Onanong Hlaoittinun

Eric Bonjour
email: ebonjour@ens2m.fr

Maryvonne Dulmet

A FUZZY ARRAY-BASED CLUSTERING METHOD IN TEAM BUILDING

Keywords: Team building, Fuzzy sets, Array-based clustering algorithm, Task assignment

A fuzzy array-based clustering method in team building.

INTRODUCTION

Nowadays, companies need to effectively manage their product development projects in order to deliver their products to the market as early as possible and to maintain their competitive advantages. Generally, design projects require a multi-competency team involving members coming from different functional departments and possessing different competencies. Team building has become an increasingly challenging issue for the project leaders, especially when facing complex development situations.

Team building approach

Generally, there are two major procedures in team building: task organization and team member selection. The solving methods existing in literature can be various. [START_REF] Chen | An Integrated Methodological Framework for Project Task Coordination and Team Organisation in Concurrent Engineering[END_REF] and [START_REF] Chen | Modeling team member characteristics for the formation of a multifunctional team[END_REF] proposed an integrated methodological framework in team members assignment: (1) Project task model, (2) Team member model and (3) taskmember assignment model. The objective of this research is to develop a framework for project task coordination and team organization from the concurrent engineering perspective in order to assign the right tasks to the right team members. [START_REF] Braha | Partitioning tasks to product development teams[END_REF] proposed a team-building approach based on task partitioning. Two main issues are addressed, (1) how to specify task dependencies, and (2) how to optimally partition the tasks among a number of teams. (Zakarian and Kusiak,99) emphasized the importance of multifunctional teams in product development. The authors proposed a hierarchical architecture using in multifunction team building based on QFD and AHP method. The proposed architecture shows the relationship among team members, product characteristics and customer requirements. (De Korvin et al.,04) developed a personnel selection model for a multiple phase project. The fuzzy compatibility method has been used in order to select the potential team members for each project phase. However, this work did not specify competency attributes in project task characterization.

Task-and team member characterization

Numerous works about team building concern psychological and sociological aspects (personality types, teamwork, leadership, communication skills, decision-making ability etc.) (Fitzpatrick,04), (Chen and Lin,04), (Acuna and Juristo,04). Technical competency is the most common attribute used in team building literature in order to characterize tasks and team members (Zarakian and Kusiak, 99), (Tseng et al.,04), (Hadj-Hamou and Caillaud, 04), (Fitzpatrick,04), (Tsai et al.,03). (De Korvin et al.,04) emphasized that the important factor in selecting human resources to a team are the technical competencies. These competencies will be required to implement the various activities for each phase of the project. Technical competencies can be seen as competencies required by a task and competencies acquired by a person or a team. Concerning competency characterization, some authors (F. Belkadi et al.) proposed two types of competency attributes: technical and cognitive knowledge. In our approach, we could focus on different types of competency attributes to characterize task and member. The proposed method in this paper is generic. For instance, attributes could be either technical knowledge (such as: to know disciplines, to use tools, to apply methods, etc), or soft capacities (such as: organizational, decisional, relational, etc). It may depend on the industrial application. Generally, discipline is defined as "a branch of learning", for example: robotic, image treatment, acoustics, thermodynamics, etc.

Competency structuring and team building

The objective of competency structuring is to give a global image of competency to the project managers and to help them to deal with a multi-functional team building problem. In team building literature, team members belong to a functional department. But in the design of innovative products, new jobs (that is, new tasks) may appear; some persons may leave or be recruited by the company. So the departments may evolve. No existing method has been proposed to link task-and personnel evolution.

Dynamics of competency

Selecting team members is a multi-criteria problem solving. Many criteria have been considered in literature such as: budget consideration; workload; availability of technical/soft competency; dynamics of competency. (Boucher et al., 2006) indicated that competencies can be seen as three distinct views: the static, functional and evolution views.

• The static view concerns identification, structuring and evaluation of competencies. • The functional view concerns the mechanisms of competency mobilization in a working context where the goal is to make an efficient use of available competencies.

•

The evolution view deals with the notion of dynamics of competency. Dynamics of competency of an individual directly depends on the tasks that they have been assigned. Assigning a task to an individual can raise or at least maintain his/her acquired skills. In our knowledge, the dynamics of competency hasn't been treated yet in team-building literature.

The structure of this paper is composed of two parts: first we focus on competency structuring using a fuzzy array-based clustering method; second, we present how to build a team from a given mission requirement.

BACKGROUND: SOLUTION APPROACH

Fuzzy relation

Principle. Since fuzzy relations from X to Y are fuzzy sets on the Cartesian product XxY, for every ( , ) x y X Y ∈ × , the quantity ( , ) R x y is interpreted as the strength of the existing R-link between x and y.

Fuzzy-Set-Theoretic Operations on Fuzzy Relations

Starting from two fuzzy relations R 1 , R 2 , from X to Y, we may consider:

• the fuzzy union of R 1 and R 2 , denoted

1 2 R R ∪ 1 2 1 2 : [0,1] ( , ) max( ( , ), ( , )), ( , ) R R X Y x y R x y R x y x y X Y ∪ × → ∀ ∈ × a • the fuzzy intersection of R 1 and R 2 ,denoted 1 2 R R ∩ 1 2 1 2 : [0,1] ( , ) min( ( , ), ( , )), ( , ) R R X Y x y R x y R x y x y X Y ∩ × → ∀ ∈ × a
Composition of fuzzy relation. There are many different ways to define a composition of two suitable fuzzy relations. The most common one is the so-called sup-min composition as introduced by Zadeh ( 1971), (Klir and Floger, 1988), [START_REF] Kerre | Introduction to the basic principles of fuzzy set theory and some of its applications: Communication and cognition[END_REF]. Let X, Y and Z be ordinary non empty sets, R 1 is a fuzzy relation from X to Y and R 2 is a fuzzy relation from Y to Z. The sup-min composition R 1° R 2 is given as the following fuzzy relation from X to Z: , 1991) emphasized that in some cases, another composition than the sup-min composition is more suitable.

[ ] , ) , ( )), , ( ), , ( min( sup ) , ( 1 , 0 : 2 1 2 1 Z X z x z y R y x R z x Z X R R Y y × ∈ ∀ → × ∈ a o If the involved universes are finite, i.e., X={x 1,…, x p }, Y{ y 1,…, y q }, Z={x 1,…, x r }, with 2 2 1 1 ) , ( , ) , ( lm m l kl l k R z y R R y x R = = then )). , min( , ), , min( ), , max(min( ) , )( ( 2 1 2 2 1 2 2 1 1 1 2 1 qm kq m k m k m k R R R R R R z x R R K o = (Kerre, E.E.

Array-based clustering approach

An array-based clustering algorithm is one of the algorithms widely studied in the literature. One common characteristic of this algorithm is that all the methods consecutively reorder the rows and columns according to an index until the diagonal blocks are formed. An array-based clustering approach is one of group technology algorithm. Originally, this approach is applied in manufacturing cell formation in order to group similar part families on dedicated clusters of machines. Examples of array-based clustering algorithms are: ROC (Rank Order Clustering) (King J.R. 1980), ROC2 (King J.R. and Nakornchai V., 1986), DCA (Direct Cluster Algorithm) developed by [START_REF] Chan | Direct clustering algorithm for group formation in cellular manufacture[END_REF], BEA (Bond-Energy Algorithm) developed by [START_REF] Mccormick | Problem decomposition and data reorganization by a clustering technique[END_REF], [START_REF] Mak | An adaptive genetic algorithm for manufacturing cell formation[END_REF]. The work of [START_REF] Chu | A comparison of three array-based clustering techniques for manufacturing cell formation[END_REF]) presented a procedure for evaluating alternative clustering algorithms under different measuring criteria.

PROPOSITION OF A TEAM BUILDING METHODOLOGY

In this paper, our proposed method is a first step to integrate task-and personnel evolutions in companies when doing team-building. This approach will group similar persons on dedicated clusters of tasks and make task assignment easier to the project leader, because of the limited team member proposed in each family. The proposed methodology is split up into 3 major phases (Fig. 1), as follows: generate a task-personnel incidence matrix; identify task-personnel families by clustering; assign tasks to team members. In this part, we describe these phases.

Generate a task-personnel incidence matrix

An incidence matrix is a matrix that shows the relationships between two classes of objects. If the first class is X and the second is Y, the matrix has one row for each element of X and one column for each element of Y. The fuzzy approach presented here is based on incidence matrices. The first phase of the method consists of four different steps:

-Identify relevant attributes to characterize both task and personnel. It may be technical or soft competencies. In our example, we consider these attributes as being disciplines. -Evaluate chosen attributes for a particular task (see in 1 2

k l kl l m lm R t d R R d p R = = . 1 2 ( )( , ) m k R R t p ° Compatibility
1 1 1 2 1 max(0, ) ( )( , ) 1 kl lm kl q l k m q l R R R R R t p = = °= - - ∑ ∑ (1)
This composition method (R 1 ° R 2 ) can be interpreted as the strength indicator of such a relational chain.

Identify task-personnel families by clustering.

ROC clustering algorithm will transform the taskpersonnel incidence matrix into task/personnel families. Algorithm principle:

Step 1: For each row of the task-personnel matrix, calculate the decimal weight.

Step 2: Sort rows of the matrix in decreasing order of the corresponding decimal weights.

Step 3: Repeat the preceding two steps, for each column.

Step 4: Repeat the preceding three steps until the position of each element in each row and column does not change. A weight for each row i and column j is calculated as follows:

Weight for row i :

∑ = - n k k n ik a 1 2 (2)
Weight for column j:

1 2 m m k kj k a - = ∑ (3)
where n is the number of member and m is the number of task.

Group Density Index (GDI). This array-based clustering method is simple to apply to the task/personnel matrix. However, it requires visual inspection of the output to determine the composition of the diagonal block formation. We adopt here the Group Density Index proposed by [START_REF] Tseng | Novel approach to multi-functional project team formation[END_REF]. This index will be used to identify the potential groups after using the ROC algorithm. The variables ' n and ' m refer, respectively, to the The task assignment contains a group of tasks (mission requirement) to be accomplished. The mission requirement is defined here as a set of tasks { n t t ...

AN ILLUSTRATIVE EXAMPLE

Problem formalization

Table 1 Task-Discipline incidence matrix (R 1 )

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 T1 0,8 0 0,2 0 0,1 0,9 0 1 0 0 T2 0 1 0,7 1 0 0 0,6 0 0,3 0 T3 0 0 0 0 0,9 0 0 0 1 0 T4 1 0 0,1 0 0 0 0 0,7 0 0 T5 0 0,8 0 1 0 0 0,4 0 0 0 T6 0,2 0,3 0 0 0 1 0 0,8 0 0 T7 0 0 0,1 0,1 1 0 0 0 1 0,7

Task-personnel incidence matrix

Integrating the fuzzy relation R 1 and R 2 , we will obtain the table 3 (R 1 ° R 2 ). The value of compatibility indicator

1 2 ( )( , ) k m R R t p °
can be obtained from the equation ( 1). The value in this table indicates the compatibility indicator that can be interpreted as the performance level of a person (p) to achieve a task (t).

