also, we use here a log transformed value of the frequency to reduce the range of values of this variable. More precisely, the three variables take the following value: log(frequency in ER + 1 ), in order to avoid a null value in case an adjectival lemma or noun-adjective combination is absent from ER.

Presentation of the Datatable The datatable contains 14,804 occurrences corresponding to 1,920 adjectival lemmas. 4,227 (28.6%) tokens appear in anteposition, and 10,577 (71.4%) in postposition. Table 1 shows that the adjectival lemmas displaying occurrences in both positions represent only 9.5% of all lemmas, yet these few lemmas correspond to 5,473 occurrences, i.e. 37.0% of the datatable, which means that very few adjectives actually alternate in usage but they are highly frequent.

Note that among the alternating adjectives (occurring in both positions), the ratio between anteposed and postposed occurrences is the reverse from that of all adjectives: there are 3,727 anteposed (68,1%) and 1,746 postposed (31,9%) adjectives. Alternating adjectives thus show a preference for anteposition. The general pattern is therefore that postposed adjectives tend to be infrequent lemmas occurring only in postposition, whereas alternating adjectives tend to be frequent and to prefer anteposition.

Statistical inference and Logistic Regression

We used logistic regression models [START_REF] Agresti | An introduction to categorical data analysis[END_REF] to estimate the distribution of adjective positions using the variables from the datatable. Formally, a logistic regression is a function for which values 1. Distribution of adjectival lemmas and tokens according to position can be interpreted as conditional probabilities. Its analytical form is as follows:

π ante = e βX 1 + e βX (1)
where, in our case, π ante is the probability for the adjective to be anteposed and β corresponds to the abbreviation of the sequence of regression coefficients α, β 0 ... β n , respectively associated with the predicting variables X 0 ... X n . Given a scatter plot, the calculation of regression consists in the maximum likelihood estimation of α and β i parameters for each variable in a logit space.

This type of modelling consists in the combining of several explicative variables (binary or continuous) to predict the behaviour of a single binary variable, here the position of the adjective. More precisely, we estimate the probability of anteposition as a function of 10 variables. Given one adjectival occurrence and the value of the 10 explanatory variables attributed to this occurrence, the model gives the probability of anteposition of the occurrence. Here, the model predicts postposition if the probabilty is below 0.5, and anteposition if it is higher or equal to 0.5. The accuracy gives the proportion of data that is correctly predicted according to this threshold. However, this measure does not evaluate completely satisfactorily the predictive power of the model because the threshold is arbitrary and does not account for the fact that a probability of 0.55 is different from a probability of 0.95. We therefore use an additional measure: the area under the ROC curve (AUC) [START_REF] Harrell | Regression modeling strategies: with applications to linear models, logistic regression, and survival analysis[END_REF], [START_REF] Bresnan | Predicting syntax: Processing dative constructions in american and australian varieties of english[END_REF]. This measure gives the discrimination capacity of the model for all the pairs of opposite responses. A model with an AUC probability close to 0.5 indicates random predictions, and a value of 1, perfect prediction. It is usually considered that a model with an AUC value equal or above 0.8 has some utility in predicting the value of the dependent variable [14, p. 247].

The methodology of this paper consists in the comparison of models based on different constraint clusters, in order to evaluate their respective relevance. The comparisons take as reference a baseline model that does not contain any explanatory variables and systematically predicts postposition. Its accuracy is of 71.4% (σ = 0.019), which corresponds to the proportion of postposed adjectives in the datatable. Moreover, for the baseline model, AUC = 0.5, given that this model does not discriminate anteposition and postposition.

The variables we use in our logistic regression models are derived from the constraints found in the literature on attributive adjectives in French. They are summarized in table 2. Each model is based on different sets of constraints according to specific properties. The first set (coord and adv) concerns the syntactic environment of the adjective, the second is based on the lexical properties of the adjectival item (derived, natio and indef), the third one on constraints linked to cognitive processing (adj-length, AP-length and freq). Finally, the fourth group examines collocationnal effects of the Noun -Adjective combination (CollocAnt and CollocPost).

Variables

Syntactic variables

The variables based on syntactic properties rely on the idea that the internal structure of the AP has an influence on the placement of adjectives. As seen in the introduction, one of them, i.e. the presence of a post-adjectival dependent, is categorical and is therefore not integrated in our study. It suggests however that the syntactic environment of the adjective may have an important role in its positioning. We thus propose here two other constraints related to different internal structures within the AP.

