Marie-Francoise Bidaut-Véron

Augusto C Ponce
email: ponce@lmpt.univ-tours.fr

Laurent Véron
email: veronl@univ-tours.fr

Boundary singularities of positive solutions of some nonlinear elliptic equations Singularités au bord de solutions positives d'équations elliptiques non-linéaires

We study the behavior near x0 of any positive solution of (E) -∆u = u q in Ω which vanishes on ∂Ω \ {x0}, where Ω ⊂ R N is a smooth domain, q ≥ (N + 1)/(N -1) and x0 ∈ ∂Ω. Our results are based upon a priori estimates of solutions of (E) and existence, non-existence and uniqueness results for solutions of some nonlinear elliptic equations on the upper-half unit sphere.

Nous distinguerons les trois valeurs critiques de q données par (4). Si 1 < q < q 1 , le comportement en 0 des solutions est décrit dans [START_REF] Bidaut-Véron | An elliptic semilinear equation with source term involving boundary measures: the subcritical case[END_REF] ; aussi supposerons-nous le plus souvent q ≥ q 1 . Si u est une solution de (3) dans R N + de la forme u(x) = u(r, σ) = r -2/(q-1) ω(σ), alors ω vérifie l'équation [START_REF] Doob | Classical potential theory and its probabilistic counterpart[END_REF]. Dans ce cas, nous avons le résultat suivant : Théorème 0.1 (i) Si 1 < q ≤ q 1 , le problème (3) n'admet aucune solution.

(ii) Si q 1 < q < q 3 , (3) admet une unique solution, notée ω 0 .

(iii) Si q ≥ q 3 , (3) n'admet aucune solution.

Le résultat d'unicité décrit en (ii) est en fait un cas particulier d'un résultat plus général :

Théorème 0.2 Pour tous q > 1 et λ ∈ R, il existe au plus une solution positive de [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF].

Ce résultat demeure si, dans [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF], S N -1 + est remplacé par une boule dans R N , et ∆ ′ par le laplacien ordinaire.

Par simplicité, nous pouvons supposer que ∂R N

+ est l'hyperplan tangent à Ω en 0. Le théorème ci-dessous donne une classification des singularités isolées du problème (3) : Théorème 0.3 Soit q ≥ q 1 , avec q = q 2 . Supposons que la solution u du problème (3) vérifie

0 ≤ u(x) ≤ C |x| -2/(q-1) ∀x ∈ Ω ∩ B a (0), (1)
pour C, a > 0. Si q 1 ≤ q < q 3 , ou bien u est continue en 0, ou bien

u(r, σ) = r -(N -1) log (1/r) 1-N 2 k N σ 1 + o(1) si q = q 1 , r -2/(q-1) ω 0 (σ) + o(1) si q 1 < q < q 3 , (2)
lorsque r → 0, uniformément par rapport à σ ∈ S N -1

+

; k N est une constante qui dépend seulement de N . Si q ≥ q 3 , u est continue en 0.

L'estimation a priori (1) est obtenue pour q 1 ≤ q < q 2 : Théorème 0.4 Si q 1 ≤ q < q 2 , toute solution u de (3) vérifie (1) pour C = C(N, q, Ω) > 0.

Les démonstrations détaillées sont présentées dans [2].

Introduction and main result

Let Ω be a smooth open subset of R N , N ≥ 2, such that 0 ∈ ∂Ω and let q > 1. Assume that

u ∈ C 2 (Ω) ∩ C(Ω \ {0}) is a solution of      -∆u = u q in Ω, u ≥ 0 in Ω, u = 0 on ∂Ω \ {0}. (3)
Our goal in this paper is to describe the behavior of u in a neighborhood of 0. This problem has similar features with the case where x 0 ∈ Ω, which has been studied by Gidas-Spruck [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF]. In our case, we encounter three critical values of q in describing the local behavior of u:

q 1 := N + 1 N -1 , q 2 := N + 2 N -2 if N ≥ 3 and q 3 := N + 1 N -3 if N ≥ 4. (4)
When 1 < q < q 1 , it is proved in [START_REF] Bidaut-Véron | An elliptic semilinear equation with source term involving boundary measures: the subcritical case[END_REF] that for every solution u of (3) there exists α ≥ 0 (depending on N and u) such that u(x) = α |x| -N ρ(x) 1 + o(1) as x → 0, (5) where ρ(x) = dist(x, ∂Ω), ∀x ∈ Ω. For this reason, we shall mainly restrict ourselves to q ≥ q 1 .

Let us first consider the case where Ω = R N + and we look for solutions of (3) of the form u(x) = u(r, σ) = r -2/(q-1) ω(σ), where r = |x| and σ ∈ S N -1

+

. An easy computation shows that ω must satisfy

     -∆ ′ ω = ℓ N,q ω + ω q in S N -1 + , ω ≥ 0 in S N -1 + , ω = 0 on ∂S N -1 + , (6)
where ∆ ′ denotes the Laplacian in S N -1 and ℓ N,q = 2(N -q(N -2))

(q-1) 2

. Concerning equation ( 6), we prove

Theorem 1.1 (i) If 1 < q ≤ q 1 , then (6
) admits no positive solution.

(ii) If q 1 < q < q 3 , then (6) admits a unique positive solution.

(iii) If q ≥ q 3 , then (6) admits no positive solution.

One of the main ingredients in the proof of Theorem 1.1 (ii) is the following Theorem 1.2 If q > 1 and λ ∈ R, then there exists at most one positive solution of

-∆ ′ v = λv + v q in S N -1 + , v = 0 on ∂S N -1 + . ( 7
)
Remark 1 We emphasize that in Theorem 1.2 we do not assume that q is subcritical. The conclusion above remains valid if, in [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF], S N -1 + is replaced by B 1 ⊂ R N and ∆ ′ by the usual Laplacian in R N . Theorem 1.2 extends a previous result of Kwong-Li [START_REF] Kwong | Uniqueness of radial solutions of semilinear elliptic equations[END_REF].

We now return to the case where Ω ⊂ R N is an arbitrary smooth set such that 0 ∈ ∂Ω. For simplicity, we may assume that ∂R N

+ is the tangent hyperplane of Ω at 0. Using Theorem 1.2, we provide a classification of isolated singularities of solutions of (3): Theorem 1.3 Let q ≥ q 1 , q = q 2 , and let u be a solution of (3). Assume that u satisfies

0 ≤ u(x) ≤ C |x| -2/(q-1) ∀x ∈ Ω ∩ B a (0), (8)
for some C, a > 0. If q 1 ≤ q < q 3 , then either u is continuous at 0 or

u(r, σ) = r -(N -1) log (1/r) 1-N 2 k N σ 1 + o(1) if q = q 1 , r -2/(q-1) ω 0 (σ) + o(1) if q 1 < q < q 3 , (9)
as r → 0, uniformly with respect to σ ∈ S N -1

+

; k N denotes a constant depending only on N and ω 0 is the unique positive solution of (6). If q ≥ q 3 , then u is continuous at 0.

Remark 2

We do not know whether Theorem 1.3 is true when q = q 2 . In this case, the equation is conformally invariant and thus other techniques are required. If Ω = R N + , then it can be proved that any solution of (3) depends only on the variables r = |x| and θ = cos -1 (x 1 / |x|).

The next result establishes the existence of an a priori estimate for the solutions of (3). According to Theorem 1.4 below, assumption (8) is always fulfilled when q 1 ≤ q < q 2 : Theorem 1.4 Let q 1 ≤ q < q 2 and let u be a solution of (3). Then,

0 ≤ u(x) ≤ Cρ(x) |x| -2/(q-1)-1 ∀x ∈ Ω ∩ B 1 (0), ( 10
)
where C depends on N , q and Ω.

Remark 3 According to the Doob Theorem [START_REF] Doob | Classical potential theory and its probabilistic counterpart[END_REF], any positive superharmonic function v in Ω satisfies Ω |∆v| ρ < ∞ and admits a boundary trace, which is a Radon measure on ∂Ω. If u is a solution of (3), then its trace must be of the form kδ x0 , for some k ≥ 0. We may have k > 0 if 1 < q < q 1 (see [START_REF] Bidaut-Véron | Asymptotics of solutions of some nonlinear elliptic systems[END_REF]), but k is necessarily equal to 0 if q ≥ q 1 . Indeed, by the maximum principle, u satisfies u ≥ kP Ω (x, 0), where P Ω denotes the Poisson potential of Ω. Since u q ∈ L 1 ρ (Ω) (by the Doob Theorem), we must have k = 0 if q ≥ q 1 . Detailed proofs will appear in [2].

