Pénélope Plot
email: plotpenelope@gmail.com

Marine Boutillon

Preserving Biodiversity and Reindustrializing France: an Autopsy of the Problem from the Perspective of Accidental Pollution Risks

Industry pollutes. This simple observation necessarily poses a problem for territories that intend to conduct a reindustrialization policy and preserve their biodiversity. As part of an internal exploratory study, INERIS approached this issue from the angle of accident risks, with three questions: 1/ If the main process accident scenarios (explosions, fires, toxic clouds) are taken into account in term of human consequences, one may wonder whether are not under-assessed / not assess at all regarding pollution. 2/ Following the logic of French methodological rules to produce achieve safety case, the hierarchy of ecosystem importance is a key parameter in the calculation of acceptability of a potential accident. The issue remains on the establishment of such Environmental scale: which ecosystem should be placed at the bottom of the importance scale, so that it is more permissible to pollute? Who makes such decisions today? On the basis of what knowledge? Within the framework of what legislation and regulatory practices? And what should be the right method and tools? 3/ Are we really prepared to deal with accidental pollution like Lubrizol in 2019 (www.aria.developpementdurable.gouv.fr/le-barpi/la-base-de-donnees-aria/) from a biodiversity perspective? Don't we tend to focus on prevention and, protection of people, without really knowing what to do to avoid and limit impacts on the ecosystems? Through an approach that combined an analysis of the literature on these issues (methods and orientations, theoretical reflections, accidentology) and a series of 21 interviews with key actors in France, the authors question a solution that seems better than the others, based on the notion of absorptive capacity/resilience of ecosystems. This approach would remain to be implemented for terrestrial ecosystems. This article presents the main steps of the demonstration.

Introduction

Are the accidental pollution scenarios well studied? Are the ecosystems (environmental issues) well considered in these studies? And are the management practices for these ecosystems satisfactory with regard to the risks of accidental pollution? These three questions led to this article. They refer to field of risk management in France, which is regulated under the regime of classified environmental installations, the ICPE (aida.ineris.fr/liste_documents/1/18016/1), which include Seveso sites. These questions also refer to a literature on environmental ethics, where it is understood that each formulation, each notion, contains a vision of the world that pre-structure the way of posing problems and seeking solutions. Especially when it comes to defining the value of an ecosystem, as it is generally required in risk assessment approaches where decisions are justified on the basis of criticality calculations (that combine several dimensions, including the characterization of ecosystem importance). But, importance for whom? This is undoubtedly the key question, which in fact refers to the following question: what do we want to manage, why, and then how? The question "why" evokes the debate on anthropocentrism and biocentrism in environmental ethics [START_REF] Afeissa | Environmental ethics, nature, value, respect[END_REF]: do we want to protect ecosystems for anthropocentric reasons, that is because they are resources (aesthetic, spiritual, etc.), or do we want to protect them for themselves. And if we want to reconcile these two ends, which one would be the ultimate end, in pragmatic and ethical terms? The answer to the how depends on the why.

The multiplicity of names is an integral part of the problem: it is difficult to identify what we are talking about, what we are trying to protect. Are we talking about environmental stakes or biodiversity? Protected spaces or areas? Ecosystems? Natural environments? The diversity of terminologies reveals the difficulty of the work: we do not know how to characterize and define what we call "ecosystems" or "natural environments". This difficulty is based on metaphysical conceptions of the world, but it is also relative to the logics of division of reality (to the representations) that we adopt according to our objectives. Each term is a division, a way of apprehending what we call "nature", "the environment" with regard to which we lack knowledge, and criteria, foundations that would allow us to adopt a valid (realistic, coherent) division. In this research, we use the term "ecosystem" as it is generally understood in ecology (the whole formed by the biocenosis and the biotope, that is the living beings and their environment), we start from the assumption that it allows the broadest point of view to take into account the natural entities.

The reasoning that we propose to follow in this article is the following:

• There seems to be a hole in the French regulatory, an insufficient consideration of accidental pollution risks that is not compensated by voluntary practices. • The current solution, based on the categorization and prioritization of environmental stakes, seems to be an aporia.

• Only an approach based on the notion of absorption capacity seems to be a possible solution, but it presents several difficulties that would have to be overcome to implement it. • A necessary condition for the adoption of such an approach would be to adopt a territorialized approach.

Methodology

This article is the result of multi-actor survey. The panel was composed of engineers from a environmental safety institute, officers of the French administration, safety managers or engineers working in chemical, mechanical and food factories, territory officers, actors of environmental association and insurance providers. The panel distribution is as follow:

Engineers from a environmental safety institute

Actors of environmental association

Industrialists

Officers of the French administration

Territory officers

Insurance providers 5 5 4 2 2 3 The scale of the panel is relatively limited so the quantified results which are presented in this paper have to be understood only as tendency. The present paper attempt to display an overview of high quality of interviews. Along all the discussions, we have selected ideas that seem to build consensus or ideas that retain our attention because they make sense regarding our searching framework. This "exploratory" work, initiated under an engineer approach, has benefited from a philosophical lightening on the on environmental ethics.

A hole in the regulatory

"Having looked at the hazard and impact studies, I always thought there was a hole in the racket. Impact study is totally disconnected from the hazard study, it looks at the impact that the plant will have in normal operation, given the discharge authorizations that have given. We are in the chronicle. But, in the event of a major accident, what is the impact on the environment? The hazard study is not interested in this because we are interested in the deaths, the injuries and the damage to the equipment. We have a real hole in the racket." (Actor of an association). This observation is shared by 95% of the people interviewed (20 persons overs 21). To be more precise, in France, the accidental risk assessment of a Seveso site (or site where major accident can occur) is performed through the so-called "Etude de Dangers" (safety case). It is the central piece of the management system for major accident scenarios (Kontogiannis et al., 2017). Schematically, this study distinguishes two phases of analysis. The first one, the preliminary risk analysis, is qualitative, it is used to scan widely in order to identify, normally, all accident scenarios. The second phase, the detailed risk analysis, is more quantitative (Omega 9, INERIS, 2015). It studies in detail the intensity of the selected dangerous phenomena, their severity and then their probability. Their acceptability is determine using the risk matrix (figure 1). If it is necessary to reduce the risk level, safety barriers can be added. The problem is that scenarios leading to pollution are only retain for the detailed analysis if they also cause damage on humans. Other scenario which "only" cause pollution are not analyzed in detail, and therefore are not properly managed. "We are not interested (especially in the hazard study) in the ecosystem, around the industrial site, we surely miss some effects. [...] The assessment is only made in relation to the effects on human beings. It is true that at present the quantification of the severity (intensity) of major accidents does not take into account the environmental component. This may change following the latest incident at the Lubrizol plant.