ROC Algorithm and GDI index

The final matrix generated by the ROC algorithm is shown in table 4. Then, the GDI index (in equation 4) will be calculated to measure the group density of the possible solution. We obtained the GDI index for each potential group as follows: GDI1=0.773; GDI2=0.62; GDI3=0.723. The final decomposition obtained is shown as follows.

Group 1 : {T4,T1,T6} with {P3,P1} Group 2 : {T2,T5} with { P4,P5,P7} Group 3 : {T7,T3} with {P6,P2}. TC-1 T4 0,94 0,72 0,72 0,17 0,11 0,11 0 T1 0,86 0,69 0,41 0,14 0,1 0,07 0 T6 0,78 0,65 0,3 0,22 0,17 0,09 0,13 TC-2 T2 0,08 0,08 0,5 0,58 0,64 0,25 0,39 T5 0 0,13 0,65 0,65 0,7 0,22 0,43 TC-3 T7 0,03 0,03 0,07 0,07 0,07 0,76 0,66 Result Interpretation. We consider here two possible cases: competency structuring and task assignment.

T3 0 0 0 0 0 0,
Competency structuring considers all existing design tasks, while task assignment considers only a set of tasks in a specific design project. From the clustered result in table 4, we obtain the competency structuring in which three homogeneous blocks (departments) are formed in order to perform three groups of task. In the next section, the task assignment case will be studied and the result of competency structuring obtained in table 4 will be used in studying our task assignment case.

Task assignment

Problem formalization. Suppose we have to build a team to perform 5 tasks for a new product development. The mission requirement is composed of {T2, T5, T6, T4, T7}, see also in table 5. Each task has been identified the relative performance level ( j e ). We assume here that each task is assigned for a single team member and this team member works full time for the task assigned.

Performance-based and cost-based solution. We consider here two possible solutions: performancebased and cost-based solution. The objective of performance-based solution is to maximize the global performance of a team as the objective of cost-based solution is to minimize the cost.

I. Evaluation procedure: performance-based solution

Numerical results

In this section, we use the result obtained from table 4 to demonstrate how our task assignment method works. Each task group selects the qualified candidates from the correspondent team member group. For example, Task 2, first task in mission assignment, is in task group 2 (TC-2) so the qualified candidates have been selected from team member group 2 (PC-2). For task 2 with the given threshold of 0.7, the candidate P4, P5 and P7 are qualified. The candidate P7 has been assigned to this task (best compatibility). Then, we continue to the task 5. This task is in the same group as task 2. The candidates P4,P5,P7 have been qualified, but P7 has been assigned formerly, so the candidate P5 will be assigned. If there are candidates with the same compatibility level, we select the one who costs less to the project. The information about candidate's salary is shown in table 4.

Table 5 Team building (I) In table 6, we note that P4 can be a good candidate (0.72) to task 4 with the lower salary compared to P3. However, P4 is not in the same group as task 4. So P3 will be allocated instead. To maintain the competency of the group, our solution will privilege P3 to be assigned to their own group first. This remark opens a perspective on competency dynamics modeling

CONCLUSION

This paper has presented a fuzzy relation and an array-based approach for team building and an illustrative example. This promising approach differs from the use of existing team building approach, because it has adopted a clustering algorithm to enable the tasks and the team members to be grouped into families (departments).

Our study in team member selection can be divided into two sections. At the beginning, we presented the method for competency structuring. The solution encourages the representation of attributes, characterizing a particular task or team member. The final solution has demonstrated the potential diagonal block (group) of tasks and team members. In the second part, we have studied the assignment of a given list of tasks, required by a project and included in the whole set of tasks. We have proposed an approach to build a multidisciplinary team corresponding to performance and cost criteria.

In this paper, some limitations should be noted, as they might lead to interesting perspectives in future research. 1) We have not considered the workload (man-hours) of team members and multi-projects task assignment. 2) In the context of competency dynamics and development, the performance level of team member

Step 1: Initialize the mission requirement with its relative performance levels, j e .

Step 2: For each task, k t , generate the possible qualified candidates, then present the compatibility indicator of the qualified member in a decreasing order. Step 3: Select the candidate for each task

Step 4: Use cost criteria if there are candidates with the same performance level.

Step 5: Calculate the global performance

Step 1: Initialize the mission requirement with its relative performance levels (table 6) Step 2: For each task, k t , generate the possible qualified candidates, then present the qualified members in an increasing order Step 3: select the candidate with the lowest salary Step 4: Calculate the global performance will gradually increase during the project execution and continuously decrease if they are not assigned to the task. The question that we might ask is: how can we apply this approach to support the global competency development of a company?

Fig. 1 .

 1 Fig. 1. Team building methodology

  indicating the lower competency level of a person compared to task. In our approach, we consider only the undercompetency case and propose the following function to calculate a compatibility indicator.

  tasks to team members.

  task-discipline and personneldiscipline matrix are shown in tables 1 and 2.

table .

 . Then (R 1 ° R 2 ) is a fuzzy relation from T to P. Let us denote T={t 1,…, t p }, D={ d 1,…, d q }, P={p 1,…, p r },

	1	( , )	1	,	2	( , )	2
	1: Task-discipline incidence matrix)
	-Evaluate chosen attributes for a team member.
	(see in table.2: Personnel-discipline incidence
	matrix)
	-Define a compatibility indicator between task
	and team member.
	-Generate a task-personnel incidence matrix. (see
	in table.3: Task-personnel incidence matrix)
	Fuzzy relation and Compatibility indicator. The
	similarity measure is one of the methods often used
	in team selection. This method finds the shortest
	distance between two skill sets, so as to find the
	appropriate candidate. Some distance measures have
	been mentioned in literature, for instance, Hamming
	distance (Canos, 04), (Boucher et al., 2006). The
	disadvantage of existing measures is that they do not
	take into account the positive (or negative) measure
	as representing over-competency (or under-
	competency). Therefore, we propose a compatibility
	indicator as a distance measure that will be applied,

instead of the sup-min composition normally used in fuzzy relation, in order to find the best correlation value between two fuzzy sets. Let T, D and P denote ordinary non empty sets. Let R 1 be a fuzzy relation from T to D and let R 2 be a fuzzy relation from D to P.

Table 2

 2 Personnel -Discipline incidence matrix (R 2 )

		P1	P2	P3	P4	P5	P6	P7
	D1	0,7	0	1	1	0	0,2	0
	D2	0	0,5	0	0,9	1	0	0,9
	D3	0	0	0,3	0,2	0,4	0	0,6
	D4	0,3	0	0	0,7	0,7	0	0,8
	D5	0	0,7	0	0	0	0,9	0
	D6	0,7	0	1	0	0	0	0
	D7	0	0,9	0	0,5	0	0,6	0
	D8	0,6	0	0,6	0,8	0,2	0	0,1
	D9	0	0,5	0	0	0	0,7	0
	D10	0	0,7	0	0,1	0	0,6	0
	Salary/month (euros)	2,500	2,350	2,650	2,100	2,150	2,400	2,300
	A design project with 7 tasks required 10 disciplines
	is used as an illustrative example. This design
	department has 7 members; each member knows a
	set of different disciplines and related performance
	levels. We may consider a set of tasks t, a set of
	disciplines d and a set of personnel p. where
	1 ( , ) k l R t d = the degree to which task k t requires
	discipline l d to be carried out, and 2 ( , )

Table 3

 3

		Task-personnel incidence matrix (R 1 ° R 2 )
		P1	P2	P3	P4	P5	P6	P7
	T1	0,69	0	0,86	0,41	0,14	0,07	0,1
	T2	0,08	0,39	0,08	0,5	0,58	0,25	0,64
	T3	0	0,63	0	0	0	0,84	0
	T4	0,72	0	0,94	0,72	0,17	0,11	0,11
	T5	0,13	0,43	0	0,65	0,65	0,22	0,7
	T6	0,65	0,13	0,78	0,3	0,22	0,09	0,17
	T7	0,03	0,66	0,03	0,07	0,07	0,76	0,07

Table 4

 4

	Composition matrix with ROC algorithm
	(competency structuring)
	PC-1		PC-2			PC-3
	P3	P1	P4	P5	P7	P6	P2

Table 6

 6 Team building (II)

		Mission requirement	T2	T5	T6	T4	T7
	Relative importance
		of each task (e j )	0.5	0,2	0 ,15	0 ,1	0,05
	Possible candidate	P5,P7	P5,P7	P1,P3	P1,P3	P6,P2,P4
	Solution based on
	(	cost criteria 1 2 )( , ) k m R R t p °	P5 (0.7)	P7 (0.64)	P1 (0.72)	P3 (0.94)	P6 (0.76)


A Michau
email: alexandre.michau@cea.fr

Keywords: Revêtements, protection contre l'oxydation, carbure de chrome, CVD, DLI-MOCVD Coatings, protection against oxidation, chromium carbide, CVD, DLI-MOCVD

La protection de l'intérieur et de l'extérieur des gaines de combustible de réacteurs nucléaires contre leur oxydation à haute température est nécessaire pour garantir leur intégrité en conditions accidentelles. Pour ce faire, le procédé DLI-MOCVD a été développé pour déposer en paroi interne de gaine des revêtements à base de chrome : chrome métallique, carbures de chrome amorphes CrC x et carbures mixtes de chrome CrSi y C x . L'optimisation du procédé de dépôt a été réalisée par le couplage d'expériences et de simulations. Il a aussi été montré que la solution de précurseur organométallique et de solvant utilisée pouvait être directement recyclée en sortie de réacteur, sans étapes de séparation et de purification couteuses, augmentant le potentiel d'industrialisation du procédé. Les propriétés physico-chimiques et structurales des revêtements déposés avec ce procédé ont été caractérisées. L'évaluation de leur résistance à l'oxydation à 1 200 °C a révélé les excellentes performances des revêtements CrC x , puisqu'ils retardent l'oxydation catastrophique des gaines de plus de deux heures pour une épaisseur de 10 µm, permettant ainsi des interventions en conditions accidentelles.