Sketch of the proofs

Proof of Theorem 1.1. Assertion (i) is proved by multiplying (6) by φ(σ) = σ 1 . Note that φ is the first eigenfunction of -∆ ′ on S N -1 + , with eigenvalue λ 1 = N -1. Integrating the resulting expression over S N -1 + , and using the fact that 1 < q ≤ q 1 =⇒ ℓ N,q ≥ λ 1 , we obtain (i). The existence part in (ii) is obtained by using the Mountain Pass Theorem; the uniqueness is a consequence of Theorem 1.2. Assertion (iii) can be deduced from the following Pohožaev-type identity: Proposition 2.1 Assume N ≥ 4 and q > 1. Then, any solution of (7) satisfies

N -3 q + 1 (q -q 3 ) S N -1 + |∇ ′ v| 2 φ dσ - (N -1)(q -1) q + 1 λ + N -1 q -1 S N -1 + v 2 φ dσ = = - ∂S N -1 + |∇ ′ v| 2 dτ.
This identity is obtained by computing the divergence of the vector field

P = ∇ ′ φ, ∇ ′ v ∇ ′ v
, where ∇ ′ is the gradient on S N -1 , and then using the fact that the first eigenfunction satisfies D 2 φ + φg 0 = 0, where g 0 is the tensor of the standard metric on S N -1 . In order to establish (iii), it suffices to observe that ℓ N,q ≤ -N -1 q-1 ⇐⇒ q ≥ q 3 .

Proof of Theorem 1.2. We first notice that any positive solution of ( 7) depends only on the variable θ = cos -1 (x 1 / |x|) ∈ [0, π/2]; this follows from a straightforward adaptation of the Gidas-Ni-Nirenberg moving plane method to S N -1 + (see [START_REF] Padilla | Symmetry properties of positive solutions of elliptic equations on symmetric domains[END_REF]). Thus, v satisfies

   v ′′ + (N -2) cot θ v ′ + λv + v q = 0 in (0, π/2), v ′ (0) = 0, v(π/2) = 0. (11)
Let w(θ) := sin α θ v(θ), where α > 0. By choosing α = 2(N -2)/(q + 3), then w satisfies

w ′ (π/2) 2 = π/2 0 G ′ (θ)w 2 (θ) dθ, (12)
where G is a function of the form G(θ) = sin β ′ θ α 1 sin 2 θ + α 2 ; the parameters α 1 , α 2 , β ′ ∈ R can be explicitly computed in terms of λ, N and q. Assume, by contradiction, that v 1 and v 2 are two distinct solutions of [START_REF] Véron | Comportement asymptotique des solutions d'équations elliptiques semi-linéaires dans R N[END_REF]. Then,

π/2 0 v 1 v 2 v q-1 2 -v q-1 1 dθ = 0. (13)
Therefore, their graphs must intersect at some θ 0 ∈ (0, π/2). We claim that v 1 and v 2 intersect at least twice in (0, π/2). If there is only one intersection point, then it can be shown that there exists γ ≥ 0 such that the function θ → G ′ (θ) w 2 2 (θ) -γw 2 1 (θ) never vanishes in (0, π/2). We then let L(t) := (t 2 -γ) -1 , ∀t ∈ R \ {γ}. By (12) and the Mean Value Theorem, there exists θ 1 ∈ (0, π/2) such that

L w ′ 2 (π/2) w ′ 1 (π/2) = π/2 0 G ′ (θ)w 2 1 (θ) dθ π/2 0 G ′ (θ) [w 2 2 (θ) -γw 2 1 (θ)] dθ = L w 2 (θ 1 ) w 1 (θ 1
) .

Since L is injective in R + , this implies

w ′ 2 (π/2) w ′ 1 (π/2) = w 2 (θ 1 ) w 1 (θ 1 ) . ( 14
)
On the other hand, by the Sturm-Liouville Theory, the function θ → w 2 (θ)/w 1 (θ) is (strictly) monotone. L'Hôpital's Rule yields a contradiction as we let θ → π/2. Therefore, v 1 and v 2 must intersect at least twice. This fact leads to another contradiction by using the Shooting Method (see [START_REF] Kwong | Uniqueness of radial solutions of semilinear elliptic equations[END_REF]). Thus, v 1 = v 2 in (0, π/2).

Remark 4

The method above follows the lines of the proof of Kwong-Li [START_REF] Kwong | Uniqueness of radial solutions of semilinear elliptic equations[END_REF]. The main difference is that we use an alternative argument based on the Mean Value Theorem in order to deduce (14). In [START_REF] Kwong | Uniqueness of radial solutions of semilinear elliptic equations[END_REF], they have to assume that the exponent q is subcritical.

Proof of Theorem 1.3. It follows from methods developed in [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF] and [START_REF] Bidaut-Véron | Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations[END_REF]. For simplicity, we shall assume that a = 1 and

∂Ω ∩ B 1 = ∂R N + ∩ B 1 . We set w(t, σ) = r 2/(q-1) u(r, σ), t = log (1/r) ∈ (0, ∞) × S N -1 + := Q. Then, w satisfies w tt -N -2 q + 1 q -1 w t + ∆ ′ w + ℓ N,q w + w q = 0 in Q (15)
and w vanishes on (0, ∞) × ∂S N -1

+

. Since w is uniformly bounded on Q, standard a priori estimates for elliptic problems yield

∂ k t ∇ ′j w ≤ M k,j in (1, ∞) × S N -1 +
for any integers k, j ≥ 0, where ∇ ′j stands for the covariant derivative on S N -1 . Thus, the trajectory T w = w(t, •) : t ≥ 1} is relatively compact in C 2 S N -1

+

. Multiplying (15) by w t and integrating over S N -1 + , we obtain d dt H(t) = N -2 q + 1 q -1

S N -1 + w 2 t dσ, (16)
where H(t) := 1 2 S N -1 + w 2 t -|∇ ′ v| 2 -ℓ N,q w 2 + 2 q + 1 w q+1 dσ.

Since q = q 2 , we know that N -2(q + 1)/(q -1) = 0. Thus, iterated energy estimates imply that w t (t, •), w tt (t, •) → 0 in L 2 (S N -1

+

) as t → ∞. Therefore, the limit set Γ w of T is a connected subset of the set of solutions of [START_REF] Doob | Classical potential theory and its probabilistic counterpart[END_REF]. By Theorem 1.1, we deduce that Γ w = {0} if q = q 1 or q ≥ q 3 , {0} or {ω 0 } if q 1 < q < q 3 . Then, a linearization argument as in [START_REF] Bidaut-Véron | Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations[END_REF] leads to the conclusion if q > q 1 . We now consider the case q = q 1 ; we borrow some ideas from [START_REF] Bidaut-Véron | Asymptotics of solutions of some nonlinear elliptic systems[END_REF] and [START_REF] Véron | Comportement asymptotique des solutions d'équations elliptiques semi-linéaires dans R N[END_REF]. We first prove, by ODE techniques, that X(t) := (17)

S N - 1 +

 1 w(t, •)φ dσ ≤ Ct -(N -1)/2 .

Using [START_REF] Kwong | Uniqueness of radial solutions of semilinear elliptic equations[END_REF] and the boundary Harnack inequality (see [START_REF] Cafarelli | Boundary behavior of nonnegative solutions of elliptic operators in divergence form[END_REF]), we derive 0 ≤ w(t, σ) ≤ Ct -(N -1)/2 in (1, ∞) × S N -1 + .

(18)

Set η(t, σ) := t (N -1)/2 w(t, σ). We verify as above that the limit set Γ η in C 2 S N -1

+

of the trajectory T η of η is an interval of the form κφ : 0 ≤ κ 0 ≤ κ ≤ κ 1 . In order to show that T η is reduced to a single point, we prove that r(t, •) L 2 ≤ Ct -1 , where

Writing the equation satisfied by z as a non-homogeneous second order linear ODE, we prove that either z(t) → 0, which implies that u is continuous at 0, or z(t) → kN as t → ∞, for some constant depending only on N .

Proof of Theorem 1.4. It is an application of the Doubling Lemma Method introduced in [START_REF] Poláčik | Singularity and decay estimates in superlinear problems via Liouville type theorems[END_REF], from which we derive the following local estimate: Lemma 2.1 Let 1 < q < q 2 and let u be a solution of (3). Then, for every

) for some constant C > 0 depending only on Ω.