We are going to evaluate more things related to post-accident, the deferred impact of major accidents, which will require a qualification of the environmental impact, particularly in terms of crops and potential fallout on the food chain." (Engineer from a environmental safety institute). It is possible to identify other shortcomings, beyond this lack of detailed analysis of accidental pollution phenomena:

• In the preliminary risk analysis phase itself, in the process of selecting the initiating events, there is a series of regulatory exclusions (Circular of May 10, 2010). Moreover, knowing that the role of this phase is to prepare the second one, the effort to be truly systematic and exhaustive will tend to focus on the causes that may lead to the hazardous phenomena to be analyzed in detail. This may lead to the exclusion or, let's say, the minimization of the probability of certain accidents, especially those that may have environmental consequences. • Some hazard potentials will not even be studied if they cannot generate fire, explosion or toxicity phenomena likely to impact human beings outside the sites. However, they can be sources of accidental pollution. This is the case of fire extinguishing water. This water can be discharged into rivers for example. There are also cases not always treated thoroughly of waste that can be deposited on the ground. The transport of hazardous substances (on site and outside) can also lead to accidental discharges that are poorly analysed. • Some natural hazards, that can aggravate certain accidental pollution, are sometimes poorly or not considered. This is typically the case of flooding. The flood will increase the extent of the pollution because the associated equipment retention facilities will not be able to function because they will be flooded. Thus, the very presence of the natural cause (of the flood) aggravates the potential consequences of a loss of containment which, without the flood, would only be local. In this type of event, the consequences can go much further. Not to mention certain hydrocarbon-type product releases with lower densities: the spread of the same slick over the water will be greater than if the product had been spread over the ground, with much larger surfaces of pollutants. • We can mention the difficulty of considering the cumulative effects of accidental pollution on a territory.

We do not do for pollution risks what we do for land use planning where there is a notion of accumulation based on the distance of effects and the associated probability levels, the level of hazard being defined in relation to the accumulation of probabilities for the same intensity or the same danger zone, we will have a global and cumulative representation of the risks on the same territory but in relation to the same issue (which is human).

The aporia of a solution based on the categorization and prioritization of ecosystems

"It's kind of like saying, 'for this ecosystem okay, there's only three species so you can go, but this one's more valuable so you have to be more careful'" (Industrial operator).

Risk management is based on acceptability criteria which combines occurrence and the severity of accidental scenarios. Risks are considered acceptable when severe accident scenarios are sufficiently unlikely or when the severity of a probable accident is very low (Circular of May 10, 2010). This approach implies means of estimating the severity of damage, which is a function of the importance attached to the target. Transposing this way of thinking to ecosystems implies being able to categorize them in terms of importance in order to prioritize them: there must be the most important ones and the least important ones, those that absolutely must not be polluted and those that could be more important. The majority of the engineers (89%) think that it must be possible to find criteria to do this, that's mean to define environmental importance scores, which, combined with substance hazard scores, would make it possible to calculate severity scores for possible/probable accident scenarios, and thus to judge their acceptability. Therefore, it should be possible to answer the following questions: Is it more serious to pollute and thus destroy the fauna and flora of a wild river or of a national park? Are the blue frames more important than the green frames, or than the zones of ecological interest (ZNIEFF) of type 1 or type 2 or 3? And then, do the decrees of protection of biotope or geotope allow to circumscribe even more important spaces that they would be all the more serious to pollute? And what about wooded areas, sensitive natural areas, UNESCO world geoparks, national parks, integral reserves or adhesion zones, regional natural parks, biogenetic reserves, etc.? For local government stakeholders, this way of thinking seems impossible to apply. They have difficulty identifying the different ecosystems in their territory. In addition, they have difficulty understanding them, delimiting them, and identifying their dynamics. Finally, and above all, they wonder what criteria should be used to rank the importance of environmental issues. "A hedge, for example, has several functions. What is the priority? Wood energy (bioenergy valorization)? Hydraulics (mudflows -runoff management -mudflows in bays / watersheds -reduction of inputs and therefore preservation of water resources -flooding (but limited effectiveness), green and blue fabric)? Valuation of biodiversity? Carbon sequestration? … How to decide? Perhaps it is up to the communities of communes to freely (arbitrarily?) define their stakes, then their priorities." (Territory officers).

The difficulty is to find solid criteria. Let's reflect on the concepts of species and protected areas.

• The concept of protected species. The difficulty is that there are a lot of species, like earthworms that are not protected, but that are really needed. The lists of protected species are partial. And this approach does not allow to apprehend the interdependence of ecosystems. The notion of protected species allows us to point out an existing problem, the rarefaction of a species, but it is not a tool for managing problems for the future. • The concept of protected spaces. Let's take the classification proposed by the IUCN (International Union for Conservation of Nature). The IUCN defines a "protected area" as "a clearly defined geographical space, recognized, dedicated and managed, by any effective legal or other means, to ensure the longterm conservation of nature and its associated ecosystem services and cultural values" (IUCN, French protected areas, 2010). However, if we look at the respective definitions of each protected area, we can see that the aspects of cultural, economic or historical value totally predominate over the ecological value of these spaces (conservation of nature and ecosystem services). There is a risk that only "hand-picked" ecosystems will be considered, since they are selected for cultural and economic purposes, while other natural environments that have no such interest would be overlooked, or their importance would be diminished. Moreover, the notion of protected space or protected area suggests this problem: while there are "protected spaces," other natural spaces are not protected, which does not mean that they are not vulnerable. The notion of protected areas is meaningless if all areas are to be protected. This conflicts with the awareness of the problem of the erosion of biodiversity and global warming which are widespread. And then, what about the constant changes in ecosystems (species migration in particular), accentuated because of the climate crisis? Are these variants satisfactorily considered by the protected area categories defined in 1994? As the ecosystems are strongly affected by climate change, it is a question of protecting them, but also of anticipating their evolutions, and even using them as protection, for example against certain risks related to climate change, such as soil erosion. This is the perspective of "Climpact Data Science" members (www.criseclimatique.com/nous.html). It consists in integrates the potential impact of climate change in order to select the best strategy for nature-based solutions implementation and management for 2050 by the use of the IPCC (Intergovernmental Panel on Climate Change) climate change scenarios and at a Very High Spatial Resolution, which can go up to 5 meters [START_REF] Mendoza | Geoprospective approach for biodiversity conservation taking into account human activities and global warming[END_REF][START_REF] Mtes | Ministry of Ecological Transition and Solidarity, Technical guide for public territorial establishments of basin and public establishments for the development and management of water[END_REF][START_REF] Kontogiannis | Total safety management: principles, processes and methods[END_REF], Hinojos Mendoza and Garbolino, 2020).

An absorptive capacity approach

"An industrialist must not pollute in any way. He can release dangerous substances, but the doses must be assimilable by the environment. Pollution is doses that cannot be assimilated." (Industrial operator). Criticality could be related to the calculation of the "assimilation capacity" of such and such quantities of such and such foreign substances by such and such environment/ecosystem. Here, the estimation of severity would be built on the concept of ecosystem resilience. Note that this vision is not new or recent. It appears in the declaration of the United Nations Conference on the Human Environment, at Stockholm (Principle 6, 1972), which says "The discharge of toxic substances or of other substances and the release of heat, in such quantities or concentrations as to exceed the capacity of the environment to render them harmless, must be halted in order to ensure that serious or irreversible damage is not inflicted upon ecosystems." This approach implies a monitoring of the pollution which crosses at the same time: the monitoring of the ecosystems initial states and the monitoring of the substances managed by the industrialists of the territory concerned. This starts with an inventory of the pollution already present in the ecosystems. This would be like adopting the water approach for terrestrial ecosystems. The Water Framework Directive (2000) concerns the good ecological status of water bodies, a European directive whose objective was to achieve a good ecological status of water bodies by a certain deadline. For example, the biological indicator for environmental bio-assessment gives an idea of the species present on a site and of the quality, of the good state of the site: if there are only pollutant-resistant species, the site will be classified as highly impacted, but if there is a large diversity of fish, fish of the 1st category, the site will have a good score. There is a scientific follow-up of the species in the environment. With the Law on Water and Aquatic Environments, the latest regulatory evolution, there are even more interpretation keys on the biological monitoring of water bodies.