La leçon de Fukushima

La sûreté d'un réacteur nucléaire se base sur un principe dit de la défense en profondeur. Ce dernier consiste en trois barrières successives de protection visant à confiner le combustible nucléaire et les produits de fission en cas d'accident. La première barrière est constituée de ce que l'on appelle les gaines de combustible. Ces tubes en alliage de zirconium d'un diamètre interne d'environ 8 mm et d'un peu plus de 4 m de longueur contiennent les pastilles de combustible UO 2 qui sont le siège des réactions nucléaires. La chaleur dégagée par ces réactions est évacuée à travers la gaine (conducteur thermique) vers le circuit primaire par l'intermédiaire d'un fluide caloporteur qui est de l'eau pressurisée pour les réacteurs nucléaires dédiés à la production d'électricité en France. C'est le circuit primaire qui constitue la deuxième barrière de confinement. La chaleur est ensuite retransmise à un deuxième circuit d'eau au sein d'un générateur de vapeur pour produire ultérieurement de l'électricité par turbinage. Si la première barrière venait à rompre, c'est le circuit primaire qui retiendrait alors les produits radioactifs présents dans le combustible. Enfin, le bâtiment en béton abritant le réacteur sert d'enceinte de confinement ; c'est la troisième barrière et l'ultime rempart dans l'éventualité où le circuit primaire romprait. Lors de la catastrophe nucléaire de Fukushima au Japon, la succession d'un séisme et d'un tsunami a entrainé l'arrêt du refroidissement des coeurs des réacteurs, menant à des conditions équivalentes à un accident de perte de réfrigérant primaire (APRP). Les gaines de combustible ont alors été soumises à une élévation brutale de leur température et pression interne ayant entrainé leur éclatement. À l'extérieur et à l'intérieur de la gaine, l'eau s'est retrouvée sous forme de vapeur portée jusqu'à 1 200 °C et la vapeur a oxydé très rapidement les parois

Vers des combustibles encore plus robustes en cas d'accident

Partie haute des gaines, CEA Saclay. © P. Stroppa/CEA, 26/04/2010. externes et internes de la gaine. Les gaines se sont désintégrées, libérant le combustible dans le circuit primaire et entrainant un relargage massif de matière radioactive. D'autres phénomènes plus complexes ont pu aussi entrer en jeu, menant à la perte d'intégrité du gainage, comme par exemple la fragilisation secondaire par l'hydrogène des alliages de zirconium utilisés. Cet accident est le type le plus grave référencé (niveau 7), avec un seul équivalent : l'accident nucléaire de Tchernobyl en 1986. Un revêtement de gaine qui pourrait passivement retarder ou atténuer l'apparition d'une défaillance structurelle de l'assemblage gaine/combustible en cas d'APRP pourrait soit diminuer le relargage de matière radioactive vers l'environnement, soit l'empêcher totalement en cas de remise en service rapide du circuit de réfrigérant.

Un gainage plus robuste en conditions accidentelles

Depuis le terrible accident de la centrale de Fukushima, la communauté internationale s'est engagée dans une politique d'amélioration continue et globale. Dans ce cadre, de nombreux travaux ont été entrepris pour augmenter les marges de sûreté des réacteurs nucléaires. Parmi ceux-ci, on peut citer les EATF (« enhanced accident tolerant fuel ») qui consistent en de nouvelles solutions pour les gaines de combustible, plus robustes en conditions accidentelles, c'est-à-dire permettant notamment de retarder, voire d'éviter ces phénomènes d'oxydation pour augmenter la durée pendant laquelle la gaine reste intègre en conditions accidentelles. À ce titre, plusieurs concepts sont étudiés pour apporter une solution à court terme. La majorité se base sur un gainage classique renforcé en paroi externe par l'application d'un revêtement protecteur. Tous les grands acteurs internationaux proposent au moins une solution de ce type. On peut par exemple mentionner le revêtement externe en chrome développé par Framatome et le CEA, déposé par un procédé en voie sèche de type PVD (« physical vapor deposition »), qui améliore grandement la résistance à l'oxydation du gainage et ses propriétés mécaniques à haute température. Cependant, la possibilité de coupler à cette première barrière externe une seconde barrière interne n'a pas encore été considérée. En effet, en conditions accidentelles, suite à l'éclatement de la gaine, la paroi interne se retrouve également exposée à de la vapeur à très haute température et sujette à une hydruration secondaire très préjudiciable à ses propriétés mécaniques. Les défis techniques à relever pour la protection interne sont nombreux. La géométrie des gaines n'est pas en soi complexe mais ses dimensions (longueur/diamètre > 500) conduisent à des études longues et couteuses de développement de procédés. Le procédé de dépôt développé devra permettre de revêtir de manière homogène en épaisseur tout l'intérieur de la gaine avec une épaisseur d'une dizaine de micromètres. De plus, le matériau déposé devra répondre à un certain nombre de contraintes environnementales et économiques (toxicité du procédé, consommation énergétique ou encore taux de production). Le choix du procédé est tout aussi important que le choix du matériau et les deux sont intimement couplés en termes de performances. Il faut évidemment que ce premier n'endommage pas le gainage et cela impose une température de traitement qui ne dépasse pas les 500 °C, ce qui est indispensable pour ne pas dégrader les traitements thermiques des alliages de zirconium de dernière génération qui s'échelonnent entre 550 et 800 °C [START_REF] Mardon | Influence of composition and fabrication process on out-of-pile and in-pile properties of M5 alloy[END_REF]. De plus, le procédé doit pouvoir être facilement et rapidement porté de l'échelle du laboratoire à plus grande échelle dans l'optique d'une éventuelle future industrialisation. L'objectif est donc multiple et requiert une approche multidisciplinaire mêlant expérimentations, caractérisations et simulations numériques, le tout en matériaux et génie des procédés. En effet, il s'agit de développer des revêtements innovants et performants par un nouveau procédé de dépôt répondant au cahier des charges exigeant des gaines de combustible nucléaire.

Une solution procédé-matériau

La technologie de dépôt retenue pour ce développement appartient à la famille des procédés en voie sèche de type CVD (« chemical vapor deposition »). C'est plus précisément la DLI-MOCVD (« direct liquid injection-metal organic chemical vapor deposition ») qui a été choisie. C'est un des procédés le plus adapté pour cette configuration de tubes longs et étroits : il doit permettre de garantir un revêtement suffisamment homogène en épaisseur sur toute la longueur, à l'intérieur de la gaine, tout en respectant les critères environnementaux imposés par REACH (en particulier l'absence d'utilisation du chrome à l'état de valence VI dans le procédé de dépôt). Les autres procédés classiques de dépôt de couches minces comme la projection thermique ou la pulvérisation cathodique magnétron ne permettent pas de déposer un revêtement à l'intérieur d'un tube de diamètre aussi faible et sur une longueur de plus de 4 m. Enfin, le dépôt en bain électrolytique ne nous paraissait pas viable au niveau environnemental à cause des solutions liquides très toxiques et nocives employées (chrome VI). Comme dans tous les procédés CVD, la variante DLI-MOCVD utilise un précurseur chimique qui après réaction avec d'autres espèces en phase homogène et/ou hétérogène, formera le revêtement désiré. Les précurseurs employés en MOCVD sont des molécules organométalliques qui ont généralement une température de décomposition bien moindre que celle des précurseurs « classiques » comme des halogénures (environ 1 000 °C). Il est donc possible, suivant le système chimique considéré, de faire baisser la température de dépôt en dessous de 500 °C, ce qui n'induit pas de modification de l'état métallurgique et donc ne perturbe pas les propriétés mécaniques des alliages de zirconium à traiter. L'apport de la technologie DLI (injection liquide directe pulsée) concerne la génération de hauts débits de phase vapeur Insertion d'un assemblage de gaines dans un réacteur. © Foro Nuclear.

réactive. Le précurseur est ici dissous ou dilué dans un solvant organique, puis cette solution est fractionnée en nuage de microgouttelettes sous vide grâce à un injecteur. L'injection pulsée se fait directement dans une chambre dont les parois sont chauffées pour évaporer la solution sans décomposition prématurée du précurseur. Les avantages de ce système d'injection sont la grande stabilité dans le temps des débits générés ainsi que les fortes quantités qui peuvent être injectées, même avec des précurseurs organométalliques à faible pression de vapeur, garantissant une forte concentration en précurseur dans la phase vapeur, condition requise pour l'alimentation des réacteurs de grandes tailles et l'obtention de fortes vitesses de dépôt. Le choix des matériaux à déposer s'est fait sur des revêtements à base de chrome, ces derniers étant déjà largement utilisés dans l'industrie automobile, maritime et des outils de coupe, à des fins de protection contre l'usure abrasive, la corrosion et parfois la combinaison des deux à hautes températures. Il est intéressant de constater que ces revêtements à base de chrome ne sont pas complètement inconnus du nucléaire. Un brevet avait déjà été publié par Framatome et Cogema pour déposer des revêtements d'oxydes de chrome par MOCVD à l'intérieur de gaines de combustible pour lutter contre un autre problème, celui de l'interaction entre la pastille de combustible et la gaine [START_REF] Hertz | Procédé de réalisation d'une couche d'isolation en oxyde de chrome entre les pastilles et la gaine d'un élément combustible nucléaire et élément combustible comportant une telle couche d'isolation[END_REF]. Un précurseur contenant du chrome à l'état de valence nulle a été sélectionné. Parmi la famille des bis(arène)chrome qui est caractérisée par une structure sandwich avec un atome de chrome au degré d'oxydation zéro, le bis(benzène)chrome (BBC, composé solide) et le bis(éthylbenzène)chrome (BEBC, composé liquide) présentés en figure 1 ont été évalués.

Les revêtements qui ont pu être déposés avec ces précurseurs sont du chrome métallique, des carbures de chrome CrC x et des carbures de chrome mixtes CrSi y C x . La diversité de ces revêtements base chrome résulte d'un besoin de multifonctionnalité : couche d'accrochage (Cr), revêtement de protection CrC x et amélioration de la stabilité thermique (CrSi y C x ). C'est donc un procédé innovant doublé d'un matériau avancé que nous avons développé.

Un développement couplé expériences-simulation

Afin d'optimiser le procédé de dépôt pour atteindre un jeu optimal de paramètres expérimentaux menant à un dépôt uniforme dans toute la longueur de la gaine, une simulation numérique de ce dernier a été construite. Un schéma réactionnel de la décomposition du précurseur a été proposé et introduit dans la simulation numérique du réacteur. Il prend à la fois en compte la thermodynamique et la cinétique de réaction du précurseur de chrome.