Apply this lemma with x 0 ∈ ∂Ω \ {0} and R = |x 0 |/2. Using elliptic regularity theory, we obtain

If ρ(x) ≥ |x|/2, then we use Gidas-Spruck's internal estimates (see [START_REF] Gidas | Global and local behavior of positive solutions of nonlinear elliptic equations[END_REF]). We thus obtain [START_REF] Poláčik | Singularity and decay estimates in superlinear problems via Liouville type theorems[END_REF].


domain: sdv shs

text:
Marc Tchamitchian

Beatrice Collange

Mireille Navarrete

Gaëlle Peyre

Multicriteria evaluation of the pathological resilience of in-soil protected cropping systems

Keywords: qualitative evaluation, cropping system, root-knot nematode

come

INTRODUCTION

Soil-based greenhouse vegetable production is often achieved in intensive cropping systems where several crops follow one another within the year. In these intensive systems, the main reasons for yield losses are soil-borne pests and diseases [START_REF] Oda | Vegetable seedling grafting in Japan[END_REF]. Until recently, they were controlled by methyl bromide fumigation or by chemical pesticides and fungicides. However methyl bromide has been banned for environmental reasons and the increasingly strict regulations on residues in food product combined with stronger concern for public health result in a drastic decrease of the homologated molecules. Growers are therefore faced with the necessity to find new ways to control soil-borne pests and diseases. Alternative techniques like solarisation, use of nematicide oilcakes, biofumigation are promising candidates [START_REF] Stapleton | Soil solarization in various agricultural production systems[END_REF][START_REF] Matthiessen | Biofumigation and enhanced biodegradation: Opportunity and challenge in soilborne pest and disease management[END_REF], but if their efficacy seems good in experimental conditions, growers and local advisers often report partial efficiency. Moreover these techniques require time and therefore may conflict with the crop sequence of the grower (solarisation must be applied during the warmest period of the year and lasts about two months; biofumigation requires to grow the crop which will be used as green manure).

There is a strong need to redesign the soil-based greenhouse cropping system to incorporate alternative pest control techniques and to combine them in order to add their beneficial effects. Although little knowledge is available in the scientific literature about the effects of these combinations of techniques, advisers and growers do have some experimental knowledge about these combinations. They also know about the conflicts that may arise when combining given crops and techniques in a cropping system. Appraising the pest control qualities of a given cropping system is a difficult task not only because of the interactions between the elements of the cropping systems, but also because long-term effects must be taken into account. Being able to assess these control qualities before putting a given cropping system to test is therefore a good way to select the promising ones. The work presented here describes a multicriteria evaluation tool qualifying the pathological control abilities (the pathological resilience) of soil-based greenhouse vegetable cropping systems. Because part of the knowledge used to build this system is expert knowledge from growers and local advisers, a qualitative methodology has been chosen. The next section gives an overview of this methodology and describes how the techniques and their combinations contribute to the final evaluation of a cropping system. The result and discussion section describes some cropping systems and their evaluation, and discusses on how such tool can be used to improve the proposed cropping system.

METHODOLOGY

Qualitative multicriteria evaluation

The goal of the approach is to be able to assess the resistance or resilience of a given cropping system to soil-borne pests, namely root-knot nematodes. It is based on relations linking the different components of the cropping system with their results on resilience. However, while some practices will directly modify the size of the nematode population, others will only have an indirect effect. As will be described later, we have defined four types of contribution to the pathological resilience of cropping systems, contributions that are finally aggregated into one unique evaluation. This is one of the reasons for choosing a multicriteria method. The other reason is that our final goal is also to characterise the environmental and the economic properties of these cropping system. Some effects of the techniques or of given modalities of the cropping techniques are not fully documented in the scientific literature, nor in reports from experimental stations. In such cases, surveys have been carried out with growers and advisers to assess these effects. Using qualitative representations allows tackling with the uncertainty but mainly with the impreciseness of such knowledge. The DEXi system [START_REF] Bohanec | Decision support[END_REF] has been chosen to implement the qualitative evaluation model, because of its ability to implement such agriculture dedicated models [START_REF] Bohanec | Multi-attribute modeling of economic and ecological impacts of cropping systems[END_REF].

With this methodology, the cropping system is described by its elements (cropping techniques, crop sequence...) and their modalities (dose, date...). These elements, inputs, are aggregated according to a chosen logic into evaluations of the effects of these elements and finally in an overall evaluation of the cropping system.

Evaluation of the effects of the cropping systems on nematode control

Cropping systems are defined as the combination of the successive crops and their associated cropping techniques, including the intercrops and intercropping techniques. To understand and clarify the effects of these techniques and crops on the evolution of the populations of pathogenic nematodes, we have chosen to refer to the way they modify the cycle of these pests. Four main actions can be identified: 1) directly reducing the population by killing nematodes, 2) creating a break in the life cycle, especially by limiting the possibilities for reproduction, 3) enhancing competitions in the soil between the different organisms, so as to reduce the populations of pathogenic nematodes, 4) confining the nematodes to the already infested fields by prophylactic actions. The final step is then to combine these elementary evaluations together. 1. Reducing populations. Several pesticide free cropping techniques may have a nematicide action. The solarisation results in an increase of the upper soil layer temperature which can reach up to 60°C [START_REF] Scopa | Greenhouse solarization: effects on soil microbiological parameters and agronomic aspects[END_REF]. It results in a decrease of the population of nematodes in these layers, although deeper layers are seldom enough heated to provide a full eradication. Therefore, the protecting effect of the solarisation depends on the frequency with which it is applied. [START_REF] Candido | Greenhouse soil solarization: effect on weeds, nematodes and yield of tomato and melon[END_REF] showed that repeated yearly application of solarisation can control the nematode infestation while a single application has an effect limited in time. From these results, the contribution of solarisation to the eradication of nematodes has been weighted by its frequency, as well as by the solar radiation available during the solarisation, approximated by the period of solarisation application. Soil steaming also provides disinfection by the action of heat, thus being rather similar to solarisation in its action mechanism. Soil steaming effect is also limited to the upper layers of the soil and to a short-term time span. The contribution of soil steaming to the resilience of the cropping system has been defined as that of the solarisation. A nematicide action can also be obtained by using specific green manure (Sorghum sudanense, Brassicacea juncea e.g.), but sudangrass is less efficient than mustard [START_REF] Collins | Soil microbial, fungal, and nematode responses to soil fumigation and cover crops under potato production[END_REF][START_REF] Lazzeri | Replacing methyl bromide in annual strawberry production with glucosinolate-containing green manure crops[END_REF]. The frequency of these crops within the cropping system also influences their long-term effects and yearly crops are more efficient than a lower frequency. According to advisers, sudangrass effect on nematode is limited to two to three years, so lower frequency will be considered as ineffective for the cropping system, although they provide a protection for the crops planted during the year following the green manure. Finally soil amendment with nematicide oilcakes (neem, mata-raton) may also provide a reduction of the nematode populations, which depends on the dose. The Fig. 1 summarizes how the effects of these different techniques are accounted for in appraising the nematode population reduction achieved.

Introducing a break in the biological cycle.