And the analysis of correlations with industrial activity and hazardous substances is important. For example, it is possible to trace the observed effect on the environment back to the substance or family of substances involved. It is very complicated, the quantity of substances that can be emitted into the environment and the nature of human activities are so large! But there is still a possibility, and important margins of progress.

Integrating biological tools into the monitoring of water bodies seems unavoidable in the years to come in order to be able to detect new substances arriving in the environment at a sufficiently early stage and for which the regulations are not yet ready.

Major difficulties and proposals

This approach seems the most pragmatic and efficient. But its implementation would pose many difficulties.

• This approach implies first of all improving the knowledge of ecosystems. There is a tremendous work to do, as the environmental knowledge are very low, according to 86% of the interviewed (the insurer did not respond, the industrialists and the members of the risk institute were mitigated 50/50). There is also a lack on research and studies on the characterization of the state and functioning of socio-ecosystems, allowing us to characterize an exceptional event, pollution or industrial accident. There is a particular lack of knowledge about aerial ecosystems. • There are gaps in knowledge about the substances, according to all the interviewed (except from the insurers who do not adjudicate).

o When you replace one substance, such as bisphenol A, with two other types of substances, bisphenol, which are just less known. What are the effects? Are they worse or better? The fact of banning a substance generates changes in production or new habits that will make new substances emerge that are not known. These new uses deserve to be looked at from an environmental point of view, and sometimes we do not have the necessary hindsight to say whether the substance is or is not dangerous for the environment. And there are so many substances! And there are no regulatory requirements on certain substances, such as emerging substances, or endocrine disruptors, etc. o There are also issues that are not understood, such as the effect of mixtures, the effect of new dangerous substances (micro plastics, etc.). o The problem of molecules vs substances. In France and in Europe, we have a marketing authorization system for products, not for molecules. This means that you can have molecules that are prohibited in some products but authorized in others. You may find yourself with certain products that are banned in conventional agriculture but that you find in products that you use at home, such as insecticides, lindanes. • There are organizational obstacles.

o The compartmentalization of expertise and institutions is an acute problem for the absorptive capacity approach, insofar as it deals with systems whose analysis implies bringing together several disciplines. "It is one of the major problems that makes that it is not sufficiently treated in France.

There are ecologists who deal with the life of batrachians, acologists who deal with the health of domestic plants, wheat and the risk of the nielle on wheat, veterinarians who deal with the health of cattle and pigs in farms and doctors who deal with human health and only that. On the other side, you have Eco toxicologists, and then on the other side, the world of industry, the inspectors of classified installations, etc. There is a compartmentalization of public establishments in France too. It often seems difficult to set up interministerial, interdisciplinary and intersectoral approaches, but this is what is at stake if we rely on the criterion of the capacity of ecosystems to absorb pollution" (Actor of an association). Regarding these difficulties, actors with a view on the subject (actors of association and officers of the French administration), strongly suggest to adopt a territorialized approach: "This brings me to the importance of a territorial approach." (Actor of an association). o According to some experts, it would be at the level of the EPCI (Public Establishment of Intermunicipal Cooperation) that the competence of monitoring pollution of ecosystems should be entrusted. Because the EPCIs have the management of aquatic environments and flood prevention competence [START_REF] Mtes | Ministry of Ecological Transition and Solidarity, Technical guide for public territorial establishments of basin and public establishments for the development and management of water[END_REF]. It reveals that the integration of a "geo" dimension complicates things considerably [START_REF] Latour | Inventing a geopolitics of nature: "Ecological issues break down the notion of space[END_REF].

Conclusion

The questions we sought to answer through our survey were the following: Are the accidental pollution scenarios well studied? Are the ecosystems (environmental issues) well considered in these studies? And are the management practices for these ecosystems satisfactory with regard to the risks of accidental pollution?

The answer to the first question is negative: in reality, the pollution scenarios are not studied to the end when they do not affect human issues. This first result has modified the rest of our research. Ecosystems are therefore not taken into account in hazard studies. But there are engineering methods that try to compensate for this lack. It is the internal logic of these methods that we focused on. These methods follow a common logic: the approach of categorizing environmental issues, based on the concepts of protected areas and their prioritization by IUCN. We have argued that this approach is an aporia because, in the context of the current global environmental crisis, the notion of protected areas appears meaningless, even counterproductive, for calculating the severity of a potential industrial accident. Moreover, this approach seems difficult to implement in practice and therefore ineffective. On the other hand, some actors have underlined the relevance of an approach based on absorption capacity, which already exists for the management of aquatic ecosystems only (for which the Water Framework Directive is the regulatory framework). It consists in basing itself on the notion of ecosystem resilience to calculate the severity of an industrial accident, and therefore it does not fall into the same dead ends as the first approach. We have identified major obstacles to its implementation for all ecosystems: the lack of knowledge of ecosystems and substances, and the compartmentalization of fields of expertise and institutions. The actors who have an opinion on the subject put forward the importance and the necessity of adopting a territorialized approach.

  Figure 1. Risk matrix allowing to determine the acceptability or not of an accidental scenario (Circular of[START_REF] Afeissa | Environmental ethics, nature, value, respect[END_REF] decree of September 29, 2005)

	Severity of consequences						Probability
								E	D	(very	C	B	A
	Level	Area	Area		Area defined	(event	improbable	(improbable	(probable	(casual
		defined by	defined by	by	the	possible but	event)	event)	event)	event)
		the	the	lethal	significant		highly
		significant	effect		irreversible		improbable)
		lethal effect	thresholds	during	a
		thresholds			human life
					effect
					thresholds
	Disastrous	More than	More than	More than
		10 persons	100		1000
		exposed	persons	persons
			exposed	exposed
	Catastrophic	Less than	Between 10	Between
		10 persons	and	100	100	and
		exposed	persons	1000
			exposed	persons
					exposed
	Important	Maximum 1	Between 1	Between 10
		persons	and	10	and	100
		exposed	persons	persons
			exposed	exposed
	Serious	No one	Maximum 1	Maximum
			person	10	person
			exposed	exposed
	Low	Contained	witin	the	Less than 1
		establishment			person
					exposed

: Unacceptable risk : Risk which can be acceptable after being reduce thanks to safety barriers : Acceptable risk


Sandra Romain

Claire Lemaitre
email: claire.lemaitre@inria.fr

SVJedi-graph: genotyping close and overlapping structural variants with a variation graph and long-reads

Structural variants (SVs) are genomic segments of more than 50 bp that have been rearranged in the genome. The advent of long-read sequencing technologies has increased and enhanced their study, and a great number of SVs has already been discovered in many species. Complementary to their discovery, the genotyping of known SVs in newly sequenced individuals is of particular interest for several applications such as trait association and clinical diagnosis. Due to SVs' large size range (up to a few megabases), long-reads are more suited for their study than short-reads. As such, our team previously released SVJedi [1], one of the first SV genotypers using long-read data. SVJedi's method of representing independently both SV's allelic sequences reduced reference bias in genotyping and showed improved genotyping performances. However, the method failed to genotype closely located or overlapping SVs due to redundancy in representative allelic sequences.