Aucun mécanisme élémentaire précis n'avait déjà été avancé dans la littérature pour rendre compte de la croissance de carbures de chrome ou de chrome métallique par décomposition du précurseur BBC ou BEBC. Une réflexion sur le mode de décomposition du précurseur et la croissance du revêtement a été engagée pour identifier les réactions chimiques prédominantes en phases homogène et hétérogène. Après une série de vérifications expérimentales et bibliographiques, mais aussi à la suite de considérations sur l'équilibre thermodynamique des produits de réaction, un mécanisme réactionnel complet pour le dépôt de CrC x a pu être proposé, consistant en quatre réactions dont une homogène et trois hétérogènes. Ces réactions émanent de la simplification d'un mécanisme plus complet basé sur quatorze réactions [START_REF] Michau | Dépôts chimiques en phase vapeur de revêtements à base de chrome sur surfaces complexes pour environnements extrêmes : expérimental et simulation[END_REF]. Le mécanisme considéré pour le BBC est présenté dans la figure 2. C'est ce modèle réactionnel de décomposition du précurseur BBC qui a été retenu pour être inséré dans un logiciel de simulation numérique multiphysique (CFD-ACE, www.esigroup.com). La cinétique a été ajustée sur une première configuration géométrique par un ensemble de six expériences de dépôt dans des tubes de 30 cm de long et de 24 mm de diamètre interne. Elle a ensuite été confrontée à une deuxième géométrie légèrement différente pour être validée grâce à deux expériences dans un tronçon de gaine de 1 m de long et 8 mm de diamètre interne. Ce sont les profils de vitesse de croissance mais aussi les compositions élémentaires des revêtements mesurées par microsonde électronique qui ont servi pour l'ajustement et la validation du modèle numérique. Les profils de vitesses de croissance expérimentaux et simulés obtenus lors des expériences de dépôt sur des tronçons de gaine à 450 et à 400 °C avec une pression de 0,67 kPa sont

Fonctionnement du procédé DLI-MOCVD utilisé

Un ou des précurseurs organométalliques sont dissous ou dilués dans un solvant organique puis la solution liquide est évaporée. Cette vapeur réactive arrive ensuite dans un tube réacteur, en fait un tube en silice avec un porte-échantillon plat ou directement un tronçon de tube de gaine, où elle est activée thermiquement par un four à mur chaud. De ce fait, la croissance du revêtement est possible sur toute surface suffisamment activée. Le BBC et le BEBC ont la particularité de se décomposer pour former un dépôt à base de chrome à partir de 350 °C, ce qui est tout à fait compatible avec les alliages de zirconium. Après avoir traversé la partie réacteur, la phase gazeuse enrichie en sous-produits est déviée vers un système de piégeage et de recyclage. Le recyclage du précurseur est une innovation du procédé rendue possible grâce au système chimique choisi. En effet, le précurseur est assez stable pour ne réagir significativement qu'au contact d'une surface. Le précurseur non consommé et le solvant sont ainsi réutilisables après condensation sélective afin de maximiser le taux de conversion du procédé et réduire son coût, sans nuire à la qualité du revêtement [START_REF] Schuster | Procédé de dépôt d'un revêtement par DLI-MOCVD avec recyclage direct du composé précurseur[END_REF], et tout en minimisant les rejets de produits chimiques.

présentés en figure 3a. On peut y voir un très bon accord entre les données de l'expérience et les résultats de la simulation malgré la complexité de la géométrie et des phénomènes réactionnels. Cette démarche couplant expériences et simulation a permis de définir une fenêtre expérimentale théorique conduisant à un dépôt uniforme en épaisseur sur un tronçon de gaine de 1 m, en réduisant la température à 375 °C et la pression à 0,13 kPa (figure 3b). Pour obtenir cette uniformité, il est nécessaire de passer par un procédé en deux phases. Un premier dépôt est fait avec une injection de la phase gazeuse réactive à un bout du tronçon, puis un deuxième en injectant à partir de l'autre extrémité, les conditions de dépôt étant gardées constantes par ailleurs. Même si cela n'a pas encore été testé aujourd'hui, il est important de noter que ceci est facilement réalisable expérimentalement sur une même installation sans avoir à interrompre longuement le procédé lors du changement d'injection et donc sans créer une interface entre les deux dépôts. Enfin, la vitesse de croissance obtenue sur toute la longueur est de l'ordre de 1,7 µm h -1 , ce qui n'est pas rédhibitoire industriellement.

Le couplage expériences-simulation a permis de mieux comprendre le procédé et d'accélérer la recherche de fenêtres expérimentales optimales. Des modèles homologues pourront être développés pour les bis(arène)M, où M est un métal de transition.

Les revêtements déposés

Suivant la température de la chambre du réacteur et la sursaturation du précurseur au voisinage du substrat, des revêtements de carbures de chrome CrC x amorphes ou cristallisés ont pu être déposés à l'intérieur de tronçons de gaine, à partir du mélange de précurseur (BBC ou BEBC) en solution dans un solvant (toluène). La phase amorphe a été privilégiée du fait de sa microstructure lisse, dense et exempte de joints de grains qu'il est possible de faire croître en dessous de 500 °C (figure 4) et qui devrait constituer une très bonne barrière face à l'oxydation haute température et à la diffusion de l'oxygène. Ces revêtements carbures sont constitués d'une matrice de carbure de chrome amorphe a-CrC x de composition très proche de Cr 7 C 3 avec un excès de C-libre. Ce dernier a majoritairement une structure graphitique turbostratique (empilement désordonné de feuillets de graphène) avec des domaines de cohérence nanométriques (environ 35 nm), le reste étant sous la forme de chaines de trans-poly-acétylène pouvant border et interconnecter les plans de graphène. Des atomes de chrome individuels seraient intercalés entre ces plans de graphène dans une configuration sandwich similaire à la structure moléculaire du précurseur bis(arène)chrome [START_REF] Bui | Graphene-Cr-graphene intercalation nanostructures: stability and magnetic properties from density functional theory investigations[END_REF] et d'autres atomes de chrome de la matrice a-Cr 7 C 3 interagiraient avec les feuillets de graphène externes des agrégats graphitiques, à l'instar du greffage du chrome sur du graphène, des nanotubes de carbone ou des fullerènes qui forme des complexes hexahapto η 6 -Cr [START_REF] Sarkar | Organometallic chemistry of extended periodic π-electron systems: hexahapto-chromium complexes of graphene and single-walled carbon nanotubes[END_REF]. Cet ensemble d'interactions formerait un réseau très désordonné 3D plus rigide qu'une nanostructure purement graphitique sans interaction avec la matrice dans laquelle elle est incluse [START_REF] Michau | Evidence for a Cr metastable phase as a tracer in DLI-MOCVD chromium hard coatings usable in high temperature environment[END_REF]. Les revêtements CrC x amorphes déposés avec une solution de précurseur et de solvant recyclés après collecte par piégeage cryogénique montrent des caractéristiques similaires, tant au niveau de la microstructure, de la cristallographie ou de la composition, malgré la concentration en précurseur bien plus faible dans la solution injectée initialement (non recyclée). Finalement, la seule différence significative a été trouvée par spectrométrie Raman. Les spectres des revêtements recyclés sont caractéristiques d'un désordre plus grand dans les nanodomaines graphitiques par rapport aux revêtements non recyclés [START_REF] Michau | Chromium carbide growth at low temperature by a highly efficient DLIMOCVD process in effluent recycling mode[END_REF], ce qui résulte d'un taux d'interactions plus grand entre le chrome et les feuillets de graphène, ces interactions étant assimilables à des défauts. L'ajout de thiophénol C 6 H 5 SH à la solution de précurseur et de solvant (BEBC et toluène) a permis de déposer des revêtements de chrome métallique cristallisé à 400 °C. Une compétition d'adsorption se met en place entre les molécules d'additifs et les ligands benzène, dont la décomposition hétérogène se trouve drastiquement diminuée avec pour conséquence une inhibition de l'incorporation de carbone. Ces revêtements sont très légèrement contaminés en soufre (moins de 1 % at. mesurés en microsonde) car l'additif bien qu'ajouté en faible quantité par rapport au BEBC (2 % mol), se décompose un peu lors du procédé. Il se trouve que les revêtements sont constitués de deux phases de chrome cristallisé qui ont pu être identifiées par diffraction des rayons X et par diffraction d'électrons rétrodiffusés (EBSD). La première phase Cr-bcc, majoritaire, est stable, et la seconde δ-Cr, minoritaire (quantifiée à 6 % par EBSD et visible en rouge sur la figure 5b), est métastable. Cette phase métastable, qui subsiste jusqu'à 450 °C puis se transforme irréversiblement en phase stable [START_REF] Michau | Evidence for a Cr metastable phase as a tracer in DLI-MOCVD chromium hard coatings usable in high temperature environment[END_REF][START_REF] Kimoto | An electron diffraction study on the crystal structure of a new modification of chromium[END_REF][START_REF] Nishida | Crystal habit and crystal structure of fine chromium particles: an electron microscope and electron diffraction study of fine metallic particles prepared by evaporation in argon at low pressures (III)[END_REF], constitue donc une signature du procédé DLI-MOCVD qui opère à seulement 400 °C [START_REF] Michau | Evidence for a Cr metastable phase as a tracer in DLI-MOCVD chromium hard coatings usable in high temperature environment[END_REF]. Une microstructuration du revêtement en multicouche a également été tentée afin de le rendre le plus dense possible dans le but de renforcer son rôle barrière et sa résistance à l'oxydation. Une monocouche à croissance colonnaire a ainsi été remplacée par un ensemble de couches pour lequel chacune des monocouches le constituant est à croissance quasi-équiaxe. La porosité générée par les espaces inter-colonnes perpendiculaires à la surface du substrat à protéger dans le cas du revêtement monocouche est ainsi évitée ou fortement minimisée et on obtient un revêtement multicouche, polycristallin et non texturé comme les analyses EBSD le montrent en figure 5a et 5c.

Performances techniques des revêtements en cas d'accident

La résistance à l'oxydation haute température des revêtements à base de chrome déposés par DLI-MOCVD a pu être évaluée en reproduisant partiellement d'hypothétiques conditions d'accident conduisant à la perte de réfrigérant primaire. Deux tests ont été mis en oeuvre. Des mesures par analyse thermogravimétrique (ATG) ont d'abord été entreprises. Elles ont permis de suivre la prise de masse d'échantillons

Raphaël BOICHOT,

professeur à l'Université Grenoble Alpes, Laboratoire Science et ingénierie des matériaux et des procédés (SIMAP), CNRS, 38000 Grenoble.

Figure 1 -

 1 Figure 1 -Molécules de bis(benzène)chrome, (C 6 H 6 ) 2 Cr, et de bis(éthylbenzène)chrome, ((C 2 H 5 )C 6 H 5 ) 2 Cr, utilisées comme précurseurs pour le dépôt.

Figure 2 -

 2 Figure 2 -Mécanisme réactionnel simplifié de décomposition du bis(benzène)chrome.

Figure 3 -Figure 4 -

 34 Figure 3 -Profils de vitesse de croissance de revêtements CrC x déposés dans un tronçon de gaine de 1 m : (a) comparaison expérimentale et simulation en simple injection (450 et 400 °C à 0,67 kPa) ; (b) simulation en double injection (400 °C et 0,67 kPa, puis 375 °C et 0,13 kPa).