Coordination (coord)

In a competence account of attributive position like in [START_REF] Abeillé | La position de l'adjectif èpithète en français : le poids des mots[END_REF], the position of coordinated adjectives is not restricted, as can be seen in example (4) (from [START_REF] Abeillé | La position de l'adjectif èpithète en français : le poids des mots[END_REF]). Presence of a Pre-Adjectival Adverb (adv) The constraint is the same as for coordination if one considers the adverbial category on a general level: the presence of a pre-adjectival modifier does not restrict the position of the modified adjective (example (5)).

( On a more specific level, [START_REF] Abeillé | La position de l'adjectif èpithète en français : le poids des mots[END_REF] point out that adjectives can be postposed with any adverb whereas only a small set of adverbs allows anteposition. This is confirmed in our datatable: 11 types of adverb10 are observed with anteposed adjectives, while 119 different types appear with adjectives in postposition. Furthermore, the adverbs found with adjectives in anteposition are not specific to this position, they also appear with postposed occurrences. From a general quantitative point of view, 74.9% of the premodified adjectival occurrences are in postposition.

Cognitive Processing Variables

Length and frequency of occurrence are constraints that have cross-linguistically been observed to play a role in different types of phenomena, amongst which the adjective alternation. These constraints are usually related to processing ease (see for instance [START_REF] Wasow | Postverbal behavior[END_REF], [START_REF] Hawkins | Efficiency and Complexity in Grammars[END_REF] and [START_REF] Bybee | Alternatives to the combinatorial paradigm of linguistic theory based on domain general principles of human cognition[END_REF]). We present the functioning of the constraints in what follows and leave the interpretation in terms of cognition to the discussion of the models performance.

Length Numerous works on word order use the notion of length: for attributive adjectives in French [START_REF] Forsgren | La place de l'adjectif épithète en français contemporain, étude quantitative et sémantique[END_REF], [START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF], for word [START_REF] Cooper | World order[END_REF], [START_REF] Benor | The chicken or the egg? a probabilistic analysis of english binomials[END_REF] and constituent [START_REF] Hawkins | The relative order of prepositional phrases in english: Going beyond manner-place-time[END_REF], [START_REF] Wasow | Postverbal behavior[END_REF], [START_REF] Rosenbach | Animacy versus weight as determinants of grammatical variation in english[END_REF], [START_REF] Bresnan | Predicting the dative alternation[END_REF] alternation in other languages. The main idea is expressed by the principle short comes first, i.e. short elements tend to appear first. Here, we consider length in terms of number of syllables and we introduce two variables: length of the adjective (adj-length) and length of the adjectival phrase (AP) (APlength) 11 .

Lemma Frequency (freq) In his corpus study, [START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF] observes that frequency is correlated with the position of the adjective: pre-nominal adjectives tend to be frequent whereas post-nominal adjectives tend to be rare. According to the author, this distribution has historical grounds. In Old French, the general pattern was the reverse of that of Modern French: adjectives were generally placed before the noun, as in English. The evolution to the preference for postposition in Modern French did not affect the most frequent adjectives because their association to anteposition was too robust to reverse the pattern. Note that this hypothesis is not particular to French, nor to the adjective alternation, see for instance the summary in [23, ch.11] of several studies that make the same observation of conservatism linked to frequency.

Lexical Variables

Most reference grammars state that adjectives are mainly placed according to their lexical properties. These properties can concern different aspects of language. We propose to examine the relevance of lexical information with the example of three classes, each based on one particular aspect: morphology (derived), semantics (natio), and syntactic behaviour (indef).

Derived Adjectives (derived) Adjectives may be derived from other partsof-speech: for instance, certain verbal forms can be used as adjectives (past participles, present participle) or the adjective is obtained by suffixation, to a verbal basis: -ible 'faillible' (faillible) / -able 'faisable' (doable) /if 'attractif' (attractive), or to a noun ('métallique' (made of metal ), 'scolaire' (academic), 'présidentiel' (presidential )). These adjectives are described as prefering postposition but anteposition is also possible as shown in example [START_REF] Abeillé | La position de l'adjectif èpithète en français : le poids des mots[END_REF]. In our datatable, the adjectives derived from another part-of-speech (noun or verb) are collected using the software of derivational morphological analysis Derif [START_REF] Namer | Acquisition automatique de sens à partir d'opérations morphologiques en français : étude de cas[END_REF]. Our data confirms the strong preference for postposition within this class (91.3%).