To overcome this limitation, we present SVJedi-graph, a long-read SV genotyper based on a variation graph to represent SV alleles. The use of sequence graphs to represent SVs for genotyping is fairly recent [START_REF] Garrison | Variation graph toolkit improves read mapping by representing genetic variation in the reference[END_REF][START_REF] Chen | Paragraph: a graph-based structural variant genotyper for short-read sequence data[END_REF][START_REF] Eggertsson | GraphTyper2 enables population-scale genotyping of structural variation using pangenome graphs[END_REF][START_REF] Hickey | Genotyping structural variants in pangenome graphs using the vg toolkit[END_REF], but existing methods are restricted to short-read data, and SVJedi-graph is the first graph-based SV genotyper using long-reads. In our method, we build the variation graph from a reference genome and a given set of SVs. The genome sequence is split in fragments at each SV's start and end positions, and each fragment becomes a node in the graph. Edges are added between nodes to indicate reference and alternative paths for each SV, and additional nodes are added for insertions. Then, the long reads are mapped on the variation graph using GraphAligner [START_REF] Rautiainen | GraphAligner: rapid and versatile sequence-to-graph alignment[END_REF] and the resulting alignments are filtered on their quality and mapping localization. Finally, the most likely genotype for each SV is predicted from the ratio between the number of reads supporting each allele.

SVJedi-graph can genotype four SV types as of now, namely deletions, insertions, inversions and translocations. Running SVJedi-graph on simulated sets of deletions showed that the use of a variation graph was able to restore the genotyping quality on close and overlapping SVs. For instance, with a simulated set of deletions that had another close deletion 0 to 50 bp apart, we obtained a genotyping rate (proportion of SVs with a predicted genotype) of 99.9% and an accuracy (proportion of accurate genotype predicted among all predicted genotypes) of 99.0%, compared to a genotyping rate of 78.9% and an accuracy of 97.3% with SVJedi on the same dataset. We also tested our method on the real gold standard dataset of Genome In A Bottle (human individual HG002), and were able to obtain a higher genotyping rate than SVJedi on the same data (97.4% against 90.2%), with a similar or slightly better accuracy (92.9% against 92.2%). SVJedi-graph is distributed under an AGPL license and available on GitHub at https://github.com/SandraLouise/SVJedi-graph.


Ph.D Philippe Sarrazin
email: philippe.sarrazin@ujf-grenoble.fr

Handballers

Dropout in Female

Keywords: Dropout, Sport, Social Exchange Model, Commitment, Motivation Dropout in Female Handballers

. Participants were 253 French handball players between the ages of 14 and 16 years. A first set of analyses, focused on the differences, showed that dropout players perceived themselves as significantly less competent, less autonomous, less related to their team, lower in progress and less supported by their coach than persistent players. The second set of analyses with SEM revealed that the commitment level was positively associated with perceived benefits and negatively with social constraints and alternatives opportunities.

Finally, a lack of commitment led to dropping out of the sport 8-months later.

RÉSUMÉ

Deux études complémentaires destinée à mieux comprendre le phénomène de l'abandon chez des handballeuses françaises à partir des postulats de la théorie de l'échange social [START_REF] Thibaut | The social psychology of groups[END_REF][START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF], ont été conduites. La première étude s'est intéressée aux sources du plaisir lié à la pratique sportive. Nous avons postulé que l'analyse coûts/bénéfices correspondait à une estimation d'atteindre les motifs les plus importants de pratique (e.g., apprendre et progresser, avoir des amis, être meilleur que les autres). Les sujets étaient 488 handballeuses françaises âgées de 15 à 19 ans. Les résultats d'analyses par équations structurelles (AES) ont révélé que le plaisir en handball était prédit par une variable latente (dénommée "bénéfices perçus" dans l'activité) sous jacente aux perceptions de compétence, d'autonomie, d'affiliation, de progrès, du soutien de l'entraîneur, et du temps de jeu moyen en match. Dans la deuxième étude, nous avons testé un modèle de l'engagement sportif basé sur les postulats de la théorie de l'échange social, en utilisant des AES et un suivi longitudinal de 8 mois. Au regard, des résultats de la première étude, nous avons remplacé le construit de plaisir par celui des bénéfices perçus. Cette analyse permet une compréhension plus complète des notions de coûts et de bénéfices développées dans la théorie de l'échange social [START_REF] Thibaut | The social psychology of groups[END_REF]. Les participants étaient 253 joueuses âgées de 14 à 16 ans. Les résultats ont montré que les joueuses qui avaient abandonné se percevaient moins compétentes, moins autonomes, moins liées à leur équipe, moins en progrès et moins encouragées par leur entraîneur que les joueuses persistantes.

De plus, l'AES a révélé que le niveau d'engagement était associé positivement aux bénéfices perçus, et négativement aux contraintes sociales et aux activités alternatives. En retour, un faible niveau d'engagement prédisait un taux élevé d'abandon 8 mois plus tard.

Mots-clés : Abandon / Sport / Modèle de l'échange social / Engagement / Motivation Dropout in Female Handballers Predicting persistence or withdrawal in female handballers with Social Exchange Theory What factors influence the degree of athletes' investment in their physical activity? Why do some people develop a strong commitment to continue their sport activity, while others fail to do so and quit their sport? Most psychology or sociology research on sport motivation has sought to answer these questions. These studies have sought to understand the paradox which exists between on the one hand a massive passion for sports, and on the other hand high levels of dropout which occurs during adolescence, particularly for girls [START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Russell | Youth sport in New Zealand[END_REF][START_REF] Sallis | Physical activity guidelines for adolescents : A consensus statement[END_REF][START_REF] Wankel | Canada[END_REF]. In a study of French female handball players, 50% dropped-out between 13 and 15 years of age after two or three years of practice [START_REF] Guillet | Utiliser l'analyse de survie pour déterminer les moments et les taux d'abandon de la pratique sportive: l'exemple du handball féminin[END_REF]. Even if some of these teenagers were to return to handball after discontinuing their initial involvement, this phenomenon has alarmed the French Handball federation administrators who view player retention as a key goal. Youth sport researchers, administrators and health professionals have become increasingly concerned with identifying the determinants of continued sport activity (see [START_REF] Martinsen | Exercise and mental health in clinical and freeliving populations[END_REF].

Different motivational theories can be used to study dropout and sport commitment (see [START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Guillet | L'abandon sportif, de l'approche descriptive aux modèles interactionnistes. [Sport dropout, to descriptive approach to interactive models[END_REF]Sarrazin & Guillet, in press;[START_REF] Weiss | Motivational orientations in Sport[END_REF], for reviews). However, one theoretical approach that seems particularly well suited to study the psychological processes underlying continued involvement and dropout in sport is based on Social Exchange Theory [START_REF] Homans | Social behavior: It's elementary forms[END_REF], particularly Interdependence Theory [START_REF] Kelley | Love and commitment[END_REF][START_REF] Kelley | Interpersonal relations: A theory of interdependence[END_REF][START_REF] Thibaut | The social psychology of groups[END_REF]) and Rusbult's Investment Model of Commitment (1980, 1983). Many youth sport researchers have employed this Social Exchange framework to explain sport commitment and/or withdrawal (e.g., [START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF][START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Johns | Understanding attrition in female competitive gymnastics: Applying social exchange theory[END_REF]Scanlan, Carpenter, Lobel, & Simons, 1993;Scanlan, Carpenter, Schmidt, Simons, & Keeler, 1993;Scanlan, Simons, Carpenter, Schmidt, & Keeler, 1993;[START_REF] Schmidt | Sport commitment: A model integrating enjoyment, dropout, and burnout[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF].