  en alliage de zirconium nus et revêtus lors d'une rampe en température de 25 à 1 200 °C à une vitesse de chauffe de 40 °C min -1 , puis lors d'un recuit à 1 200 °C, le tout sous atmosphère d'air sec ou d'air humide (27,5 % d'humidité relative mesurée à 25 °C). Les analyses ont montré que les revêtements en carbures de chrome amorphes étaient les plus performants. Les résultats sous air humide sont présentés sur la figure 6 pour des revêtements CrC x amorphes de différentes épaisseurs, ainsi qu'une comparaison à un échantillon nu d'alliage de zirconium. L'oxydation catastrophique à 1 200 °C sous air sec peut être retardée de plus de deux heures pour une épaisseur de revêtement CrC x de seulement 10 µm et de plus d'une heure et demie sous air humide. La protection conférée par les revêtements est efficace et est d'autant plus longue que l'épaisseur du revêtement est grande. Un deuxième test plus représentatif des conditions d'accident de perte de réfrigérant primaire a été mis en oeuvre. Il consistait en un chauffage à 1 100 °C sous air sec pendant 14 minutes suivi d'une trempe à l'eau d'un échantillon d'alliage de zirconium recouvert de CrC x amorphe, censée simuler un renoyage brutal du coeur du réacteur après une perte de réfrigérant. Là encore, le revêtement est bénéfique pour retarder la défaillance de l'échantillon par oxydation puisque les différentes caractérisations effectuées ont permis de vérifier que le substrat en alliage de zirconium n'était pas oxydé et préservait donc son intégrité. Comme on peut le voir sur l'observation en microscopie électronique à balayage en figure 7b, c'est le revêtement qui s'oxyde en premier suivant un mode de dégradation qui lui permet de rester adhérent avec une microstructure toujours dense malgré sa recristallisation. Le profil élémentaire mesuré par spectrométrie à décharge luminescente en figure 7a confirme les observations, à savoir que seule la partie externe du revêtement s'est oxydée, laissant du revêtement non oxydé sur le substrat, lui-même non oxydé. De plus, une zone d'interdiffusion entre le revêtement et le substrat est visible et ne peut que renforcer l'adhérence du revêtement CrC x sur le substrat en alliage de zirconium, déjà satisfaisante sans ce phénomène. Ces deux tests d'oxydation haute température montrent que la diffusion de l'oxygène dans les échantillons revêtus et la cinétique d'oxydation se trouvent fortement ralenties par la présence des revêtements déposés par DLI-MOCVD. Ils jouent un rôle de barrière sacrificielle. Des essais complémentaires sur des tronçons de gaine revêtue par DLI-MOCVD menés récemment au CEA [11] ont été réalisés à 1 200 °C sous vapeur d'eau pendant dix minutes suivi d'une trempe à l'eau. Les conclusions sont similaires : le revêtement en carbure de chrome amorphe d'une épaisseur initiale d'environ 20 µm empêche l'oxydation de la gaine. Il faudrait que cet essai sévère dure beaucoup plus longtemps pour que l'alliage de zirconium ne s'oxyde à son tour.

Figure 5 -

 5 Figure 5 -Analyses EBSD d'une coupe d'un revêtement biphasé multicouche de chrome déposé à 400 °C et 6,7 kPa : (a) contraste de bande ; (b) cartographie de phases montrant la phase métastable en rouge ; (c) figure de pole inverse montrant l'absence de texture (axe z).

Figure 6 -

 6 Figure 6 -Analyses thermogravimétriques sous air humide (27,5 % d'humidité relative mesurée à 25 °C) d'échantillons en alliage de zirconium nu et revêtus par CrC x amorphe pour différentes épaisseurs de revêtements : (a) rampe en température de 25 à 1 200 °C et (b) recuit à 1 200 °C.

Figure 7 -

 7 Figure 7 -Analyses par spectroscopie de décharge luminescente et par microscopie électronique à balayage (coupe) d'un revêtement CrC x amorphe de 9 µm déposé sur une plaque en alliage de zirconium ayant subi une chauffe de 14 min à 1 100 °C sous air sec suivie d'une trempe à l'eau.

  Transverse de Compétences Matériaux et Procédés, CEA, Gif-sur-Yvette.

Michel PONS,directeur de recherche au CNRS, Université Grenoble Alpes, SIMAP, CNRS, 38000 Grenoble.Éric MONSIFROT,président de la société DEPHIS (développement et mise en oeuvre de revêtements innovants, www.dephis.com), Étupes (Doubs).

Un réacteur pilote en test

Le procédé DLI-MOCVD est original et adaptable pour déposer des revêtements satisfaisant au cahier de charges contraignant des gaines de combustible nucléaire et de la protection interne contre l'oxydation de ces gaines. Les revêtements à base de chrome élaborés ont des caractéristiques structurales et chimiques à fort potentiel pour la protection interne des gaines en milieu radiatif et oxydant. De plus, ces revêtements présentent des propriétés mécaniques remarquables offrant des potentialités d'utilisation au-delà du secteur nucléaire, par exemple en tribologie (dureté élevée, résistance à l'usure abrasive accrue, tenue haute température). Ces travaux ont aussi permis de concevoir, réaliser et démarrer un premier pilote de DLI-MOCVD équipé d'un réacteur de 100 cm de long et 15 cm de diamètre interne. Ce réacteur pilote servira de moyen d'élaboration préférentiel pour développer de nouvelles solutions de revêtements, autant au niveau de leur architecture (multicouche, nanocomposite, couche à gradient de composition) que de leur composition (phases spécifiques originales), mais aussi permettra de traiter des pièces de géométrie complexe de plus grande taille ainsi que des ensembles d'environ quinze tronçons de gaine pour les protéger en face interne. Des essais plus représentatifs sont en cours au CIRIMAT et au CEA pour continuer le développement du procédé DLI-MOCVD et des revêtements en carbures de chrome amorphes pour la protection interne des gaines. Dans tous les cas, ces revêtements devront se coupler à une protection externe pour une sûreté accrue du combustible. Ces travaux sur la protection interne sont à l'heure actuelle pionniers au sein de la communauté scientifique qui se concentre uniquement sur la protection externe.


Le Lann

J Van Baaren

Are aphid parasitoids from mild winter climates losing their winter diapause?

Keywords: Climate change, Phenotypic plasticity, Phenology, Overwintering, Seasonal adaptations, Loss of diapause

Using fresh data and both field and laboratory experiments, we present new evidence of climate change impacts on overwintering strategies in parasitoid wasp species from mild winter areas.

Introduction

There is extensive evidence that climate change can impact various organisms' functional traits and can lead to rapid eco-evolutionary changes, including trait loss through relaxed selection [START_REF] Carroll | Evolution on ecological time-scales[END_REF][START_REF] Lahti | Relaxed selection in the wild[END_REF]. Similarly, an increasing number of studies on both animals and plants indicate that modifications in mean temperatures have considerable impacts on species distribution, abundance, physiology and phenology [START_REF] Hughes | Biological consequences of global warming: is the signal already apparent?[END_REF][START_REF] Walther | Ecological responses to recent climate change[END_REF][START_REF] Parmesan | Ecological and Evolutionary Responses to Recent Climate Change[END_REF]. There is, however, limited evidences suggesting that climate change may also induce drastic shifts in overwintering strategies, with species delaying migration (e.g. [START_REF] Gordo | Do changes in climate patterns in wintering areas affect the timing of the spring arrival of trans-Saharan migrant birds?[END_REF] or remaining active throughout the winter [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF].

In temperate areas, an increase in mean temperatures in winter is expected, leading to a milder, later and shorter winter period (IPCC 2013). This change in seasonality is likely to have widespread impacts on ectothermic organisms such as insects, whose fitness is largely determined by how well their phenology tracks seasonal patterns (alternation between favorable and adverse conditions). Insects typically enter diapause as the photoperiod declines in autumn which is used as cue of upcoming deleterious conditions [START_REF] Tauber | Seasonal adaptations of insects[END_REF]Saunders 2002). This photoperiodic response is modulated and selected by winter temperatures and consequently, diapause incidence varies between populations along winter severity gradients [START_REF] Danks | Insect Dormancy: An Ecological Perspective[END_REF]. For example, in the parasitoid Nasonia vitripennis Ashmead, the incidence of diapause is higher, and occurs sooner, in northern populations (which experience earlier and harsher winters) compared to southern populations [START_REF] Paolucci | Adaptive latitudinal cline of photoperiodic diapause induction in the parasitoid Nasonia vitripennis in Europe[END_REF]. Climate warming may impose a selective pressure on insects' diapause, which may be altered in the same way as if northern populations were moving southward. As a consequence, for a given population in a given area, diapause level may currently be lower than some decades ago.

Changes in diapause expression can occur either through adaptations to novel climatic conditions or through phenotypic plasticity when facing higher temperatures [START_REF] Bradshaw | Genetic shift in photoperiodic response correlated with global warming[END_REF][START_REF] Vázquez | Ecological and evolutionary impacts of changing climatic variability[END_REF]. Insect populations experiencing warmer winters could show (i) a delay in the onset of diapause, (ii) a decrease in the proportion of individuals entering diapause and, ultimately (iii), a loss of the capacity to enter diapause if there is a selective advantage to individuals maintaining their activities during winter (e.g., increased resource availability, increased cost of diapause; [START_REF] Hance | Impact of Extreme Temperatures on Parasitoids in a Climate Change Perspective[END_REF][START_REF] Bale | Insect overwintering in a changing climate[END_REF]. These potential shifts in overwintering strategies could have cascading consequences on community structures, species interactions and ecosystem functioning [START_REF] Parmesan | A globally coherent fingerprint of climate change impacts across natural systems[END_REF][START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF] but are, to date, scantily documented in host/parasitoid systems [START_REF] Hance | Impact of Extreme Temperatures on Parasitoids in a Climate Change Perspective[END_REF][START_REF] Chaianunporn | Evolutionary responses to climate change in parasitic systems[END_REF].

The Brittany region, in Western France, is characterized by an oceanic climate. Since the early 1980s, studies in this area have reported the winter guild of cereal aphid parasitoids to be dominated by two species which remained active and showed low levels or absence of winter diapause in the field: Aphidius rhopalosiphi De Stefani-Perez (Hymenoptera: Braconidae) and Aphidius matricariae Haliday, with a proportion of diapausing parasitoids in each population of around 25% [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF][START_REF] Krespi | Etude de la biocénose parasitaire des pucerons des céréales dans le bassin de Rennes : cas particulier d'Aphidius uzbekistanicus Luz[END_REF][START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF], Table 1). In contrast, two other parasitoid species, Aphidius avenae Haliday and Aphidius ervi Haliday, as well as all aphid hyperparasitoid species, were presumed to enter diapause in winter, because they were only encountered as active adults (or as non-diapausing prepupae inside a mummy) during late spring, summer and early fall [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF]Krespi et al. 1997, Table 1). This situation has changed in the past few years (since winter 2011/12), with A. avenae (and to a lower extent A. ervi) now being active in winter in cereal fields, and representing respectively up to 52% and 3% of the total parasitoid guild each winter [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF][START_REF] Tougeron | Comparing thermal tolerance across contrasting landscapes: first steps towards understanding how landscape management could modify ectotherm thermal tolerance[END_REF]. [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF] suggested that the change in the aphid parasitoid guild composition was related to climate warming and to increasing availability of anholocyclic cereal aphids during winter, leading to a shift in overwintering strategies in some parasitoid species. Indeed, under mild climates of Western Europe, anholocyclic cereal aphids have been active throughout the year [START_REF] Dean | The overwintering and abundance of cereal aphids[END_REF][START_REF] Leather | Aspects of Aphid Overwintering (Homoptera: Aphidinea: Aphididae)[END_REF][START_REF] Langer | Seasonal activity and distribution of cereal aphid parasitoids in Belgium[END_REF][START_REF] Dedryver | Coexistence in space and time of sexual and asexual populations of the cereal aphid Sitobion avenae[END_REF], and have been serving as reservoirs allowing some parasitoids to overwinter as active adults whereas others entered diapause (e.g. [START_REF] Langer | Overwintering strategies and cold hardiness of two aphid parasitoid species (Hymenoptera: Braconidae: Aphidiinae)[END_REF][START_REF] Legrand | Autumn, winter and spring dynamics of aphid Sitobion avenae and parasitoid Aphidius rhopalosiphi interactions[END_REF]). This pattern is often considered as a "spread-the-risks" strategy (polyphenism), as a local adaptation to both winter temperature conditions and to host availability [START_REF] Hance | Impact of Extreme Temperatures on Parasitoids in a Climate Change Perspective[END_REF]). Overwintering as an active adult rather than as a diapausing prepupae may consequently become a more common strategy in insects experiencing a warmer climate. For the above reasons, aphid parasitoids from Brittany are excellent models to study diapause expression in the context of climate change.