The main goal here is to limit the reproduction potential of the nematodes by modifying a key element essential to complete their life cycle. The most effective break is provided by the absence of host plants at periods where the soil temperature is high enough to allow nematode activity. The main tools in such a cropping system are the choice of crops and varieties and the choice of plantation dates. For example, delaying the salad plantation from September to a colder period (end of October, November) will achieve this break because, although the salads are host plants, they are grown in soil temperature preventing or at least severely decreasing the activity of nematodes. Unfortunately, most common vegetable crops (tomato, pepper, cucumber, egg-plant, melon) are host plants and very few resistant cultivars exist (some do for tomato, but the resistance is broken for high soil temperatures, [START_REF] Tzortzakakis | Occurrence of resistance-breaking populations of root-knot nematodes on tomato in Greece[END_REF]. A gradation in the effectiveness of a cropping system to achieve the creation of a break in the life cycle of the pest can be defined as a function of the number of host crops planted during the year. The use of grafted plants deserves a special attention. Although some rootstocks are resistant to nematodes, many are not and only provide an increased vigour to the scion. This increase in vigour may mask the depletive effects of the nematodes, but examination of the roots generally shows, in infested soils, high infestation levels. Such rootstocks, although they allow a good production level and look tolerant to nematodes, have to be considered, as host plants allowing the multiplication of the pest. Finally, weeds in the greenhouse (generally on the sides along the plastic cover, close to the extremities or along the central path when it is not covered by a plastic mulch), or weeds outside the greenhouse but close to it may play the role of a reservoir so far as many common weeds are host plants too. Weed control therefore also contributes to providing a break in the life cycle of the nematodes (Fig. 2.). 3. Enhancing the competitions in the soil. We consider here the practices that favour the microfauna and microbial activities. [START_REF] Brussaard | Soil biodiversity for agricultural sustainability[END_REF] have listed the different agricultural management practices that affect the soil and their effects on the soil microbial and fauna activities. The most beneficial practices encompass organic amendments, green manure, fertilisation, tillage and crop rotation and sequences. At the opposite (negative effects), they list pesticides, soil contaminants, but also monoculture. Organic amendments can be realised either through fresh animal manure, composts or dehydrated products. The content in microorganisms and the positive influence of these different amendments is related to their characteristics. Fresh manure is more effective than a dehydrated product. The dose at which they are applied also influences their effect on the soil biodiversity. Green manure also provides a beneficial effect on the total soil microbial and fauna population and on its diversity. There are some evidences that biocidal green manures have a positive effect on the total populations on the soil, the suppression of some species being probably compensated for [START_REF] Scholte | Effect of farmyard manure and green manure crops on populations of mycophagous soil fauna and Rhizoctonia stem canker of potato[END_REF]. Therefore no differences are made between standard green manures and biocidal ones so far as the effect on soil biodiversity is concerned. Finally, the effect of the diversity of crops during the year is accounted for (Fig. 3.). Monoculture brings no beneficial effect [START_REF] Brussaard | Soil biodiversity for agricultural sustainability[END_REF] while a higher diversification of crop species will (up to three different crops in a year, or up to four over a two years period). 4. Prophylaxis. Although prophylaxis is not really a biological process acting on the cycle of the pest, it has consequences at the population and spatial distribution level. It can be used to avoid the contamination of new spots. The main way to achieve this goal is to avoid transporting crop residues and soil with the mechanical tools. Washing the tools between two greenhouses and planning the operations so as to start working on infectionless greenhouses and finishing with the infected ones are simple to put into practice. Weed management inside and outside the greenhouse also contributes to prophylaxis in so far that their removal will not offer refuge areas to the nematodes (Fig. 4.).

Combining these effects.

To characterise the overall pathological resilience of a given cropping system requires that we combine the evaluation of the previous effects. The contribution of some of these processes depends on the infestation level. Indeed, population reduction and cycle breaking at low intensities cannot be successful in highly infested situations, while they can in low infestation level. Therefore, the evaluated efficiency of the population reduction and of the cycle breaking is combined to the infestation level, to determine how effective the cropping system is in this respect. This result is then combined to the efficiency with which soil competition is sustained by the cropping system. The combination of these three processes (population reduction, life cycle breaking and soil competition enhancement) results in the evaluation of the intrinsic resilience of the cropping system, intrinsic because these characterisations concern the very greenhouse on which the cropping system is applied. Finally, this evaluation is combined with the evaluation of the prophylactic practices to obtain the overall resilience of the cropping system, including its capacity to resist to external infestations (Fig. 5.). The final evaluation grade ranks from none (no resilience at all) to high (eradication of high infestation levels on the long-term and good resistance to the development of new infestations), with two intermediate levels. Fair corresponds to a low resilience where the return to a clean situation from an infested one is not possible and where a new infestation has a high probability to develop. Good corresponds to a case where a low infestation level can be contained and eradicated, while high infestation levels will not, associated to a low probability for the development of a new infestation.

RESULTS AND DISCUSSION

Several soil-based greenhouse cropping systems have been described by surveys with the growers. They have been analysed through the multicriteria model described above. These analyses allow identifying four types of cropping systems (Fig. 6). The most successful (type 2) are balanced systems mostly obtaining good to high grades in each of the four components of the resilience. These systems rely on the combination of techniques such as solarisation and green manure to obtain at the same time a reduction of the populations and a break in the life cycle of the nematodes. Green manure also supports the competitions in the soil. These techniques are applied regularly, once every two years, in turn and are associated to prophylactic measures. Some cropping systems are also balanced (type 3), but combine these techniques at lower frequencies and do not adopt prophylaxis. Although balanced, they obtain a low rank in terms of resilience. Two other types of cropping systems were identified. Type 1 mainly relies on soil competitions to control the pest populations, which is not enough to obtain a good grade. Finally, one farmer mainly relies on prophylaxis to contain the infestations, and the corresponding cropping systems rank low in terms of resilience.

The infestation level of greenhouses corresponding to these cropping systems have been observed by unearthing melon roots and ranking the knots on the roots according to the scale designed by [START_REF] Zeck | A rating scheme for field evaluation of root-knot nematode infestation[END_REF], to analyse the correspondence between the qualification of the resilience of the cropping systems and their infestation level. The unbalanced cropping systems (types 1 and 4) were systematically highly infested with nematodes. The balanced types (2 and 3) correspond to variable levels of infestations, ranging from low (a few knots on some scattered plants in the greenhouse) to high (several knots per plant, affecting the functions of the roots, for most of the plants sampled in the greenhouse). The balanced cropping systems that obtained a good ranking of their pathological resilience (type 2) correspond to low infestation levels, while those that obtained a low rank (type 3) correspond to variable levels, from low to high. These observations show that the only cropping systems that are consistently associated with low infestation levels are the effective balanced ones (type 2), while the others can be associated with high infestation levels, either because they are not balanced or because they do not use the appropriate techniques intensively enough.

CONCLUSION

Based on the combination of scientific and expert knowledge, the contributions of the different elements of soil-based greenhouse vegetable cropping systems have been combined to provide an overall evaluation of the resilience of cropping systems to rootknot nematode infestations. The evaluations of existing cropping systems have been shown to be consistent with observed infestation levels in these cropping systems. The computer tool used to implement this qualitative evaluation model also allows identifying the weak points of the evaluated cropping system. It is therefore a valuable tool to analyse with the growers their cropping systems and enhance them. It is also a valuable tool to assist advisers and growers in the task of designing new cropping systems that will be resistant to nematode infestations. This tool will be extended to include other soil-borne pests and diseases and to also provide an assessment of the environmental and economic performance of these cropping systems.

Figures

Population Reduction

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 5 .Fig. 6 .

 12356 Fig. 1. Evaluation tree for the practices contributing to the reduction of the nematode population by a lethal action (rounded boxes denote a basic node describing a modality of a cropping technique; square boxes denote an aggregated evaluation obtained by combining the levels of the boxes immediately below).


est destinée au dépôt

Sequence analyses of Megabase-sized contigs of the wheat genome

Frédéric Choulet, Philippe Leroy, Franck Giacomoni, Jerome J. Salse, Etienne

Paux, Catherine C. Feuillet

To cite this version:

Frédéric Choulet, Philippe Leroy, Franck Giacomoni, Jerome J. Salse, Etienne Paux, et al. With 17 Gb and an hexaploid composition, molecular characterization of the bread wheat (Triticum aestivum L.) genome is a challenge and its genome structure and composition remain largely unknown. Our current knowledge is limited to the analysis of individual BAC sequences and of random BAC end and plasmid sequences. To improve our knowledge on the structure and evolution of the wheat genome, we have sequenced a dozen of Mb-sized contigs (up to 3.2 Mb; 8-12x coverage) originating from different regions of chromosome 3B for which a physical map has been recently established in our laboratory. Altogether, these data account for 16.5 Mb of sequences and represent the first set of large contiguous wheat genome sequences to be analyzed. Automatic annotation has been performed using the web-based TriAnnot pipeline (http://urgi.versailles.inra.fr/projects/TriAnnot/; EU-Auvergne Lifegrid project) that is under final stage of development. TriAnnot allows direct submission of BAC sequences and uses Triticeae specific libraries, algorithms and combiners to provide gene models. Similarity-based identification of the transposable elements is also computed and a more sophisticated approach for characterization of nested elements is under development. TriAnnot benefits from a user friendly interface and from a modular grid-based architecture.

The gene density over the 16.5 Mb is 1 gene per 139 kb. Locally, important variations of the gene content is detected, from 0 to 10 genes per BAC, revealing a non-random distribution of the genes along the chromosome. Intergenic region as small as 500 bps were observed while a region of 620 kb without genes has also been found. Curation of the TE annotation has been performed over the larger contig (3.2 Mb). With 60 different TE families detected in the region, it revealed that the wheat genome is characterized by an important diversity of TEs. However, a few number of elements are over-represented suggesting that wheat genome expansion has occurred by a massive amplification of a small number of specific TEs. Finally comparative analyses has been performed with other available cereal genomes. First comparisons reveal that, for some regions, wheat may have undergone many DNA rearrangements that led to numerous micro-synteny breaks when compared to the other cereal genomes that exhibit a more ancestral genome structure. The latest results on gene and TE annotation, on the architecture of the annotation pipeline and on comparative analyses will be presented. This project is supported by the Agence Nationale de la Recherche (ANR-Genoplante-SMART).