Generally, these researchers have employed the construct of commitment to describe a set of factors that explain persistence to a course of action or a relationship -even in the face of adversity (e.g., [START_REF] Becker | Notes on the concept of commitment[END_REF][START_REF] Brickman | Commitment[END_REF][START_REF] Kelley | Love and commitment[END_REF][START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF]. Commitment is a term that signifies the motivational force behind persistence. It is generally defined as an individual's intent to stick with an activity or a relationship and to feel psychologically "attached" to it [START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF]. In the sport domain, Scanlan, Carpenter, Schmidt, et al. defined commitment as a "psychological construct representing the desire and resolve to continue sport participation" (1993, p.6). In short, commitment represents individuals' psychological state of attachment to their participation or a motivational force for continued involvement. This construct must clearly be distinguished from its antecedents and consequences [START_REF] Kelley | Love and commitment[END_REF]. Its consequences can be actual behavior, like persistence to a relationship (e.g., [START_REF] Bui | Testing the rusbult model of relationship commitment and stability in 15-year study of heterosexual couples[END_REF][START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF][START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF][START_REF] Duffy | Satisfaction and commitment in homosexual and heterosexual relationships[END_REF][START_REF] Sprecher | Investment model, equity and social support determinants of relationship commitment[END_REF], job turnover (e.g., [START_REF] Rusbult | A longitudinal test of the investment model: The impact of job satisfaction, job commitment, and turnover of variations in rewards, costs, alternatives and investments[END_REF] or sport dropout. Three major classes of what [START_REF] Kelley | Love and commitment[END_REF] labels "causal conditions" (or antecedent) for commitment can be identified. The first class identifies the extent to which the relationship is viewed as attractive, for example, in terms of love, liking, satisfaction or enjoyment. The second class of causal conditions reflects the degree to which alternatives to the current commitment are viewed as more or less attractive, and the final class considers the restraining forces or barriers to termination (i.e., personal investments and social constraints -see Figure 1).

Insert figure 1 here

In their social exchange model, [START_REF] Thibaut | The social psychology of groups[END_REF] begin with the assumption that human behavior is governed primarily by the desire to maximize positive experiences and to minimize negative ones. From this perspective, people participate in relationships and activities only so long as the outcomes of participation are sufficiently favorable. Favorability is determined by the balance between rewards and costs with rewards and costs viewed as generic terms referring to a variety of potential consequences. In the majority of models, the cost/benefits analysis is expressed by an "attractive" variable, like satisfaction (e.g., [START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF][START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF] or enjoyment (e.g., Scanlan, Carpenter, Schmidt, et al., 1993), that summarizes the individual's affective experience for an activity or a relationship. Individuals should be satisfied (or enjoyed) with their relationship or activity when the benefits outweigh the costs, and dissatisfaction occurs when costs outweigh benefits. In turn, greater satisfaction or enjoyment is expected to be related to greater commitment (see Figure 1).

According to [START_REF] Thibaut | The social psychology of groups[END_REF], the decision to remain in a relationship or activity is not based solely on the balance between rewards and costs. The decision to persist or to drop out also depends on the availability and attractiveness of the alternatives. Consequently, someone may choose to stay involved in sport even if costs are exceeded by rewards because no alternative opportunities are available. Similarly, an athlete who perceives that the rewards outweigh costs in a program may discontinue involvement because a more desirable alternative activity is available. Moreover, in six of the nine studies on athletic dropouts reviewed by [START_REF] Gould | Future directions in youth sports participation research[END_REF], "conflict of interest" or the desire to participate in different activities (including different sports) was found to be a prominent reason for dropping out of a sport.

A third class of causal conditions for commitment considers the "forces or barriers" which are supposed to retain the individual in the activity [START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF][START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF]. Several forces have been examined by researchers although two constructs have frequently been used: personal investments and social constraints. In the sport domain, personal investments reflect personal resources such as time, effort and money that individuals put directly into their involvement and which cannot be recovered if they leave (Scanlan, Carpenter, Schmidt, et al., 1993). It is hypothesized that greater personal investments will promote greater sport commitment.

Nevertheless, the relative importance of these resources may vary by sport. For example, in contrast to elite figure skating or horse-riding in which financial demands can be high, the investment of money required for recreational sport programs is typically low.

Social constraints addresses the sense of social pressure to participate, such as feeling one has to stay to please various significant others (e.g., [START_REF] Becker | Notes on the concept of commitment[END_REF][START_REF] Kelley | Love and commitment[END_REF]Scanlan, Carpenter, Schmidt, et al., 1993;[START_REF] Sprecher | Investment model, equity and social support determinants of relationship commitment[END_REF]. In the sport domain significant others have included parents, friends, head-coach and to other people in general (Scanlan, Carpenter, Schmidt, et al., 1993). It was hypothesized that greater pressure from others to stay involved would increase commitment as this pressure is a consequence of the negative sanctions a person feels would be experienced at the hands of important others if he or she were to leave [START_REF] Becker | Notes on the concept of commitment[END_REF][START_REF] Kelley | Love and commitment[END_REF][START_REF] Sprecher | Investment model, equity and social support determinants of relationship commitment[END_REF].

The Social Exchange paradigm has been applied to dating couples (e.g., [START_REF] Bui | Testing the rusbult model of relationship commitment and stability in 15-year study of heterosexual couples[END_REF][START_REF] Duffy | Satisfaction and commitment in homosexual and heterosexual relationships[END_REF][START_REF] Sprecher | Investment model, equity and social support determinants of relationship commitment[END_REF], friendships [START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF]), organizations (e.g., Farrell & Rusbult, 1981), and work [START_REF] Rusbult | A longitudinal test of the investment model: The impact of job satisfaction, job commitment, and turnover of variations in rewards, costs, alternatives and investments[END_REF]) and found to be effective in predicting commitment and distinguishing between individuals who stay in a relationship or job and those who leave. In general, greater commitment is associated with higher satisfaction, less attractive alternatives, and greater investments. To date, to our knowledge three studies have tested sport commitment within the broader social exchange paradigm (Scanlan, Carpenter, Schmidt, et al., 1993;[START_REF] Carpenter | A test of the Sport Commitment Model using structural equation modeling[END_REF][START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF]. In general, in these studies, sport Dropout in Female Handballers enjoyment was the dominant predictor of commitment (β = .22 to .61) along with personal investments (β = .19 to .36) and to a lesser extent social constraints (β =-.07).

These studies have helped test and develop the sport commitment construct. However, several aspects of the model require greater elaboration. First, the costs/benefits analysis is always expressed by a global rating of positive affect, like enjoyment (e.g., Scanlan, Carpenter, Schmidt, et al., 1993), that summarizes the individual's affective experience for an activity or relationship. It is assumed that in rating attractiveness individuals perform the cost/benefit analysis, although no assessment is made of the actual costs and benefits. While sport enjoyment has been found to be a major determinant of commitment, a global rating provides little insight into the actual sources of enjoyment to allow practical information to be gleaned to help coaches.