Semantic Classes It is usually said that objective adjectives, i.e. adjectives for which the semantic content is perceptible or can be infered from direct observation, are postposed. Objective adjectives are classified into sub-groups like form, colour, physical property, nationality, technical terms... In order to estimate the relevance of lexical classes according to semantic properties, we test the predictive capacity of adjectives denoting nationality12 (natio). In theory, these adjectives strongly tend to be postposed, but they may also occur in anteposition (example [START_REF] Noailly | L'adjectif en français[END_REF]): [START_REF] Noailly | L'adjectif en français[END_REF] cette this très very italienne Italian invasion invasion de of l'Albanie Albania "this very Italian invasion of Albania" (in a typical Italian fashion way) [26, p. 142] The strong preference for postposition of these adjectives is confirmed by our data: only one pre-nominal occurrence is observed (example (8)). Indefinite Adjectives (indef) A relatively closed set of adjectives are special in the fact that their syntacitc properties show a hybrid behaviour between determiners and adjectives. On the one hand, indefinite adjectives may introduce and actualise the noun, like determiners. On the other hand, they may co-occur with a determiner and can be placed in post-nominal position, even though they favour anteposition (89% in our data). These latter properties are specific to attributive adjectives. The adjectives identified as indefinite in the datatable are: 'tel' (such), 'autre' (other ), 'certain' (some/sure), 'quelques' (few ), 'divers' (various), 'différent' (different), 'maint' (numerous), 'nul' (null /lousy), 'quelconque' (any/ordinary), 'même' (same/itself ).

Collocation Variables

It is well known that the nature of some Adjective-Noun combinations is strongly collocational in French [START_REF] Gross | Les expressions figées en français: noms composés et autres locutions[END_REF]. This implies that the position of attributive adjectives in French should also be influenced by collocational effects. Collocations are here defined according to [28, p. 151]. Adjective-Noun collocations may be non-compositional sequences as well as more compositional ones. The sequence 'libre échange' (lit. free exchange) is an example of the former: it refers to a specific economical system, not to exchange in general. As an illustration of the latter case, the meaning of 'majeure partie' (major part) is predictable from the meaning of the two components. It is nevertheless a collocation because the order between the elements is fixed by convention of use. As mentioned in section 2, the collocation score in our datatable is based on the frequency of Adjective-Noun (CollocAnt) and Noun-Adjective (CollocPost) bigrams in the ER corpus.

Prediction Model of Attributive Adjective Position

The prediction model is built with all the variables described in part 3 and maximized with a backward elimination procedure based on the AIC criterion [START_REF] Akaike | A new look at the statistical model identification[END_REF] 13 . The adj-length constraint's contribution to the model is not significant according to the procedure. It was thus eliminated. The model is presented in figure 1 14 .

The coefficients combined with each variable are estimated from the distribution of the variables in our datatable. In the case of boolean variables, these coefficients are multiplied by 1 when the predictor is true, and by 0 when it is false. As for the numerical variables (AP-length, freq, CollocAnt, Col-locPost), their participation to the models consists in the multiplication of the coefficient by the numerical value of the variable itself. In this model, all the variables have positive values, so we can straightforwardly interpret the sign of the coefficients: positive coefficients indicate that the variables prefer anteposition, whereas negative coefficients show that the variables favour postposition. As we expected, the variables coord, AP-length, derived, natio, adv and Col-locPost tend to favour postposition, whereas freq, indef and CollocAnt vote for anteposition Compared to the baseline model performances (accuracy of 71.4% and AUC = 0.5), this model has significantly better predictive capacities. The prediction performances associated with the procedure of decision are presented in table 3. One can see that the global model correctly predicts the position of 92.6% of the datatable. Moreover, the concordance probability is AUC = 0.969 (σ = 0.003), which indicates that the model predictions are very accurate. To have a graphical idea of the goodness of fit of the model, the plot in figure 2 gives the relation between the observed proportions and the corresponding mean expected 14 The condition number of the model is κ = 13.35. It indicates that the collinearity of the model is moderate [START_REF] Belsley | Regression diagnostics: identifying influential data and sources of collinearity[END_REF]. When the predictors of a regression model are collinear, the interpretation of the contribution of each predictor can rise problems. Given that we do not interpret the values of the coefficients, but only to the sign of these coefficients, the moderate collinearity of our data does not affect the validity of our results.