Databases and web-based tools for annotation and genome comparisons Sequence analyses of Megabase-sized contigs of the wheat genome

	Frédéric Choulet, Philippe Leroy, Franck Giacomoni, Jérome Salse, Etienne Paux, Catherine
	Feuillet
	UMR INRA/UBP 1095, Genetic Diversity and Ecophysiology of Cereals, F-63100 Clermont-
	Ferrand, France
	fchoulet@clermont.inra.fr

. Sequence analyses of Megabase-sized contigs of the wheat genome. 2. Workshop on TritiGEN. COST Action FA604, Apr 2008, Albena, Bulgaria. hal-02818229 WG2A:


Vincent Berthon

Frédéric Rimet

Agnes Bouchez

Using diatom life-forms

come

We investigated whether the biological traits of diatoms in watercourses could be used to assess aquatic environments, especially at the saprobic and trophic levels. We used three kinds of biological traits: life-forms, size classes, and ecological guilds. We wanted to find out whether there was any significant difference in the distribution of these biological traits in watercourses with differing quality.

The saprobic level was estimated using the Dissolved Oxygen, Biological Oxygen Demand, Chemical Oxygen Demand, Dissolved Organic Carbon, NH 4 + and NO 2 -. The trophic level was estimated using the concentrations in NO 3 -, PO 4 3-and total phosphorus.

We worked on a large data set including the distribution of 315 diatoms species in 2007, determined at 328 stations located on 212 watercourses, plus several abiotic parameters. This was the first time that the biological traits of diatoms had been investigated using such a large data set.

Our investigations have shown that the abundances of some biological traits differ significantly between the different quality classes. This was particularly true of the stalked diatoms, the motile and low-profile guilds. Their responses were as significant as those of the indices currently used as the reference values.

The study reported shows that the biological traits of diatoms could be used as bioindicators of the saprobic and trophic levels of environments, and highlights their advantages: the resilience of the ecological profiles, the fact that they provide information about the structure and architecture of biofilms and quicker species identification. In the future, our goals will be firstly to refine our research into the impact of the size of watercourses on different biological traits. Secondly, to use combinations of biological traits to enhance the distinction between saprobic and trophic levels, and finally to look at biological traits in other settings, such as in the presence of micropollutants, a WFD priority, or conductivity, for" which indices have already been developed using diatoms.

  Using diatom life-forms and ecological guilds to assess organic and nutrient concentrations in rivers: a case study in rivers in south-eastern France. BERTHON Vincent, RIMET Frédéric and BOUCHEZ Agnès INRA, UMR Carrtel, 75 av. de Corzent, BP 511, F-74203 Thonon les Bains cedex, France vincent.berthon@thonon.inra.fr Abstract The Water Framework Directive (WFD) of the European Union has set a target of achieving good ecological status for aquatic environments in Europe by 2015. In order to achieve this we need to determine the quality of aquatic environments at present, and to do this we can use biological indicators such as diatoms. There are several indices based on diatoms, such as the Biological Diatomic Index and the Pollution Sensitivity Index, but these indices can be difficult and time consuming to use.


Gaël Plumecocq
email: gael.plumecocq@u-paris10.fr

THE REGIONAL ADMINISTRATION OF SUSTAINABLE DEVELOPMENT : A CONVENTIONAL STUDY APPLIED TO THE NORD -PAS DE CALAIS REGION 1

Keywords: Sustainable development, public policies, local public organisations, legitimacy, coordination

This paper is based on the idea that analyzing sustainable development (SD) regarding legitimacy is possible provided we consider a particular vision of sustainability that gets around problems of common humanity and of common dignity. As we consider the Nord -Pas de Calais Region's public organisations we can see the implementation of SD raises a double questioning. First on a new civic reality proof that competes or completes the elective proof by the establishment of participative procedures. Then on the industry ground at work in transversal organisations. These two elements are constituent of a new mode of coordination based on SD projects or LA21 projects.

The aim of this paper will not be to attempt to give a definition of what sustainable development is or should be. As a preliminary we would simply recall that it refers to a modality of development of societies in the long period. That is to say that it is a way to raise the level of well-being for all individuals and also that it is a mode of development that creates the conditions of its reproduction. In this sense sustainable development is a concept a large majority agrees on and meets certain legitimacy. But beyond this consensus there are several problems. Two of the main problems are what we would call the problem of political values of sustainable development, and the problem of implementing sustainable actions. The latter refers to the fact that when sustainable development is applied it is appropriated by actors, which gives it a precise meaning regarding the local actors' conditions. The blur of the concept necessarily requires a framework of interpretation in the applications of sustainable development. Regarding the first problem the way of how sustainable development is implemented puts at stake values of a wider perspective on general well-being. These two are the source of dissensus of how sustainable development has to be applied and the ensuing political values.

As long as these two problems are concerned ways of implementing sustainable development depend on its modalities of legitimacy. We put forward the idea that sustainable development reconfigures principles of public policies and administrations of local communities. Using interviews led in local communities of the Nord -Pas de Calais Region (North France) we will demonstrate that this survey was carried out at different levels of institutional public responsibility (region, department, towns/cities or rural areas) covering all decision instances regarding sustainable development. The stakes of this question of legitimacy are particularly relevant in the French context because of the high number of these territorial scales, which complicates issues of coordination. This paper will attempt to highlight that coordination failures come from matters of public policies legitimacy when sustainable development is involved.

The theory of the economies of worth developed by Luc Boltanski and Laurent Thévenot (1991) provides an interesting understanding of the stakes of legitimacy and coordination. We will start by presenting the model and its theoretical limits that define the application's cogency of this theory. Then after presenting the framework of the problematic we will be able to apply it to the communities of the Nord -Pas de Calais Region and to show how issues of legitimacy renew public policies, on the ground of a new civic proof that competes or completes the elective proof, and on the ground of an industrial renewal of the administration's practices. This led to the establishment of the project as the main modality of sustainable development coordination.

Economies of worth: understanding conflicts of SD

Issues of legitimacy bring on two different types of problems that can be well understood using the theory of the economies of worth. This question applied to sustainable development cannot be solved within standard economic theory by resorting to the framing of rationality. The first problem deals with the question of the common humanity defined in sustainable development conflicts that involve "non human beings" such as fauna, flora or various natural elements. We will call the second problem the common dignity problem that provides "non yet human beings" (the future generations) to participate to the debate that will affect their living conditions. We will then be able to present the model of understanding legitimacy actions regarding its conditions of application on what sustainable development is.

Common dignity: how can future generations argue?

The first issue of sustainable development lies on the principle of solidarity. Following this principle, one of the dimensions of sustainability is to promote a social development regarding both spatial and temporal solidarity. The economist has tools to understand spatial solidarities, through the Marxian point of view of the domination relationships or through the neoclassical point of view of trade as a vector of development. As for temporal solidarities, the question is more intricate. In general temporality and the uncertainty that time brings on, has led to economic dead ends. From Arrow to the Savage's hypothesis of contingents markets2 no author has successfully developed tools to solve this problem [START_REF] Postel | Les règles dans la pensée économique[END_REF]. This question of uncertainty is more accurate in a sustainable development perspective. As Latour emphasizes (1995), what characterizes sustainable development is the increasing level of the unknown and of what we doubt about. Science seems to have passed from a vision that closes horizons of the unknown, that is to say that scientific developments reduce the field of things that are unknown, to a new paradigm in which we realize that the more forward we go, the more things are left to discover [START_REF] Callon | Agir dans un monde incertain. Essai sur la démocratie technique[END_REF]. In an economic language, sustainable development calls the hypothesis of the future states of the world into question. In other words it is impossible to know either the number or the forms of the future states of the world [START_REF] Godard | Stratégies industrielles et convention d'environnement : de l'univers stabilisé aux univers controversés[END_REF], which prevents the possibility of putting in probability events that may occur and which requires dealing with a wider frame of understanding than the standard economic one.

From a sustainable point of view, we can summarize this question by the issue of the representation of the future generations in the current debate of sustainable development. Usually they are represented through a utility actualization rate that is generally set to the interest rate. This of course works in the particular case of a risky economy where all the elements, including time can be controlled and put in probability, which is not the case in sustainable development economy [START_REF] Godard | Stratégies industrielles et convention d'environnement : de l'univers stabilisé aux univers controversés[END_REF]. In this context, how can we represent the future generations? Amartya Sen has developed a conceptual framework that can help in this matter. His starting point is the theory of Lancaster on the characteristics of goods. For Sen, nothing in this theory is said about the modalities of consumption of these characteristics. That led him to build his own theory of the consumer based on that principle: a consumer is a collection of functions "the person succeeds in doing with the commodities and characteristics at his or her command" (Sen, 1985, p. 10). In this set of "functionings" there are those which can be achieved and those which cannot because the individuals do not have the ability to do so, or because it is forbidden. So there exists a sub-set of "functionings" that Sen calls "capabilities" and that represent a certain freedom of choice upon the "functionings".