Second, one of the major limits of these studies is that they stopped with athlete desire and resolve to continue sport participation. As noted by [START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF], all research to date has focused solely on the antecedents of commitment. Future research needs to explore the consequences of commitment, that is, the actual behavior of persistence or dropout.

The present research

The main goal of this research was to understand dropout in French female handballers using Social Exchange Theory postulates. To this end, two complementary studies were carried out. In the first study, the aim was to more fully explore the sources of enjoyment by emphasizing the key variables in the costs/benefits analysis. The second study tested the model presented in This study examined the sources of enjoyment by highlighting the variables which take place in the costs/benefits analysis. As was pointed out above, attraction for, or favorability of sport involvement rests on the balance between rewards and costs. In the sport domain, rewards may involve tangible consequences such as medals, diplomas and other trophies, even sometimes money. But they are also psychological such as the achievement of desired goals, and selfadministered in the form of self-approval consequent to success in meeting internal standards of performance [START_REF] Bandura | Self-efficacy: Toward a unifying theory of behavioral change[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF]. Studies of participation motivation provide information on the goals or motives young people have for participating in sport. This work has shown that young people are attracted to sport by a variety of reasons including skill improvement and mastery, fun (e.g., the excitement of competition), increased physical fitness (e.g., be physically active, get in shape), affiliation with others (e.g., make friends, be part of a team), feelings of competence (e.g., be better than the others), and recognition and approval from significant others [START_REF] Gill | Participation motivation in youth sports[END_REF][START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Gould | Motives for participating in competitive youth swimming[END_REF][START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF][START_REF] Ryckman | Male and Female Adolescents' motives related to involvement in organized team sports[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF][START_REF] Wankel | Factors underlying enjoyment of youth sports: sport and age group comparisons[END_REF][START_REF] Weiss | Children's motivation for participation in and withdrawal from sport: Identifying the missing links[END_REF]. More importantly, these variety of reasons for sport involvement seem to be universally accepted as the primary reasons for participation in different sports [START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF], and are consistent with literature on the sources of enjoyment. In reviewing the enjoyment literature, [START_REF] Scanlan | The construct of sport enjoyment[END_REF] summarized the predictors of enjoyment to be: learning/improving skills, being with friends/being on a team, feeling competent, receiving instruction and encouragement from coaches, and winning. In a field study with a large youth Dropout in Female Handballers sample diverse in age, ethnicity, and gender, Scanlan, Carpenter, Lobel, & Simons (1993) corroborated the existence of these categories to predict enjoyment for youth sport athletes.

We postulate that the costs/benefits analysis consists in each athelete estimating the probability of reaching the most desired consequences for him or her. For example, the more an athlete wishes to learn and to improve skill the greater the anticipated benefit. On the other hand, feeling incompetent will make the costs of sport involvement rise and enjoyment fall. As [START_REF] Rusbult | A longitudinal test of the investment model: The impact of job satisfaction, job commitment, and turnover of variations in rewards, costs, alternatives and investments[END_REF] noted, costs and benefits are very connected insofar as the absence of a specific reward frequently implies the presence of a cost. Consistent with this, the sport literature on dropout indicates that the absence of the motives for participation are key explanations for dropout. These factors include fear of failure, excessive competitive pressures, dislike for the coach, interpersonal difficulties with teammates, and boredom [START_REF] Gould | Reasons for attrition in competitive youth swimming[END_REF][START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF]. In this study the favourability of sport involvement (i.e., the balance between rewards and costs) is conceptualised as a latent variable subjacent to individual perceptions of the costs and benefits of involvement. In turn, the higher these perceptions are, the higher sport enjoyment. Since enjoyment has been a key predictor of commitment, articulating the costs and benefits of participation will provide a clearer picture of the key facets of enjoyment.

METHOD

Participants

The population for the study was 488 French women aged from 15-19 years (M = 17.06; SD = 1.32), who participated in an organized handball program during the 1996-97 season and who competed in either sub-district area (a French department; n = 185), district area (n = 178) or national (n = 125) competition level.

Questionnaire

The first part of the questionnaire included demographic information such as date of birth, number of years of practice, amount of time played per week, and the level of participation. The second part assessed several perceptions of the players as well as their level of enjoyment of their sport experience. It also included 10 filler items.

Perceptions. The questionnaire evaluated perceptions related to the most important consequences of participation, namely perceptions of competence, autonomy, relatedness, progress, coach's support. These perceptions were drawn from one major source: a review of the extant literature on youth sport motivation (e.g., [START_REF] Gill | Participation motivation in youth sports[END_REF][START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Gould | Motives for participating in competitive youth swimming[END_REF][START_REF] Harter | The self-perception profile for adolescents[END_REF][START_REF] Nicholls | The competitive ethos and democratic education[END_REF][START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF][START_REF] Ryckman | Male and Female Adolescents' motives related to involvement in organized team sports[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF][START_REF] Vallerand | Toward a hierarchical model of intrinsic and extrinsic motivation[END_REF][START_REF] Wankel | Factors underlying enjoyment of youth sports: sport and age group comparisons[END_REF][START_REF] Weiss | Children's motivation for participation in and withdrawal from sport: Identifying the missing links[END_REF]. Moreover, a pilot study with Female handballers from 14 to 18 years [START_REF] Guillet | Abandon et investissement chez les joueuses de handball[END_REF] showed that these five dimensions were most important for their involvement. Two items measured each of these five perceptions.

The heading asked the subjects "When you play handball, do you feel you …". Ratings were made on a 5-point scale with opposite categories at the ends (e.g., for perceptions of progress: (1) "do you feel you can't learn anymore" and (5) "do you feel you can learn even more"). To avoid order effects, half of the items used a reversed score. Moreover, one item measured the amount of playing time because several studies have shown that this perception influenced players' satisfaction (Griffin, 1978[START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF]. Ratings were made on a 5-point scale, with (1) "almost never", (3) "the first or second half", and (5) "all the match".

Enjoyment. Following [START_REF] Scanlan | Social psychological aspects of the competitive sport experience for male youth sport participants: IV. Predictors of enjoyment[END_REF] enjoyment was measured by two items ("how much fun do you have?" and "how much do you like to play handball?"). Ratings were made on a 5-point scale, with (1) " very little " and (5) " very much ".

Procedure

In Spring 1997, at the middle of the handball season, the questionnaire described above (and others) was sent to 1100 female handballers taken randomly among the registers of the French federation of handball. A postage-paid reply envelope was also provided. A letter accompanying the questionnaire explained that the purpose of the study was to know more about why girls played handball and how they lived this sporting experience. It was clearly stated to participants that anonymity and confidentiality of their answers would prevail at all times. Four hundred and eighty eight questionnaires were returned (44% of returns).

RESULTS AND DISCUSSION

With structural equation modeling (LISREL 8, Jöreskog & Sörbom, 1993) we tested a model presented in Figure 2 that included 13 observed variables and 7 latent variables: perceived competence, progress, relatedness, autonomy, coach's support, benefits, and sport enjoyment).