probability for the model 15 . It shows that the fit is very good for probabilities under 0.5, and not quite as good for higher probabilities. Syntactic Model (coord and adv). The comparison based on accuracy shows that the effect of the syntactic constraints is insignificant when they are not combined with other constraints. The Syntactic model accuracy is 71.4% (σ = 0.02), and the classification table in 4 shows that this model cannot predict anteposition. The value of the concordance probability (AUC = 0.534, σ = 0.008) confirms that the predictive power of these variables is very poor. This lack of predictive power can be partly explained by the fact that these two variables are relevant for a very small set of data: adv and coord represent respectively 5.2% and 5.4% of all the data. In addition, both constraints favour postposition, which is already the default position predicted by the baseline model. This means that these constraints can only be relevant when other constraints are also taken into account.

Predicted position % Correct P A observed P 10574 3 99.9% position A 4227 0 0% Overall accuracy: 71.4% (σ = 0.02) Table 4. Classification table for Syntactic model Lexical Properties Model (natio, indef and derived) Lexical properties are relevant when they are not combined with the other constraints (Lexical properties model accuracy = 74.7% and AUC = 0.717). However, the table in 5 indicates that the lexical properties that we used do not predict satisfactorily anteposition: only 12.9% of anteposed adjectives are correctly accounted for. This is mainly due to the fact that only one of the variables (indef) favours the prenominal position. Nevertheless, one can see that these three constraints alone enable the model to consider anteposition, which was not the case with syntactic constraints. This observation suggests that speakers may be sensitive to this type of information and encourages us to extend the lexical classification for all the adjectives of the datatable, in particular those that favour anteposition, in order to improve our modelling. Frequency-Length Model (AP-length and freq). The variables of length and frequency have an important predictive power (accuracy 81.7% (σ = 0.009), AUC = 0.869 (σ = 0.010)). In particular, the predictions for anteposition are much higher than observed with the two preceding models (65%). These two constraints may thus play an important role in the placement of adjectives. As expected, the model tends to predicts anteposition for short and frequent adjectives, and postposition when the adjective is longer and/or less frequent 16 . Collocation Model (CollocAnt and CollocPost). The Collocation model shows that the frequency of bigrams represents the best predictor. The Collocation model accuracy is of 89.9% (σ = 0.013) and the AUC value increases up to 0.940 (σ = 0.006). This result suggests that the order of the adjectivenoun sequence depends highly on the nature of both the noun and the adjective, and on the frequency with which these elements appear in a specific order. It thus appears here again that frequency is a good predictor for the placement of adjectives. However, the fact that this model is more performant than the previous one seems to show that frequency is a better predictor when it takes into account more information than the adjective isolated from its context of appearance.

Predicted position %

Discussion

The models presented above show that the constraints playing a significant role in the adjective alternation are information specific to the adjectival item and to its context of use, rather than constraints based on a more general and abstract level. These specific informations relate to different aspects of language. On the one hand, the constraints tested in the lexical model (natio, indef and derived) concern inherent linguistic properties. On the other hand, length of the AP, frequency of the adjective, and collocational effects are more related to the way language is processed and used: how speakers place the AP according to its linear constitution during discourse, and how they retrieve the units (or sequences) in accordance with their past experience of these elements. The importance of the predictive power of the second set of specific constraints suggests that adjective alternation may be best accounted for in terms of cognitive approaches to language.