This framework is particularly useful to solve the problem of the future generations. The question raised by Sen is to know what the society has to act on to develop individual as well as collective well-being. That is to say what is worth promoting by the society? According to him, social evaluation could go either on well-being or on overall goals, that is to say goals that are sought for although they reduce individual well-being 3 . Each one of them can be evaluated from what can be achieved (well-being achieved, agency achievement) or from the freedom to achieve (well-being freedom, or agency freedom). As far as Sen is concerned, social evaluation should promote well-being freedom without preventing the individuals' freedom agency [START_REF] Sen | Capability and well-being, IN The Quality of life[END_REF] in emphasizing on extending capabilities set. The capabilities theory found new modalities of decision inasmuch as well-being achieved can only be self-evaluated, but well-being freedom grounded on capabilities basis can be socially evaluated. Considering the problem of what information should count in the process of making a decision that would affect the future generations, a Senian response would be to focus on capabilities. The principle of intergenerational solidarity which is central in the sustainable development as defined by the Brundtland Commission (1989), would move from a conception of "meeting the needs of the present without compromising the ability of the future generations to meet their own needs", to not reducing their capabilities in providing it.

Common humanity: the status of "non human beings"

Although this definition of sustainable development has gradually ended to be academically recognized and institutionalized, it is common place to underline that this concept is blur enough to be accepted by most social actors. It results that there are several ways to understand what sustainable development is [START_REF] Godard | Le développement durable : paysage intellectuel[END_REF]. The status of "non human beings" is a key question to tear its different versions apart as well as an issue for the legitimacy of sustainable development. In order to simplify we will say that two visions are opposed: the Deep Ecology vision in which the "non human beings" are defended not only for themselves but as a part of an ecosystem that interrelate every element of the natural environment as a guarantee of sustainability; the technical-economist vision in which to some extent the technical capital can replace the natural capital. From the point of view of the economies of worth the ecosystemic vision of sustainable development can be apprehended inside the axiomatic because it would suppose that these "non human beings" have the ability to speak for themselves, which is obviously not the case. The technical-economist vision of sustainability is easily apprehensible in the model for it moves these "non human beings" from subjects of conflicts that are defended as human beings to objects mobilized in argumentations they are not part of, but regarding a proof that has to be established. For instance arguments that those natural elements (ground water, the ozone layer, bees) are useful for mankind because they guarantee life on earth.

In fact, we can see that these "non human beings" tend to acquire some legitimacy through the evolutions of the law 4 . The recognition of rights is indeed an institutionalization that is a good sign of legitimacy. Though this legislation takes the form of soft laws, that is to say laws that do not compound sanctions or that are not obligatory (Delmas-Marty, 2004), nevertheless they emphasize on the right for these "non human beings" to exist. The foundation of such rights is legitimate regardless of either one or another vision of sustainability, in a utility principle. There is no need to insist on the utility dependence relationship between humanity and natural elements in the technical-economist vision. As for the ecosystemic vision, Jeremy Bentham provides a timeless argument. For him, the "day may come, when the rest of the animal creation may acquire those rights which never could have been withholden from them but by the hand of tyranny. The French have already discovered that the blackness of the skin is not a reason of why a human being should be abandoned without the redress to the caprice of a tormentor. It may come one day to be recognize, that the number of the legs, the villosity of the skin, or the termination of the os sacrum, are reasons equally insufficient for abandoning a sensitive human being to the same fate? What else is it that should trace the insuperable line? Is it the faculty of reason, or, perhaps, the faculty of discourse? But a full-grown horse, or dog, is beyond comparison a more rational, as well as a more conversable animal, than an infant of a day, a week, or even a month, old. But suppose the case were otherwise, what would it avail? the question is not Can they reason? nor, Can they talk? but, Can they suffer?"5 .

These arguments are representative of the two radical drifts in the relationship between mankind and its environment at stake in sustainable development: an anthropocentric issue that follows the "Enlightment" vision and places mankind (and its ability to think) at the center of humanity; and a biocentric problem that uplifts natural elements to a human level [START_REF] Godard | Le développement durable : paysage intellectuel[END_REF]. Bentham is led to this argument, not because he built animals on a human model, but rather conversely because his conception of rational homo oeconomicus works as an animal which weighs up its pleasures and its pains. These arguments can be challenged by a philosophical one that brings them back together. The question raised by Bentham is to draw the line between what is human and what is not. And eventually what kind of humanity would result from these two conceptions of sustainable development? Following Kant's moral law, it is possible to say that without the elements of nature that are "non human beings" we may not be as human as we are with them [START_REF] Latour | Moderniser ou écologiser ? A la recherche de la « septième » cité[END_REF]. Considering that what makes us human is at stake, this supposition requires the implementation of the precaution principle. So we have to draw the line again between what is human and what is not as well as we have to rethink sustainable development relatively to this key question. Between visions of an object-nature in the anthropocentric version and a subject-nature in the biocentric version, we can choose to build an intermediary version of sustainability on the consensual ground of the project where every stakeholder has a role to play [START_REF] Ost | La nature hors la loi. L'écologie à l'épreuve du droit[END_REF]) and that will be developed in the following part.

Presentation of the model

The interpretation chart developed by Luc Boltanski and Laurent Thévenot (1991) provides an interesting framework to understand issues of legitimacy. It lies on the different ways of justifying actions or points of view during debates or conflicts. These justifications are seen as valid as long as they are accurately mobilized in reference to the objects that frame the conflicts, in a proof of reality; moreover as long as they are put forward regarding superior common principles. Each one of them gets its legitimacy from works of political philosophy and divide legitimate justifications in six common worlds (or cities or conventions). So we can qualify different modalities of legitimate treatments of nature [START_REF] Godard | Environnement, mode de coordination et systèmes de légitimité : analyse de la catégorie de patrimoine naturel[END_REF]):

-The market world of justifications is drawn through the Adam Smith work. It is built on the superior principle of price as the foundation of a legitimate order. As a sign of value the price is seen as a social acceptance for a product expressed through a market demand. So the legitimate nature in a market world is treated as goods that can be sold. Goods that can be the object of a market transaction; that can be appropriated or that have an entrance fee. The legitimate value attached to this kind of nature reveals itself in a disposition of a consumer to pay for it.

-The industrial world is attached to the Saint-Simon work. The superior principle that gives this world legitimacy is the efficiency. An activity is legitimate from this point of view as long as the outcome is produced using an efficient way of combining costly means. Therefore the cost of production related to the outcome quality is an indicator of industrial legitimacy 6 . So nature is legitimate in this world as it is exploited through an efficient and productive work and as we get goods from it.

-The domestic world is founded in legitimacy in the work of Bossuet. The superior principle is honesty as knowledge of oneself and as recognition of one's own place in a social organisation bringing into play the register of familiarity (intimacy, proximity, locality, oldness, etc.). Goods are seen as legitimate as they are attached to familial or local tradition (for instance "terroir" 7 products). The domestic nature is defined relatively to these elements of proximity or intimacy (pets vs. wild animals) or proximity (e.g. the NIMBY effect).

-The civic world gets it legitimacy from the work of Rousseau through the superior principle of equality or the ability to dedicate oneself to the common good. Typically, the civic world is in tension with the market in the sense that prices produce differences between the individuals. That does not mean that civic production cannot exist (for instance public services are meant to give everyone access to services). As a result civic nature provides free access and does not discriminate the individuals in its use.

-The inspiration world comes from the work of Augustine. It is founded on the superior principle of grace or mercy. This principle is particularly important as we consider the issues of social legitimacy. Indeed, social acceptance supposes to pass through a social proof of publicity toward the society. There is a risk of drifting to marketing communications (economic sphere) or to populism (political sphere). The inspiration nature is a nature that invites us to meditation and causes a spiritual stimulation in particular by the recognition of aesthetic elements.

-Finally the world of fame or renown lies on Hobbes' work and on the superior principle of honour whose celebrity is seen as a sign of social recognition. So the legitimacy of actions depends on the fame of individuals that supports them but can also appear through objects (for instance a trade mark). Legitimate nature from this point of view is the one that is able (by its geographical position, its proper characteristics, fauna, flora, etc.) to draw the attention and mobilize the public opinion.