Insert figure 2 here Since the variables were highly non-normal (tests of zero multivariate skewness = 29.29, p < .001 and zero multivariate kurtosis = 69.22, p < .0001), PRELIS 2 [START_REF] Jöreskog | Prelis 2: User's reference guide[END_REF], a preprocessor of LISREL, was used to generate the polychoric correlation and its corresponding asymptotic covariance matrix [START_REF] Jöreskog | New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares[END_REF]. Both matrices were used as input for the LISREL 8 program [START_REF] Jöreskog | Lisrel 8 : User's reference guide[END_REF] and analyzed by the Generally Weighted Least Squares (WLS) method of estimate [START_REF] Jöreskog | New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares[END_REF][START_REF] Jöreskog | Lisrel 8 : User's reference guide[END_REF].

In view of the current state of controversy regarding measure of overall goodness of fit, it is generally recommended to report multiple indices [START_REF] Bollen | Structural equations with latent variables[END_REF]. Based on the suggestions of Dropout in Female Handballers structural equation researchers (e.g., [START_REF] Bentler | Comparative fit indexes in structural models[END_REF][START_REF] Bollen | Testing structural equation models[END_REF], the following fit indexes were used to evaluate the adequacy of the measurement model: the goodness-of-fit index (GFI; [START_REF] Jöreskog | Lisrel 8 : User's reference guide[END_REF], the normed fit index (NFI; [START_REF] Bentler | Significance tests and goodness of fit in the analysis of covariance structure[END_REF], and the comparative fit index (CFI; [START_REF] Bentler | Comparative fit indexes in structural models[END_REF]. Structural coefficients and residuals variances for each construct are displayed in Figure 2. Goodness-of-fit indices revealed that the model adequately reflected the data (GFI = .98; NFI = .97; CFI = .98). All estimated parameters were significant (t > 2.00).

Results corroborated the existence of a latent variable named perceived benefits subjacent to perceptions of competence, autonomy, relatedness, progress, coach's support and to time of play. Moreover, the more the players perceived that the benefits were high, the more enjoyment (β = .95) they felt. After having controlled measurement error, perceived benefit explained 91% of the variance in enjoyment toward handball. These results are consistent with the literature on the sources of sport enjoyment (e.g., Scanlan, et al., 1993;[START_REF] Scanlan | Social psychological aspects of the competitive sport experience for male youth sport participants: IV. Predictors of enjoyment[END_REF][START_REF] Scanlan | The construct of sport enjoyment[END_REF][START_REF] Wankel | Factors underlying enjoyment of youth sports: sport and age group comparisons[END_REF]. The results show that enjoyment can be derived from intrinsic sources (e.g., progress, competence) and extrinsic sources (e.g., relatedness, coach's support). Consequently, as argued by Scanlan and colleagues (Scanlan & Simon, 1992;[START_REF] Scanlan | Social psychological aspects of the competitive sport experience for male youth sport participants: IV. Predictors of enjoyment[END_REF], enjoyment and intrinsic motivation are not synonymous constructs and have to be clearly distinguished. In study 2 we tested a sport commitment model based on the social exchange postulates, presented in Figure 1, using structural equation modeling analyses and a prospective design over 8 months. In view of the results of study 1 we replaced the construct of enjoyment proposed by Scanlan, Carpenter, Schmidt, et al. (1993) with perceived benefit. As noted above, this analysis provides a more comprehensive understanding of the enjoyment construct and is more consistent with the notion of cost and benefits outlined in social exchange theory [START_REF] Thibaut | The social psychology of groups[END_REF]. It was hypothesized that the greater the perceived benefit attached to handball, the more players have invested in their sport, the less attractive their alternatives to involvement, and the more constrained they feel to continue playing, the greater their commitment. In turn, high commitment will lead to low dropout behavior 8 months later.

Questionnaire

The questionnaire was made up of three parts. The first part included demographic information such as date of birth and the level of participation. The second part comprised items assessing key constructs employed in past research on sport commitment and their associated measures [START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF]Scanlan, Carpenter, Schmidt, et al., 1993) but modified to make them specific to French handball players. Personal investment was measured by asking players how much time per week and how many years of practice they had put in to handball. A pilot study [START_REF] Guillet | Abandon et investissement chez les joueuses de handball[END_REF]) revealed that money was not an important investment in Dropout in Female Handballers this activity and was accordingly omitted. Commitment was measured using four items (e.g., "I am determined to continue playing handball"). Two items were used to provide a measure of social constraints [e.g., "I feel I have to play handball to please people important for me (parent, coach)"]. The involvement alternatives construct was measured using two items [e.g., "I would like to do something else (to be with my friends, to make another sport or another leisure,…) instead of participating handball"]. The Cronbach alpha coefficients from these last three subscales were, respectively, .86, .81 and .88, indicating acceptable internal consistency (Nunnally, 1978).

The third part of the questionnaire assessed the personal perceptions of the handball players. Perceived handball competence was measured using three items (e.g., "When you play handball, do you feel you can dominate the others players") adapted from the Perceived Competence in Life Domains Scale (PCLDS, Losier, Vallerand, & Blais, 1993). Perceived handball progress was measured using three items (e.g., "When you play handball, do you feel you can progress"). Participants' feelings of autonomy in handball environment was measured using four items (e.g., "When you play handball, do you feel you can express yourself as you want it") adapted from Perceived Autonomy Toward Life Domains Scale (PALDS, [START_REF] Blais | Predicting physical activity intentions using goal perspectives and self-determination theory approaches[END_REF]. Perceived handball relatedness was measured using four items (e.g., I feel attached to the girls of my team), adapted from the Feelings of relatedness Scale (FRS, [START_REF] Richer | Construction et validation de l'Echelle du Sentiment d'Appartenance Sociale (ESAS)[END_REF]. Perceived coach's support was measured using four items (e.g., I feel that my coach is really concerned with me) adapted from the "Echelle des Comportements Interpersonnels" (ECI; Pelletier & Otis, submitted). The Cronbach alpha coefficients for these five subscales were, respectively, .83, .88, .83, .93, and .88, indicating acceptable internal consistency. All the above items were assessed using 7-point Likert scales ranging from (1) "strongly disagree" to (7) "strongly agree". Finally, the players evaluated their average time of play in match on a 7-point category scale with (1) "almost never", (4) "the first or second half", and ( 7) "all the match". Procedure

The assessment was conducted at midseason to ensure that all athletes would have sufficient experience with their current program. In Spring 1999 the questionnaire described above was sent to 532 14 to 16-years old players in a French handball league. A postage-paid reply envelope was also provided. A letter accompanying the questionnaire explained the purpose of the study and it was clearly stated to participants that anonymity and confidentiality of their answers would be ensured. Two hundred and fifty three questionnaires were returned (47 % of returns). Eight months later, that is after the beginning of the 1999/2000 season, the French Federation of Handball was contacted in order to establish a list of players who were still playing and those who had dropped out (i.e., those which did not re-register). Through these procedures a total of 23 drop-out cases were identified 1 .

RESULTS

Two sets of analyses were carried out. The first set of analyses focused on the differences between the dropout and persistent players on the means of the different subscales. The second set of analyses tested the model proposed in Figure 1. Our primary method of analysis was structural equation modeling (LISREL 8;[START_REF] Jöreskog | Lisrel 8 : User's reference guide[END_REF]. This method, which is particularly useful in longitudinal research [START_REF] Bentler | Multivariate analysis with latent variables: Causal modeling[END_REF], allows examination among all the constructs involved in a model using a latent representation of constructs that is not influenced by measurement error.