In this study, we asked to what extent the diapause could be affected by rapid climate changes in aphid parasitoid populations from a mild winter region, in Western Europe. The following questions were addressed: (i) are these populations expressing winter diapause in both the field and laboratory; (ii) if yes, under what condition of photoperiod and temperature; and (iii) in what proportion for each species and conditions? To answer these questions, we first conducted a field survey in winter 2014/15 to assess levels of diapause incidence in natural populations of aphid parasitoids in cereal fields and to determine if A. avenae and A. ervi remained constituent of the host-parasitoid food web in Brittany as observed since 2011/12 [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF][START_REF] Tougeron | Comparing thermal tolerance across contrasting landscapes: first steps towards understanding how landscape management could modify ectotherm thermal tolerance[END_REF]. Then, we quantified diapause induction in the four cereal aphid parasitoids species under different combinations of photoperiod and temperature in the laboratory. We aimed at highlighting changes in diapause expression by comparing current diapause expression to those recorded about thirty years ago in the same area and on the same species (details in Table 1). According to previous studies on these insect populations (e.g. [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF][START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF], the following hypotheses were tested: (i) the incidence of parasitoid diapause is higher at lower temperatures and photoperiods; (ii) the incidence of parasitoid diapause varies together with the seasonal occurrence of each species in natural environments, with A. matricariae and A. rhopalosiphi expressing no or little diapause, and A. avenae and A. ervi having the highest diapause incidence; and (iii) as a response to mild winters and the availability of hosts in winter, overall parasitoid diapause incidence is low in Brittany populations. Brittany, Western France in the 1970-1980s. For both studies, aphid mummies that may contain either diapausing or non-diapausing parasitoids were collected and the time from mummy collection to emergence of adult parasitoids and hyperparasitoids was determined under outdoors conditions. This provides information on the proportion of diapause among these species. [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF] sampled in wheat fields mainly at Le Rheu in Brittany, and in other locations in Western France. They conducted surveys from late October to early April for six years, starting in 1975. They reported that the aphid community was dominated by Sitobion avenae and Rhopalosiphum padi. [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF] collected mummies on wheat from October to March in 1984 and1985. Sampling periods will be roughly named the "winter period" (i.e. the period during which diapause can occur). In this table we report pooled data for all sampling years and the main conclusions of the authors concerning diapause expression in aphid parasitoids that emerge from winter-collected mummies. We only show data from species of interest in the present study.

Parasitoid species

Total

Material and Methods

Meteorological data

We analyzed minimum, maximum and average daily temperature between (i) 1976-1985, and (ii) 2010-2015. These periods correspond to the range of sampling dates in (i) [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF] and [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF] and (ii) [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF] and [START_REF] Tougeron | Comparing thermal tolerance across contrasting landscapes: first steps towards understanding how landscape management could modify ectotherm thermal tolerance[END_REF] and the present study in Brittany. In our analysis we chose to only account for the evolution of the temperature conditions between the two time periods and not for inter-annual variations within a given time period. Data were analyzed for seasonal periods of parasitoid diapause induction and maintenance; the fall (from September 22 to December 21) and the winter (from December 22 to March 20). We also analyzed for each season, across the two time periods the variation in the average number of days with cold spell events (minimum temperature ≤0 °C, close to potential freezing temperature and above activity and developmental thresholds of most Aphidius parasitoids [START_REF] Sigsgaard | The temperature-dependent duration of development and parasitism of three cereal aphid parasitoids, Aphidius ervi, A. rhopalosiphi, and Praon volucre[END_REF][START_REF] Alford | Could Behaviour and Not Physiological Thermal Tolerance Determine Winter Survival of Aphids in Cereal Fields?[END_REF], and heat spell events (maximum temperature ≥22 °C, stressful for Aphidius parasitoids (Le Lann et al. 2011b). Data were recorded by a Météo France weather station situated next to the sampled fields (48°04'06"N, 1°44'00"W, elevation: 36 m) with a classic resistance temperature detector probe (1976)(1977)(1978)(1979)(1980)(1981)(1982)(1983)(1984)(1985) and a Pt100 probe (2010-2015, Pyrocontrole, Meyzieu, France).

Winter field sampling

In order to assess for potential diapausing primary and secondary parasitoids in the field in winter and to build an aphid-parasitoid quantitative food web, we sampled aphids and aphid mummies in different cereal crops from the 5 th to the 29 th of January, 2015, in Brittany, Western France. A preliminary prospection on several crops allowed us to assess the presence of aphids and to select a total of seven different fields in which we performed the sampling. Fields were separated one from another by at least 500 m. Precise locations of the fields were as follow (°North; °West): 48.09458; 1.81386, 48.11095; 1.81403, 48.10777; 1.78203, 48.48282; 1.60453, 48.10046; 1.81459, 48.10636; 1.81395 and 48.12238; 1.53869. We visited each field twice per week. Field borders were excluded to avoid potential margin effects. A standardized surface of 1000 m² was prospected in each field and every aphid and mummy found were collected and stored in the lab at 20 °C, with a Light:Dark (LD, h) 16:8 photoregime. Living aphids were kept on winter wheat 10 days to wait for potential mummification and were identified thereafter. Following emergence, parasitoids and hyperparasitoids were freeze-killed at -20°C and identified (along with the species of aphid they emerged from), using an optical microscope and the identification key developed by [START_REF] Hullé | Encyclop'aphid, a key for aphids and their parasitoids[END_REF]. Hyperparasitoids were only identified to the genus level. Aphid mummies from which no parasitoid emerged were kept for 70 days in gelatine capsules (L = 2 cm, Ø = 0.5 cm) at 20°C, with any emergence scored daily. Remaining mummies were then dissected and their content identified as a dead individual or a diapausing parasitoid prepupae.

Biological material

Laboratory cultures of Aphidius species were established from individuals collected in Brittany during different sampling sessions in fall 2014. From 84 to 125 females and from 31 to 78 males (depending on the species) were sampled in five cereal fields in a 30 km area around the city of Rennes (48.113 °N, 1.674 °W) in 2014. The genetic pool was refreshed in January 2015 by adding 57 non-diapausing parasitoids from the seven fields that we used in this study, and mentioned above. This was done to ensure a sufficient genetic diversity in the laboratory parasitoid culture. They were reared for less than 10 generations before being tested. To control for host effect on parasitoid diapause incidence we used a single aphid clone of Sitobion avenae (Fabricius) that was established from one single parthenogenetic female collected in 1990 at Le Rheu, Brittany. Parasitoids were maintained on parthenogenetic S. avenae aphids, reared on winter wheat (Triticum aestivum L. v. Saturnus).

Insects and plants were maintained in Plexiglas cages (50x50x50 cm) at 20 ±1 °C, 70 ±20 % RH and 2 000 lx under a 16:8 LD photoregime in climate-controlled chambers.

Conditions for diapause induction

In order to test the effects of photoperiod and temperature on parasitoid diapause incidence during larval and pupal development, nine constant conditions were used, representing the combinations of three photoregimes (10:14, 12:12, 14:10 LD) with three temperature regimes (14 °C, 17 °C, 20 °C). These values correspond to temperatures and photoperiods encountered by the parasitoids from August 15 to November 30, 2014, in natural conditions in Brittany (Météo France). These temperature and photoperiod treatments are known to be diapauseinducing in aphid parasitoids from temperate regions at equivalent latitude and represent standard treatments when assessing for diapause expression in insects, which helps at better comparing our results to other studies' (Brodeur and McNeil 1989a;[START_REF] Langer | Overwintering strategies and cold hardiness of two aphid parasitoid species (Hymenoptera: Braconidae: Aphidiinae)[END_REF][START_REF] Polgár | Diapause induction in aphid parasitoids[END_REF]. Only five climate chambers were available at the same time. Thus, we first tested 5 treatments on the four species (20 °C 10:14 LD / 20 °C 14:10 LD / 14 °C 10:14 LD / 14 °C 12:12 LD / 14 °C 14:10 LD) and next we tested the last 4 treatments (20 °C 12:12 LD / 17 °C 10:14 LD / 17 °C 12:12 LD / 17 °C 14:10 LD) + 1 repetition of one previous treatment (20 °C 10:14 LD) to control for any bias in the experiment such as artificial selection in the cultures, cohort or generational effects. There were no differences in diapause incidence between these two batches of experiments at 20 °C, 10:14 LD, for any of the four species (GLM, df=1, F=0.08, p=0.79).

Insect production for the experiments

Because host size and life stage have been shown to influence parasitoid diapause incidence (Brodeur and McNeil 1989a), aphid cohorts of homogenous size were produced for our experiments. For each parasitoid species, mummies were collected from the culture, isolated in gelatin capsules, and then maintained in climate chambers until emergence. On the day of emergence, five females were placed in a plastic tube for 12-24 h with access to two males for mating and honey and water for feeding. The next day, under standard rearing conditions, the 5 females were exposed together for 24 h to 150 (± 10) S. avenae second instar aphids on a wheat pot in a cage, also with access to honey and water.

Diapause induction

After 24 h, parasitoid females were removed from the cage and the 150 potentially parasitized aphids were randomly and equally distributed on 5 wheat pots (≈ 30 aphids per pot). Pots consisted of plastic tubes (L = 16 cm, Ø = 5 cm) filled with vermiculite substrate and closed with a fine mesh netting. Each of these "microcages" was placed under one of the experimental photoperiod/temperature conditions described above. Temperature was set using MIR-153 climate chambers (Sanyo, Osaka, Japan) and controlled daily using the incorporated probe. Light was provided by 20 W fluorescent tubes with an intensity of 2000 lx (4000 K cool white color) in each climate chamber. Relative humidity was maintained at 80 ±10 %.

Starting one week after the experiments began, microcages were checked daily. Once aphid mummies were formed, they were isolated individually in gelatin capsules and kept under their respective treatments. Parasitoid emergence was verified twice daily. This whole procedure was repeated from 5 to 11 times for each treatment and species. Mummies from which a parasitoid did not emerge were dissected 15 days after the last adult emergence in the same cohort, and classified as dead parasitoids or diapausing prepupae (see Appendix S1 for more details and pictures of the dissections).