These figures of legitimate justifications are obviously natural forms that define various modalities of coordination [START_REF] Godard | Environnement, mode de coordination et systèmes de légitimité : analyse de la catégorie de patrimoine naturel[END_REF]: coordination by the prices, by fame, by efficiency, etc. But the arguments or the objectification process of the legitimate common world put at stake in the social reality are most of the time compounded with elements qualifiable in several of them. As a result, we can highlight multiple forms of justifications in compromise with one 6 There is an obvious link between market and industrial work that can be analysed in terms of prices. Through this point of view the issue of "fair trade" can be seen as a tension of market and industrial legitimacy as the market price is not high enough to remunerate productive factors. So "fair trade" movement is to impose a new market for old goods that integrate new elements of product quality (ethics, solidarity, democracy, etc.). 7 "Terroir" is a French word that mark attachment to local land related to a well-established cultural identity.

another. These compromise forms of legitimacy and of coordination are de facto less stable and sustainable than the pure ones. Regarding this variety of principles of legitimacy we will try to show how sustainable development issues applied in French territorial collectivities renew the management of local organisations.

New proof of legitimacy: the appliance of SD

Such a large implementation of sustainable policies is no doubt inherent to the Nord -Pas de Calais Region (North France) where we find an increasing number of public organisations adopting local agendas 21 [START_REF] Cerdd | Projets territoriaux de développement durable agendas 21 locaux, Loos-en-Gohelle[END_REF]. We can explain progress in this region by its past based on a mono-industrial economy and on the exploitation of a single natural resource (the coal). As a result the entire region is marked by the scar of its economic development, so the people have soon realized that it has to move from a non sustainable development to a sustainable one. In the public structures, this new type of policies have led to renew modalities of organizing labour (industrial world of worth) and to use different means to unite civil society (civic world of worth), around sustainable projects as a new form of coordination of public policies.

Participation on a civic ground

Governance is often seen as the fourth pillar of sustainable development as it appears in reference documents published at the international level (e.g. chapter 28 of the Agenda 21 adopted in the 1992 Rio de Janeiro's Conference). When it comes to its implementation, there are as many forms of governance as ways to comprehend sustainable development. For instance we can separate participation that implicates citizens in the decision making process, from the consultation of actors on goals or means that public action should promote or adopt, from the implication of organized actors such as non governmental organisations, associations, firms, other departments or possibly from other public agencies [START_REF] Evans | Local Agenda 21 and the shift to 'soft governance[END_REF]. So governance can be analyzed following two criteria: the nature of actors that participate to the decisions on the model of firms' governance by shareholders (or on a larger extent on the stakeholders as in the Corporate Social Responsibility's approaches); and the degree theses actors are effectively involved in the decision process or in the definition of the aims. Note that there is a link between these two criteria.

Regarding the actor criterion, we can see three distinctive types: citizens or people that are not organized, associations or NGOs that defend collective interests on particular subjects, and firms that are collective actors defending their own interests. The involvement of these actors depends on their category. Firms are excluded from the public decision for in the French context this would be seen as a strategy of lobbying in promoting the firm's interest. Therefore it would not be accepted as legitimate. But on particular projects some firms are associated as consultants bringing technical diagnoses. Most of the time, they are big firms in a situation of national monopoly and of providing public services (e.g. La Poste, EDF, the SNCF 8 , etc.). Regarding the rest of the firms, the relationships with public organisations are asymmetrical as they are subordinate to agencies through the public commands (in housing, public structures, etc.) and through subsidies.

Citizens are the category of actors that participate the least. They are not organized enough to have access to proper information. So the citizens' participation needs to be preceded by a phase of education on what sustainable development is. This factor is important on explaining the French delay on governance issues, where sustainable development has been lately appropriated by public actors, following the 2000 European request for sustainable cities (Emelianoff, 2005b). And yet information is a central issue for governance or participation [START_REF] Evans | Local Agenda 21 and the shift to 'soft governance[END_REF]. For Zaccaï, one of the rules of the governance rule should be to "increase what is called in English "capacities building", to increase the capabilities" (Zaccaï, 2003, p. 3) by promoting publicity or sustainable development events. In this matter, French initiatives are obviously weak.

Associations or NGOs are actors that are involved most subsequently in sustainable public policies. Generally the participation is set on a conflict ground where local interests are in dispute with public actions. However there are some exceptions. For instance, in the city of Lille the local agenda 21 (LA21) has been elaborated in cooperation with local associations for the protection of the environment. The president of the most active one is now deputy mayor in charge of the sustainable development policy of the city. The city of Tourcoing has also followed this path with the difference that the deputy mayor in charge of the LA21 comes from the local world of social associations.

Then experiences on governance and participation are not really successful. And yet there are arguments that new governance of administration and citizens' participation tend to renew civic legitimacy of public agencies. Sustainable issues have indeed led to question the legitimacy of the elected representatives as they have never been legitimate to limit the citizens' liberties, even to protect their environment. So "the general organisation of the society which is behind the legitimacy of the representative democracy's principle has now become obsolete" (Bourg, 2005, p. 412), and there is a need for a renewal of the democracy procedure that governance and participation can provide. But as we have seen above, this would require that the stakeholders be well informed and sufficiently responsible to renounce some part of their liberties.

So as we consider the questions of governance, we have come to distinguish issues of implementation from opportunities of principles. As [START_REF] Beaurain | Gouvernance environnementale locale et comportements économiques, IN Développement durable et territoire[END_REF] noticed there are two kinds of works on governance: "approaches that associate governance to a renewal of conceptions of the democratic process […] and approaches that insist on drifts that occur in the use of this notion" (p. 3). As far as we are concerned, and as we have shown above, we do not see these two streams as contradictory and in our study of local communities in the Nord -Pas de Calais Region we have come to notice that both these arguments are relevant. The first one is in the principles of sustainable development and the second one in attempts to implement governance procedures. So in the theoretical principles of sustainable development, decision-makers and administrative personel refer to the public participation as a new modality of public agencies' governance, which renews the civic world of legitimate justification. But in practice they face numerous difficulties in setting in place the LA21 forum as in the rest of Europe (Emelianoff, 2005b, Evans and[START_REF] Evans | Local Agenda 21 and the shift to 'soft governance[END_REF]. Therefore, in order to be considered as legitimate, this new form of justification needs to confront its stakes to the civic framework of the public action in a proof of reality. This has consequences on modalities of organisation of local agencies as we consider governance actors that we have left aside up to now: actors of the inside of the public organisations, and in particular departments in charge of sustainable policies.

Transversality on an industrial ground

From the "economies of worth" point of view, the French public organisation used to work on the compromise between industrial and civic worth, in the sense that there is a "relation between worth of the general interest that justifies public services and practical demands for action and organisation that submit this worth to proof of reality" (Thévenot, 2001, p. 127) 9 . So elements of industrial worth appear in the management of the public institutions. A usual organisation works on two different divisions of labor levels: between each department in charge of the various axes of the political action; and between the elected representatives that choose the political orientations and the technical employees who have to implement them. So usually, each department led its own policy axe, as every of them is managed by a head of department, a distinctive administration that is accountable to the deputy in charge of this political axe.

For instance, any French mayor has deputies in charge of every political axe. Each one of them answers for the mayor and is responsible for the choices that are made and their implementations. He has to work with the head of department and the entire department administration. Basically we can represent the organisation chart as a two-layered triangle (one representing the political organisation and the other one the administrative organisation on top of which there is the technical department's chief). What also characterizes this division of labor is that no department has to deal with other departments' business. Each one has competences in a particular matter (public lightening, housing, culture, education, social policies, and so on). This partitioning of public action is seen all over Europe as a main difficulty of implementing transversality and LA21 [START_REF] Lafferty | Sustainable communities in Europe[END_REF]. Note that this does not mean that there is no mutual aid between services. Also on matters requiring the competences of several departments, there are spaces of cooperation. For instance projects of renovating houses may involve public road services, as well as social policies and green spaces management.

But the adoption of a sustainable development approach challenges this way of managing public administration. We remain in the industrial world of worth because we deal with a process that is still turned toward efficiency. What changes, is the proof of reality that forces efficiency to compound with the requirement of sustainability. Empirically, this demand is applied inside administrations with the notion of transversality questioning traditional management. So, we can see transversality as an empirical translation of sustainable development concept that takes sense in the implementation of sustainable development policies or actions. Yet as above mentioned, the concept of sustainable development does not have a single definition. The French institutions have adopted a conventional and consensual one grounded on a triple goal: "an objective of social fairness, economic efficiency and environmental upgrading" [START_REF] Mate | Les outils et démarches en vue de la réalisation d'Agendas 21 locaux[END_REF]. In this implementation the point is to emphasize on consequences of actions of every department on social, economic and environmental fields. This is summarized in a transversal management of public administrations that decompartmentalize actions, which is seen all over Europe as a sign of sustainability [START_REF] Evans | Local Agenda 21 and the shift to 'soft governance[END_REF]. So in a sustainable approach, every department has to evaluate its own outcomes on these three domains.