As mentioned in the description of the length variable (sec. 3.2), the tendency to place short elements first is not specific to adnominal adjectives in French. It is also observed in other works for various phenomena in other languages. The general preference for such a placement is explained by the fact that it eases the on-line processing of the structure within which the element occurs: for example, [START_REF] Hawkins | The relative order of prepositional phrases in english: Going beyond manner-place-time[END_REF], [START_REF] Wasow | Postverbal behavior[END_REF], [START_REF] Rosenbach | Animacy versus weight as determinants of grammatical variation in english[END_REF], [START_REF] Bresnan | Predicting the dative alternation[END_REF] , who study different constituent to constituent ordering phenomena, state that anteposition of the short element helps to faster plan/recognise the overall structure of the immediately dominating constituent. This idea can be applied to the Adjective-Noun combination. A short AP in anteposition leads to a faster production/reception of the Head-Noun in comparison with a longer one, and hence to a faster access to 1) the complete internal constitution of the AP, 2) more information concerning the structure of the NP. The significant contribution of length in the prediction of adjective alternation may thus be viewed as another support for an explanation in terms of processing ease. In a similar perspective, Usage-based models (see for example [START_REF] Bybee | The emergent lexicon[END_REF], [START_REF] Croft | Radical Construction Grammar[END_REF], [START_REF] Goldberg | Constructions at Work: the nature of generalization in language[END_REF]) consider that frequency plays an important role in the constitution of the speaker's linguistic knowledge. These approaches view linguistic knowdledge as mental representations based on the storage of instances of language encountered by the speaker. This means that speakers store isolated words like it is traditionally assumed for the constitution of the lexicon, but also that they memorize information about specificities related to their context of appearance. In our study, the assumption is that speakers would have mental representations corresponding to the adjective, and representations of specific ordered Adjective-Noun sequences in which it appears. Furthermore, these models consider that every occurrence of an instance affects the corresponding mental representations. Of particular interest here, [START_REF] Bybee | Alternatives to the combinatorial paradigm of linguistic theory based on domain general principles of human cognition[END_REF] notes that the repetition of a language instance strengthens its representation and makes its execution more fluent. The instance also becomes more entrenched in the morpho-syntactic structure in which it usually appears, which leads to more resistance for a change of structure. Applied to adjectives, this means that a highly frequent item (or sequence) is highly ac-cessible, and thus easy to process. When the item is tested in isolation (freq), if processing ease plays an important role in the placement of adjectives as it was suggested for length, one would expect highly frequent adjectives to favour anteposition. Concerning collocationnal effects (CollocAnt and CollocPost), the prediction of this approach is that a collocationnal sequence would be reproduced in the same morpho-syntactic configuration, i.e the order between the Adjective and the Noun should be maintained as it is usually encountered. As it was observed for length, the good results of the models involving frequency constraints are in accordance with theses assumptions and can be seen as a support for this type of approach.

Conclusion

We examined in this article the question of the alternation of attributive adjectives in French using quantitative methods applied to corpora. One can draw several conclusions from the logistic regression models that we proposed. First the satisfactory results of the general model show that a good part of the modelling can be done on the basis of the form without considering the semantics due to position. The importance of the form is also outlined by the fact that the constraints identified as having some relevance when isolated from the others are all based on a knowledge linked to the specificities of the item, or to the specific context in which it appears. Nevertheless, the prediction performances may be improved by taking more semantics into account: adding information for other lexical classes, including semantics, should naturally enhance the model. Furthermore, the importance of collocational effects suggests that semantics should also be considered on a specific relational level between the noun and the adjective. It thus raises the question on how to capture and formalise semantic relations in a quantitative study. Finally, the results of our study show that the best models are based on length and frequency, and collocational effects. This confirms the role of the nature of the items involved. It also suggests that usage may have an important role in the construction of linguistic knowledge, and hence in the placement of adjectives.

To conclude, the model proposed in this article is restricted to the journalistic genre. A future perspective in our work would be to extend this study to other genres, in particular spoken data, in order to test the relevance of our conclusions for French more generally. Furthermore, a comparison between the probabilities given by our model and speakers' preferences on the basis of experiments would enable us to see if future psycholinguistic work will confirm our hypothesis that the effects of usage statistics on adjective position in French is mediated by cognitive processes whereby linguistic representations are directly sensitive to the statistics of language use experienced by language users.

  proud of his son"

(

  neighbour is too talkative'

  British merchant bank"

πante = e Fig. 1 .

 e1 Fig. 1. Formula of prediction model, significant effects are coded *** p<0.001, ** p<0.01, * p<0.1

Fig. 2 .

 2 Fig. 2. Observed proportions of anteposition and the corresponding mean predicted probabilities for the prediction model (the line represents a perfect fit).

4. 1

 1 Comparison of models with different sets of constraints In order to compare the effect of different constraint clusters, we propose 4 prediction models based on different groups of variables: a Syntactic model containing coord and adv; a Lexical property model with natio, indef and derived; a Frequency-Length model containing the variables AP-length and freq and a Collocation model containing CollocAnt and CollocPost.

Table 2 .