Statistical analyses

We considered both the number of diapausing individuals and the number of non-diapausing individuals, including dead ones, for each temporal replicate (i.e. each wheat microcage with 30 parasitized aphids at any given condition). First, a Generalized Linear Model (GLM) with a quasi-binomial error distribution (to account for overdispersion) was fitted to the data in order to assess differences in the proportion of individuals in diapause between the four species and treatments (i.e. photoperiod and temperature), including the interactions between these explanatory variables. Second, for each of the two species that had at least some individuals entering diapause, another GLM with quasi-binomial errors was run to assess diapause incidence differences among treatments (photoperiod, temperature and their interaction as explanatory variables). To assess for a potential effect of differential mortality rates among conditions, we re-ran the model after removing dead individuals in the dataset, thus only considering diapausing versus emerged parasitoids. We attempted to include the identity of the wheat pot as a random factor in our analysis, but this procedure consistently generated convergence errors in our generalized linear mixed models. Thus, our final analyses rest on the assumption that there was no temporal effect on diapause induction, which is probably justified because the experiments were all conducted within a few weeks (i.e. over the course of a maximum of three parasitoid generations). All statistical analyses were carried out using the R software (R Development Core Team 2015). The significance of each explanatory variable was tested with the 'Anova' function from the package car, using a F test for diapause quasibinomial data [START_REF] Fox | An R Companion to Applied Regression[END_REF].

Results

Meteorological data

From 1976 to 2015, the daily average temperature during the potential season of diapause induction increased by an average of 0.77 °C in fall and 1.13 °C in winter (Figure 1, Table 2). Furthermore, days with cold spell events during both fall and winter decreased in frequency since the 1970s, while the frequency of days with heat spell events more than doubled in the fall (Table 2).

Winter field sampling

As observed by [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF], aphids and their parasitoids are generally encountered at very low abundances in cereal fields in winter compared to spring. A total of 93 aphids and aphid mummies were collected. Sixteen aphids were unparasitized and a total of 77 mummies were formed, i.e. a parasitism rate of 83%, as defined by the total number of mummies (sampled mummies + aphids than turned into mummies) divided by the total number of individuals (mummies + unparasitized aphids). Among these mummies, 57 hatched within the few days after sampling (<7 days). Adult emergence was greatly delayed in 23% of the aphid mummies with 2 A. avenae, 7 A. ervi and 9 hyperparasitoids from three genera (Alloxyta sp., Asaphes sp., Phaenoghyphis sp.) emerging more than two months after sampling. These individuals were considered to be in diapause and represented 7%, 64% and 56% of the total number of mummies of their species or group of species, respectively. The 75 individuals were included in the quantitative food-web (Figure 2). The two remaining mummies contained unidentifiable dead individuals.

The aphid-primary parasitoid food web in winter 2014-2015 (Figure 2) was dominated by A. avenae and A. rhopalosiphi. Aphidius ervi and A. matricariae represented 15 and 5% of the total parasitoid abundance, respectively. The three hyperparasitoid genera mentioned above were also detected at high abundances (21% of the food-web total abundance), and for the first time in winter. Sitobion avenae and Metopolophium dirhodum (Walker) dominated the aphid community and Rhopalosiphum padi (L.) was present at a lower abundance.

Diapause expression in the laboratory

A total of 1,482 mummies were formed in laboratory tests. Overall, there was a significant difference in diapause incidence among species (GLM, df=3, F=149.1, p<0.001); there was no diapause observed in A. rhopalosiphi (n=312 mummies, 18 dead, 294 emerged) nor in A. matricariae (n=311 mummies, 40 dead, 271 emerged), regardless of temperature/photoperiod treatments, whereas diapause was observed in the two other parasitoid species, A. avenae and A. ervi, but at overall low levels of expression. The maximum diapause incidence was observed at 14 °C and 10:14 LD for both A. avenae (13.4 ±1.6 %) (Figure 3a) and A. ervi (11.2 ±4.9 %) (Figure 3b). There was no diapause observed at 14:10 LD for either species. Aphidius ervi diapause was never observed at 20 °C, i.e. under the more "summer-like" conditions. However, there was an interaction effect between species and temperature treatments (GLM, df=6, F=14.5, p<0.001), a marginally non-significant interaction effect between species and photoperiod treatments (GLM, df=6, F=2.1, p=0.06) and a significant three-way interaction effect between species, photoperiod and temperature (GLM, df=12, F=4.3, p<0.001), showing that parasitoid response to temperature and photoperiod treatments was species-specific. Responses of species showing diapausing were thus analyzed separately in different models. Photoperiod and temperature significantly influenced diapause induction in A. avenae and A. ervi (Table 3), with diapause levels increasing with a decrease in photoperiod and temperature. The interaction of these two factors, however, only influenced diapause incidence for A. ervi, suggesting that the influence of temperature on diapause varies with the photoperiod treatment (and reversely). When removing dead individuals from the analysis we found the same results, showing that they were not biased by parasitoid mortality.

Discussion

This study aimed to understand how recent species-specific changes in the overwintering strategies within a parasitoid guild were linked to the phenotypic expression of diapause.

Results obtained for A. avenae and A. ervi conform to the general pattern of insects from temperate areas relying on photoperiod and temperature stimuli to enter diapause, confirming our first hypothesis on diapause induction cues. However, we also revealed that only individuals from two out of four parasitoid species entered diapause under the conditions tested, and that diapause incidence was very low for both species that did enter diapause (<15%). This result confirms our second hypothesis regarding interspecific differences, as well as our third hypothesis about little diapause expression. By comparing current diapause levels to those recorded thirty years ago in Western France (Table 1, [START_REF] Krespi | Etude de la biocénose parasitaire des pucerons des céréales dans le bassin de Rennes : cas particulier d'Aphidius uzbekistanicus Luz[END_REF]) and by analyzing current diapause levels in other aphid parasitoid species in from more northern or southern areas [START_REF] Langer | Overwintering strategies and cold hardiness of two aphid parasitoid species (Hymenoptera: Braconidae: Aphidiinae)[END_REF][START_REF] Sigsgaard | A survey of aphids and aphid parasitoids in cereal fields in Denmark, and the parasitoids' role in biological control[END_REF][START_REF] Lumbierres | Seasonal parasitism of cereal aphids in a Mediterranean arable crop system[END_REF][START_REF] Gómez-Marco | Untangling the aphid-parasitoid food web in citrus: Can hyperparasitoids disrupt biological control?[END_REF] we argue that climate warming can trigger shifts in parasitoid diapause expression.

Winter field sampling

Field data show that most individuals within populations of the four primary parasitoid species were active in January. We provide first evidence that aphid hyperparasitoids have become active during the winter in cereal fields in Brittany and at a relatively high abundance (>20% of total parasitoid abundance). We also found some diapausing A. avenae and A. ervi, as well as some diapausing hyperparasitoids in the field, but no diapausing A. rhopalosiphi or A. matricariae, in line with our laboratory results on diapause incidence. In warmer climates in Spain (39 °N), [START_REF] Gómez-Marco | A sown grass cover enriched with wild forb plants improves the biological control of aphids in citrus[END_REF] showed that Aphis spiraecola was parasitized during winter by Aphididae parasitoids. [START_REF] Lumbierres | Seasonal parasitism of cereal aphids in a Mediterranean arable crop system[END_REF] also showed that winteractive aphids on cereal crops in Catalonia (41 °N) were parasitized by a diversity of aphid parasitoids, including A. rhopalosiphi, A. matricariae and A. ervi, suggesting that a part of the parasitoid population overwintered as active adults. At the opposite in colder climates such as Zealand (56 °N, Denmark), Aphidius spp. are absent of the fields before May since they cannot overwinter as active adults on their aphid hosts which are purely holocyclic (i.e. they produce diapausing eggs in winter) [START_REF] Sigsgaard | A survey of aphids and aphid parasitoids in cereal fields in Denmark, and the parasitoids' role in biological control[END_REF]. However, diapause incidence in the field may have been under-estimated by the sampling method we used [START_REF] Brodeur | Overwintering microhabitat selection by an endoparasitoid (Hymenoptera: Aphidiidae): induced phototactic and thigmokinetic responses in dying hosts[END_REF]. Indeed, some aphid parasitoids have the capacity to modify host behaviour prior to mummification and Brodeur and McNeil (1989b) showed that aphids containing parasitoid larvae destined to enter diapause frequently leave the host plant and mummify in concealed microhabitats where they become better protected against adverse climatic conditions. Moreover, we cannot exclude that A. ervi or A. avenae, the more generalist species in our study, did enter diapause at higher levels in populations exploiting different plant-aphid associations.

The host-parasitoid trophic web in winter 2014/15 showed a strong dominance of A. avenae, which represented more than 50% of the primary parasitoid relative abundance, as well as a dominance of S. avenae and M. dirhodum for the aphid community and also the presence of hyperparasitoids. In field studies conducted since 2011 in Western France, similar community compositions were encountered in spring or during mild winters, whereas cold winters were usually associated with the dominance of A. rhopalosiphi, A. matricariae parasitoids and R. padi aphids [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF][START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF][START_REF] Tougeron | Comparing thermal tolerance across contrasting landscapes: first steps towards understanding how landscape management could modify ectotherm thermal tolerance[END_REF]. This is in line with our meteorological measurements indicating that the average temperature in January 2015 was 6.1 °C. It could be considered as a mild winter since temperatures were higher than estimated minimal developmental threshold of Aphidius spp., which lays between 2.2 and 4.5 °C in species we studied [START_REF] Sigsgaard | The temperature-dependent duration of development and parasitism of three cereal aphid parasitoids, Aphidius ervi, A. rhopalosiphi, and Praon volucre[END_REF].

Diapause expression in the laboratory

Under laboratory conditions, diapause incidence was low in A. avenae and A. ervi, and no diapause was observed in A. rhopalosiphi and A. matricariae. In the former species, few individuals (<15%) entered in diapause, even when placed under conditions corresponding to late-November temperature and photoperiod in Brittany (14 °C, 10:14 LD), which are thresholds typically known to induce high levels of diapause in parasitoids from temperate regions with relatively cold winters. For instance, the Québec population of the parasitoid Aphidius nigripes (Ashmead) experiencing harsh winters started to gradually enter diapause in July and expressed 100% of diapause in early-September [START_REF] Brodeur | Seasonal Ecology of Aphidius nigripes (Hymenoptera: Aphidiidae), a parasitoid of Macrosiphum euphorbiae (Homoptera: Aphididae)[END_REF]. Differential resistance to cold temperatures may partly explain the interspecific differences in diapause levels. Indeed, A. avenae is almost 2 °C less cold tolerant than A. rhopalosiphi based on walking abilities after thermal stress (Le Lann et al. 2011a). These cold tolerance differences could suggest that a "risk-spreading" strategy is under balancing selection for species that are not cold tolerant enough to survive all types of winters.