Our study of local communities in the Nord -Pas de Calais Region has led us to highlight three main institutional changes that bring out the implementation of transversality: developments of transversal themes, changes in the organisation chart, and the set up of transversal projects (Emelianoff, 2005a). The last one will be treated later on. Developing themes is a privileged way to make public action transversal because it does not need radical institutional changes and therefore it is easier to establish. The institutional level of the Nord -Pas de Calais Region for instance chose to emphasize the themes of climate change and biodiversity preservation. This strategy needs both a political momentum to convince departments to apply these themes in their daily actions, and an institutional control on every department to make sure that every one take these themes into account and evaluate the consequences of its actions through these criteria.

Regarding institutional changes, transversality can take various forms. It can be the creation of a position at the highest level of the organisation chart which is the case, for instance in the cities of Valenciennes and Loos-en-Gohelle where the person in charge of the mayor's personal staff is also in charge of sustainable development 10 . Or in a more informal way when the person responsible for the LA21 or the matters of sustainable development is closely related to the mayor (as it used to be in the city of Dunkerque) or the region's president (as it was the case in the Nord -Pas de Calais Region). It can also be the creation of positions dedicated to sustainable development in every department. This solution is generally rejected on the ground of the waste of public resources that would bring efficiency down, and the lack of independence of departments. But as a non exclusive way of implementing transversality that we have found in every local community investigated in, the policy of sustainable development falls to a department specially created for this purpose (and in general also to promote LA21). And the place of this department in the organisation chart marks the degree of transversality. In a large number of public agencies, the departments in charge of the implementation of transversality are attached to the departments in charge of environmental issues. We can see that as a sign of poor transversality (Emelianoff, 2005b).

The rise of the LA21 project as vector of coordination

These two new proofs of reality of the public action are summarized in the sustainable development project of LA21 that lies on a participative approval of populations and produce transversality as it brings closer every department concerned by the project. Note that the project can be consistent with every modality of implementing transversality (modification in the administration organisation or definition of transversal themes that departments have to take into account). An empirical study on the implementation of LA21 in the Nord -Pas de Calais Region brings out three main concerns for the actors (CERDD, 2007): creating transversal "ways of working" inside organisations, developing procedures on population's consultation or participation, and issues of sustainable town-planning. LA 21 summarizes all these dimensions of sustainable actions that imply changes in organizing the public agencies. Let us not forget that the Nord -Pas de Calais Region is a densely populated area with thirty-one cities of over 20,000 inhabitants11 , which explains concerns about sustainable town planning. On a more general conception of LA21, this dimension can be extended to the land settlement.

The question we will now try to answer would be to consider LA21 from the point of view of coordination. We have seen in the previous part that the settlement of legitimacy defines a situation where justifications meet one another. It results that each one of the legitimate justifications -market, industry, domestic order, civic order, inspiration, fame-lie on an order of values that command a modality of coordination (by prices, by efficiency, by social position inside a domestic organisation, etc.). [START_REF] Boltanski | Le nouvel esprit du capitalisme[END_REF] have given prominence to another form of coordination coming from a compromise between two of the six original forms of legitimacy. Studying management literature of the French 1990's, they have come to see that they result from a dual criticism of the capitalism founded on the Fordist modes of production, and expressed in the French revolution of May 68. These criticisms were propounded on a social ground (on the idea that the wages should keep increasing) and on an inspiration ground (on the idea that the working environment was alienating). According to these authors, capitalism has recuperated the criticisms from the inspiration world that they call the "artist criticism", in order to elude the "social criticism". The result that appears in the management literature is the settlement of a new labour organisation (a new mode of coordination) that replaces Fordism. The authors call this new mode of coordination "project management", founding a new "spirit of capitalism". In this world grounded on a compromise between market and inspiration justifications, coordination is assured by the projects that gather every skill needed to its achievement. The legitimacy comes from the ability for each participant to include himself in numerous projects as it is seen as a sign of competence and of individual value.

Although this analysis has been criticised (e.g. [START_REF] Boltanski | Institutions et critique sociale. Une approche pragmatique de la domination, IN Tracés[END_REF] confessed he did not see the importance of the financial aspects that seemed to be the real heart of the post-fordist neo-liberal capitalism) "project management" remains a valuable mode of coordination. And we can analyze LA21 on the angle of a new mode of coordination grounded on sustainable development projects. The difference between the LA21 project and the neo-liberal project management is that the former does not result from a compromise between market and inspiration justifications. It keeps being in line with both civic and industrial worlds of justification. What does change is the forms of the reality proofs, which make sustainable development an empirical notion. Now the question is to evaluate the quality of this form of coordination regarding the sustainable development criterion. It follows from what we have set up that LA21 can be a means of coordination at two different levels. Inside the agencies, LA21 project is a new mode of organizing labour between different departments as well as between the elected representatives and the employees. This modality of coordination means questioning the usual organisation of the public administrations, that is to say challenging the industrial mode of coordination. But we have come to see that coordination by sustainable development projects goes beyond the limit of internal organisation. For instance the Nord -Pas de Calais Region has initiated the settlement of a territorial climate-plan in coordination with both the Nord Department and the Pas de Calais Department outside his internal policy of LA21. This modality of coordination brings governance into play in the field of sustainable development. So the participative dimension of sustainable development project either competes or completes the civic mode of coordination coming from the representative democracy. These cooperation spaces created in the settlement of the project are often informal from an employee to another. So the efficiency of this mode of coordination offer mixed results regarding a sustainable development principle for it only lasts the time of the project. Therefore a sustainable coordination is related to the rigour of the follow-up. So LA21 project or sustainable project appears as a mode of coordination which cannot be generally applied as it is not stable enough to pass the industrial or civic reality test.

Conclusion

There is no doubt that sustainable development is growing as a legitimate modality of action, particularly in the communities of the Nord -Pas de Calais Region. For now it seems that this legitimacy lies on the old compromise between industrial and civic ways of justification of public action [START_REF] Thévenot | Les justifications du service public peuvent-elles contenir le marché ? , IN Services publics et droits fondamentaux dans la construction européenne[END_REF]. What sustainable development changes in public policies is the forms of these industrial and civic proofs of reality, through a transversal organisation of work that questions the old division of labour and through the principle of governance that can either reinforce or compete with the elective proof of reality. This led to a renewal of coordination of the local public policies through sustainable development projects.

But this renewal of the reality proof does not seems stabilized enough to produce coordination at national or international level. For instance other European countries have focused their sustainable policies on other modalities of implementation, as showed in the example of the urban sustainable planning (Emelianoff, 2005b). We are still far away from the demand of coordination required in a consistent sustainable development international policy as enhanced in every consensual international document (for instance eight of the twenty-seven principles of the 1992 Rio Declaration emphasize matters of cooperation). It seems that we are now in a phase shared by most communities of the Nord -Pas de Calais Region, where each one elaborates its own internal procedures to compound sectorial objectives with requirements of sustainable development. The project appears as an internal modality of implementing new modes of organisations as well as a vector of sensitizing the employees. Sustainable development project is therefore meant to create links between employees of different services, to share information on skills of each one or on institutional resources, as well as actually achieve the project.

According to this hypothesis it is possible to imagine that certain forms of futures markets do exist regarding probable occurring circumstances. For instance, a market for a car door under the circumstance I have a car accident tomorrow.

Sen illustrates overall goals using the example of an individual who would choose to build a monument to his hero rather than fulfil primary needs such as eating.

For instance, since 2008 French public organisations are allowed to press charges if its territory is environmentally damaged.

Bentham J., 1789, Introduction to the principle of morals and legislation, Chapter 17, T. Payne editor, London, pp.308-309.

La Poste is the French mail company; EDF is a firm that produces and distributes the electricity and the SNCF is the French railway company.

From now on, all quotations will be our translation.

The position of the head of the mayor's personal staff is to some extend off the chart because he belongs neither to the political world nor he is part of the technical organisation. He is only responsible for the mayor. That is to say that his civic legitimacy comes from him whereas the technical legitimacy of sustainable policies comes from the involvement of the society.

The region counts four millions of inhabitants on a

12,500 km² surface. As a result the population density is almost 400% the density average of the French territory.