 2 Summary table of variables and their values (bool = boolean and real = real number)

Types Description coord bool adjective in coordination or not adv bool adjective with pre-modifying adverb or not derived bool derived adjective or not natio bool adjective of nationality or not indef bool indefinite adjective or not adj-length real length of the adjective in syllables (log scale) AP-length real length of the AP in syllables (log scale) freq real adjective frequency in the ER corpus (log scale) CollocAnt real score for the adjective-noun bigram (log scale) CollocPost real score for the noun adjective bigram (log scale)

  However, 94.6% of coordinated adjectival occurrences (i.e. 758 occurrences) are postposed in our data. Usage-based data thus indicate that coordination is a factor that strongly favours postposition.

	4)	une	belle	et	longue	table	/	une	table	belle	et	longue
		a	beautiful	and	long	table	/	a	table	beautiful	and	long
		"a long and beautiful table"

Table 3 .

 3 Classification table for prediction model

	Predicted position % Correct
	P	A
	observed P 10222	355 96.6%
	position A 748	3479	82.3%
	Overall accuracy: 92.6% (σ = 0.008)

Table 5 .

 5 Classification table for Lexical properties model

	Predicted position % Correct
	P	A
	observed P 10506	71	99.3%
	position A 3681	546	12.9%
	Overall accuracy: 74.7% (σ = 0.02)

Table 6 .

 6 Classification table for Frequency-Length model

		Correct
	P	A
	observed P 9334	1243 88.2%
	position A 1475	2752 65.1%
	Overall accuracy: 81.7% (σ = 0.009)

Table 7 .

 7 Classification table for Collocations model

	Predicted position % Correct
	P	A
	observed P 10327	250 97.6%
	position A 1249	2978 70.5%
	Overall accuracy: 89.9% (σ = 0.007)

In some cases, alternation leads to meaning differences for the adjective (see for instance[START_REF] Waugh | A semantic analysis of word order : Position of the Adjective in French[END_REF],[START_REF] Wilmet | La place de l'épithète qualificative en français contemporain : étude grammaticale et stylistique[END_REF],[START_REF] Noailly | L'adjectif en français[END_REF]). The decision between the different possible accounts of how these differences could be generated is beyond the scope of this article. We thus leave aside these semantic considerations and focus here on the form of the adjective.

This subset corresponds to the part that was manually corrected.

We identified attributive adjectives using the following pattern in the treebank: an adjective occuring with a nominal head within a NP is an attributive adjective.

Cardinal numerals such as trois 'three', vingt 'twenty', soixante 'sixty'... are sometimes annotated as adjectives in the FTB.

[START_REF] Noailly | L'adjectif en français[END_REF] Examples of dates containing adjectives: "[13 ]ADJ [mars]N ", "[lundi]N[START_REF] Bybee | The emergent lexicon[END_REF]ADJ

".[START_REF] Arnold | Heaviness vs. newness: the effects of structural complexity and discourse status on constituent ordering[END_REF] Nouns or adjectives are viewed as abbreviations if their last letter is a capital

letter. 9 http://www.cnrtl.fr/corpus/estrepublicain/

The

adverbs are: 'encore' again, 'désormais' from now on, 'moins' less, 'peu' not much, 'plus' more, 'si' so, 'tout' very, 'très' very, 'trop' too, 'bien' well, 'aussi' also.[START_REF] Abeillé | Enriching a french treebank[END_REF] We obtain the number of syllables using the speech synthesis software Elite[START_REF] Beaufort | elite : système de synthèse de la parole à orientation linguistique[END_REF]. It counts the number of syllables for every token, taking into account the actual form of the adjective (feminine versus masculine, for instance) as well as the possible effects of sandhi phenomena, like the liaison phenomenon. The length associated to each adjectival type corresponds to the mean of all its tokens length. For both variables, we use the log transformed value of the length in order to reduce the effect of outliers.

Using the dictionnary Prolexbase[START_REF] Tran | Prolexbase : Un dictionnaire relationnel multilingue de noms propres[END_REF].

We compute the mean probability of success of ten equally sized bins of probabilities (0 -0.1, 0.1 -0.2, 0.2 -0.3. . . ) and we compare this mean with the proportion of observed success in the data.

Note that frequencies are biased by the journalistic nature of corpora: adjectives of nationality are frequent despite the fact that they are postposed in most cases. Nevertheless, the variable natio of the global prediction model votes for postposition, which neutralizes the frequency effect.

Acknowledgements

We would like to express our gratitude to Benoît Crabbé for his support and advise in the work that lead to this paper, and to the anonymous reviewers for their valuable comments.