Two hypotheses can explain the absence of diapause expression in A. matricariae and A. rhopalosiphi and partial diapause expression in A. ervi and A. avenae: (i) the photoperiod and temperature conditions we tested, although encompassing the conditions potentially encountered in Western France, are not suitable to reach the threshold that induces diapause. (ii) These species have genetically lost their capacity to enter diapause, whatever the conditions encountered by the parasitoids. Trait loss can occur through rapid evolutionary changes, within few years [START_REF] Thompson | Rapid evolution as an ecological process[END_REF][START_REF] Carroll | Evolution on ecological time-scales[END_REF] and it has previously been demonstrated that the diapause character can be genetically lost -or its expression reducedin parasitoids, when maintained in non-diapause rearing conditions (i.e. summer-like temperatures and hosts availability) within a small number of generations [START_REF] Danks | Insect Dormancy: An Ecological Perspective[END_REF]. For example, [START_REF] Gariepy | Why two species of parasitoids showed promise in the laboratory but failed to control the soybean aphid under field conditions[END_REF] showed that a strain of the parasitoid Binodoxys communis reared for 350 generations (≈ 7 years) in such conditions genetically lost its ability to enter diapause. Another example of such changes in the pattern of seasonal activity is the genetically-based shift towards shorter day-length thresholds for diapause induction in populations of the pitcher plant mosquito (Wyeomyia smithii) in North America over 30 years, due to climate warming [START_REF] Bradshaw | Genetic shift in photoperiodic response correlated with global warming[END_REF]. Our results clearly highlight that if climate gets warmer, diapause might no longer be expressed in A. avenae and A. ervi since, for any tested photoperiod, diapause incidence was significantly reduced when temperature increased.

Current diapause incidence in all four parasitoid species is now lower than the levels reported in the 1980s in the same area (Table 1). In the 1980s, A. rhopalosiphi and A. matricariae were active in the winter but between 24 and 29 % of the individuals entered diapause whereas the rest did not [START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF]. In contrast, we did not find any diapause induction for both species in the laboratory experiment. Moreover, A. avenae and A. ervi were never encountered as active adults or as non-diapausing prepupae within a mummy in cereal fields in winter until 2011, suggesting that they all entered in diapause before winter, even if their overwintering sites or overwintering hosts remained unspecified [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF][START_REF] Krespi | Etude de la biocénose parasitaire des pucerons des céréales dans le bassin de Rennes : cas particulier d'Aphidius uzbekistanicus Luz[END_REF][START_REF] Krespi | Variability in the development of cereal aphid parasitoids and hyperparasitoids in oceanic regions as a response to climate and abundance of hosts[END_REF]. In contrast, we found little diapause induction in both species in the laboratory experiments. The current marginal diapause incidence could be interpreted as a response to both continuing host availability throughout the winter season and/or increasing winter temperatures that could have modified diapause induction thresholds across the years. First, on cereal crops, anholocyclic hosts have been available throughout the winter and increased in abundance in Brittany, at least since the 1970s [START_REF] Rabasse | Overwintering of primary parasites and hyperparasites of cereal aphids in western France[END_REF]. Aphid density in winter has been shown to be higher in warmer years [START_REF] Andrade | Spatiotemporal variations in aphid-parasitoid relative abundance patterns and food webs in agricultural ecosystems[END_REF] and to increase with climate warming [START_REF] Zhou | Effects of temperature on aphid phenology[END_REF]. Second, we showed in this study that maximum winter temperatures have increased by about 1.4 °C, along with a 34% decrease in the frequency of winter cold spell events since the 1976-1985 period. This supports the hypothesis of a decrease in the selective pressures maintaining diapause over the past 30 years, allowing the maintenance of additional parasitoid species in winter. In addition, one would expect that in more northern or cold areas, diapause incidence might currently be similar to those of Western France (48 °N), 30 to 40 years ago. Almost all individuals from a Northern United-Kingdom A. ervi population (54.2 ° N) entered diapause when exposed to 15° C and LD 10:14 (Christiansen-Weniger and Hardie 1999). In A. rhopalosiphi and A. ervi populations from Belgium (50.3 °N), diapause expression was lowered at 40% on average at 15° C and LD 09:14 [START_REF] Langer | Overwintering strategies and cold hardiness of two aphid parasitoid species (Hymenoptera: Braconidae: Aphidiinae)[END_REF]. Latitudinal clines of diapause expression are known in some insect species (e.g. [START_REF] Dedryver | Coexistence in space and time of sexual and asexual populations of the cereal aphid Sitobion avenae[END_REF][START_REF] Winterhalter | Patterns Of Phenotypic And Genetic Variation For The Plasticity Of Diapause Incidence[END_REF][START_REF] Paolucci | Adaptive latitudinal cline of photoperiodic diapause induction in the parasitoid Nasonia vitripennis in Europe[END_REF] highlighting that variation in diapause expression across a latitudinal gradient is analogous to temporal changes in diapause levels at a given location, following climate warming.

In a climatic scenario where relatively warm winter conditions persist, the capacity to enter diapause might be maintained in species able to abridge diapause as a way to reduce its fitness costs [START_REF] Ellers | A trade-off between diapause duration and fitness in female parasitoids[END_REF][START_REF] Ito | Negative genetic correlation between diapause duration and fecundity after diapause in a spider mite[END_REF]. Alternatively, the cost of diapause may increase with climate warming (i) if there is a lack of ability to terminate diapause, especially for insect species in which a period of chilling is required to do so [START_REF] Tauber | Seasonal adaptations of insects[END_REF][START_REF] Mehrnejad | Diapause strategy in the parasitoid Psyllaephagus pistaciae[END_REF], and (ii) when mild or more variable winters induce energetic and metabolic costs in insects that are in diapause (e.g. [START_REF] Williams | Thermal Variability Increases the Impact of Autumnal Warming and Drives Metabolic Depression in an Overwintering Butterfly[END_REF], especially in species that cannot shorten their diapause duration or that are in a deep stage of dormancy. In these cases the capacity to delay or avert diapause may provide a selective advantage that could be maintained in insect populations [START_REF] Bale | Insect overwintering in a changing climate[END_REF], especially when winter environmental conditions allow winter activities, including reproduction. In any case, whether an observed change in overwintering strategies can be attributed to individual phenotypic plasticity or to local adaptation by genetic changes remains unknown and requires long term analyzes as well as further investigations on the cost and conditional expression of diapause. For instance, translocation experiments between parasitoid populations from harsh and mild winter areas and study of their diapause reaction norm may provide interesting insights on their capacity to deal with different climatic conditions.

Perspectives and conclusions

From an ecological services perspective, a loss of diapause in parasitoids could increase levels of aphid populations suppression, since parasitism in winter and early spring is crucial for effective natural biological control [START_REF] Langer | Seasonal activity and distribution of cereal aphid parasitoids in Belgium[END_REF][START_REF] Neuville | The delay in arrival of the parasitoid Diaeretiella rapae influences the efficiency of cabbage aphid biological control[END_REF]. However, if hyperparasitoids persist in winter as we showed here, this could have undesirable consequences for natural biological control of aphids in the following spring [START_REF] Gómez-Marco | Untangling the aphid-parasitoid food web in citrus: Can hyperparasitoids disrupt biological control?[END_REF]. Ultimately, modifications in insect phenology due to climate change -including diapause incidence and duration -could have important impacts on guild and community structure, which could in turn change species interactions and coexistence in food-webs [START_REF] Andrade | Impact of change in winter strategy of one parasitoid species on the diversity and function of a guild of parasitoids[END_REF], with unpredictable consequences on ecosystem services, such as naturally present biological pest control.

To conclude, field and laboratory data suggest that in Western France two aphid parasitoid species may have lost their capacity to enter diapause, whereas for two other species a small fraction of their populations entered diapause. The diapause expression is marginal, even under abiotic conditions corresponding to late-November. We also provide support to the idea that photoperiodic responses are liable to evolutionary changes and that a reduction or a loss of diapause expression can occur within a few decades in short-living organisms experiencing warmer winters. We predict that the loss of diapause will become a widespread response to climate change among arthropods.

Figure 1 :

 1 Figure 1: Average minimum and maximum daily temperatures from September 22 to March 20 calculated across two periods: 1975-1985 (solid lines) and 2010-2015 (dotted lines). The corresponding photoperiod (at 48 °N) is indicated for the 1 st day of each month.

Figure 2 :

 2 Figure 2: Quantitative food web showing the parasitoid and aphid community composition in winter 2014-2015 in cereal fields. Upper bars represent parasitoid of the genus Aphidius relative abundance. A. m. abbreviation stands for Aphidius matricariae. Percentages include diapausing and non-diapausing parasitoids, with lowerscript letter "d" indicating the proportion of individuals in diapause. Lower bars represent aphid relative abundance for each species. The thickness of the arrows between two bars is proportional to the relative number of trophic interactions between species (e.g. 64% of the parasitoids emerging from M. dirhodum mummies were A. avenae). The total number of aphid-parasitoids pairs represented is n=75.

Figure 3 :

 3 Figure 3: Prepupal diapause incidence (%) in Brittany populations of (a) Aphidius avenae (n=620, 85 dead, 513 emerged, 22 in diapause) and (b) Aphidius ervi, (n=239, 31 dead, 199 emerged, 9 in diapause) when parasitized aphids were reared under different photoperiodic (Light:Dark (hours): 10:14; 12:12; 14:10) and temperature conditions (14, 17 and 20 °C, blue, yellow and red), from left to right, respectively. The number of parasitoids tested is provided on the figure for each condition.

Table 1 :

 1 Summary of results on overwintering parasitoids in

Table 2 :

 2 Minimum

	Years

, average and maximum daily temperatures and mean frequency of days with cold (≤0 °C) and heat spells (≥22 °C) (± standard error of the mean) for fall (from 22nd September to 21st December) and winter (from 22nd December to 20th March) calculated across two periods: 1975-1985 and 2010-2015. Data were provided by Météo France.

Table 3 :

 3 Factors influencing diapause incidence of Brittany populations of Aphidius avenae and Aphidius ervi.

	Factor \ Species	Aphidius avenae			Aphidius ervi
		F	df	p > F		F	df	p > F
	Photoperiod	52.15	2	p<0.001	***	42.22	2	p<0.001	***
	Temperature	13.62	2	p<0.001	***	61.29	2	p<0.001	***
	Photoperiod x Temperature	1.87	4	p=0.14	NS	4.49	4	p<0.01	**
	Results from Generalized Linear Models (GLMs) with quasi-binomial errors are shown for both species.
	Significance of each term was assessed with iterative F-tests. *** p<0.001, ** p<0.01, NS=Not Significant.

Formerly named Aphidius picipes.

Formerly named Aphidius uzbekistaniscus. a Rabasse and Dedryver (1982); b Krespi et al. (1997).

Acknowledgments

This study was funded by the French Région Bretagne (grant ARED awarded to KT) and by the Canada Research Chair in Biological Control awarded to JB. All field and laboratory work conducted in this study comply with French and Canadian laws. All applicable institutional and/or national guidelines for the care and use of animals were followed. We thank the handling editor and one anonymous reviewer for their valued comments on an earlier version of this manuscript. We are grateful to Jimmy Debuire, Stéphanie Llopis, Valérie Briand and Josée Doyon for technical support and Paul K. Abram for English revision. The authors declare that they have no conflict of interest.

Author Contributions

This work is part of the Ph. D. thesis of the first author. All authors conceived and designed the experiments. KT performed the experiments and conducted field work. KT analyzed the data and wrote the manuscript. All co-authors substantially contributed to revisions.