Persistent vs dropout : Personal perceptions A preliminary multivariate analysis of variance (MANOVA) was conducted with type of player (dropout vs persistent) as an independent variable and perceptions of competence, progress, autonomy, relatedness, coach's support, and time of play as dependent variables.

Results revealed a significant main effect for the type of player, Wilk's lambda = .82, Rao's R (6, 246) = 9.3, p < .0001. Follow-up univariate analyses of variance (ANOVAS) revealed significant differences between dropout and persistent players for all six variables (see Table 1). Dropout players perceived themselves as significantly less competent, less autonomous, less related to their team, lower in progress and less supported by their coach than persistent players. In addition, dropout players cited a lower time of play in matches than persistent players. The means and standard deviations of the perception subscales as a function of type of players appear in Table 1.

Insert table 1 here

Social constraints, alternatives opportunities, commitment, and personal investments A second MANOVA was conducted to determine whether differences on social constraints, involvement alternatives, commitment, and personal investments (i.e., years of practice and number of hours of training per week) existed as a function of player status. Results revealed a significant multivariate effect for the type of player, Wilk's lambda = .77, Rao's R (5, 247) = 15.07, p < .0001. Follow-up analyses revealed significant differences between dropout and persistent players for social constraints, involvement alternatives, commitment, and years of practice (see Table 2). Persistent players perceived less pressure from significant others, had less attractive alternatives, had higher commitment and had invested more in term of years of practice, than dropout players.

Insert table 2 here

Test of a sport commitment's model: a two step modeling approach We tested the model presented in Figure 1 using structural equation modeling. In light of the already high number of variables in the model, we decided to reduce the number of variables prior to testing the model. First, the average scale score on the perception sub-scales were used for each of these constructs. Next, the items on the commitment sub-scale were randomly aggregated to form only two composite scores for this construct [START_REF] Bentler | Multivariate analysis with latent variables: Causal modeling[END_REF][START_REF] Byrne | Structural Equation Modeling with EQS and EQS/Windows[END_REF].

Correlations between the two pairs of items composing each of these indexes were .70 and .75.

Although the measurement (factor structure) and structural (substantive) submodels can be assessed simultaneously with LISREL, we adopted [START_REF] Anderson | Structural equation modeling in practice: A review and recommended two-step approach[END_REF] two-step modeling approach which consists in evaluating them separately (see also [START_REF] Gramzow | Aspects of Self-Regulation and Self-Structure as predictors of perceived emotional distress[END_REF]. The first step (the measurement model) corresponds to a confirmatory factor analysis with observed and latent variables. One goal was to check if the factorial structure of the 'benefit' variable identified in study 1 was replicated. The second step (structural model) tested the theoretical model by examining the predicted relations among the latent factors and actual dropout behavior. The primary advantage of this two-step approach is a reduced potential for interpretational confounding. If the measurement and structural specifications are attempted simultaneously, then the strengths and patterns of relations between the measured variables and the latent factors (i.e., the measurement model) can change dramatically as the function of the structural model is assessed. Thus, the factor structure becomes dependent on the specific substantive model under examination and may lead to poor overall or ambiguous model fit [START_REF] Gramzow | Aspects of Self-Regulation and Self-Structure as predictors of perceived emotional distress[END_REF].

Step 1 : Measurement model

We specified a measurement model representing the hypothesized five-factor structure, subjacent with the 14 manifest variables. As recommended by Anderson and Gerbin (1988), the latent factors have been allowed to correlate freely during assessment of the measurement submodel. As in study 1, because the variables were highly non-normal (tests of zero multivariate skewness = 85.65, p < .001 and zero multivariate kurtosis = 105.28, p < .001), the polychoric correlation and its corresponding asymptotic covariance matrix were used and analyzed by the WLS method of estimate.

The measurement model provided an adequate fit to the data, GFI = .99; NFI = .98; CFI = .98. All λ were significant (t > 2.00). Standardized estimates, residuals variances and interfactor correlations for this model are displayed in Figure 3.

Insert Figure 3 here

Step 2: Structural model After assessing the adequacy of the factor structure we focused next on the pattern of structural relations among these five latent dimensions and actual dropout behavior assessed through a dichotomous variable (1 = dropped out; 2 = re-enrolled). Structural coefficients and residual variances for each construct are displayed in Figure 4 (to reduce the Figure the measurement model was not reported). Goodness-of-fit indices revealed that the model adequately reflected the data (GFI = .97; NFI = .95; CFI = .97). All estimates parameters were significant (t > 2.00) except for the effect of personal investments on commitment. The results revealed that social constraints and involvement alternatives were negatively related to commitment (β = -.14 and β = -.19, respectively). Conversely, perceived benefits had a strong positive influence on commitment (β = .79). In turn, high commitment negatively predicted actual drop out 8 months later (β = -.66).

Insert Figure 4 here GENERAL DISCUSSION Past research has highlighted that 50% of French woman handball players dropout between the age of 13 and 15 [START_REF] Guillet | Utiliser l'analyse de survie pour déterminer les moments et les taux d'abandon de la pratique sportive: l'exemple du handball féminin[END_REF]. This high level of dropout has alarmed the French Handball Federation and research is needed to identify the underlying factors. This is particularly important if the goal is to increase the physical activity levels of this population. The purpose of this research was to explain the phenomenon of withdrawal in female handball with social exchange postulates [START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF]Scanlan, Carpenter, Schmidt, et al., 1993;[START_REF] Thibaut | The social psychology of groups[END_REF].

According to sport commitment models based on social exchange postulates, the most immediate predictor of actual behavior of dropout versus persistence is the athlete's level of subjective commitment to the activity (Figure 1). Low levels of commitment are expected to lead to high sport dropout. Sport commitment is hypothesized to be a function of four antecedents: (1) athlete's costs/benefits analysis of the sport experience, (2) perceived attractiveness of the best available alternative to the sport participation, (3) level of investment and (4) athlete's feelings of social constraints. This model (see Figure 1) posits that the more athletes perceive that the benefits outweigh the costs, the more they have invested in their sport, the less attractive their alternatives to involvement and the more constrained they feel to continue playing, the greater their commitment. The present results provide strong support for the proposed model.

On the Consequences of Commitment

Results revealed that female handball players who had dropped out had lower levels of commitment. Moreover, results of structural equation modeling, consistent with past research on relationships [START_REF] Bui | Testing the rusbult model of relationship commitment and stability in 15-year study of heterosexual couples[END_REF][START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF][START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF][START_REF] Duffy | Satisfaction and commitment in homosexual and heterosexual relationships[END_REF][START_REF] Sprecher | Investment model, equity and social support determinants of relationship commitment[END_REF] and job turnover [START_REF] Rusbult | A longitudinal test of the investment model: The impact of job satisfaction, job commitment, and turnover of variations in rewards, costs, alternatives and investments[END_REF] supported the hypotheses that a lack of commitment leads to dropping out of sport, in this study, as assessed 8-months later. These results extend the research on sport commitment (e.g., [START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF] by demonstrating that sport commitment is linked to actual stay/leave behaviour. In this study, commitment predicted 44 % of the variance in the actual behaviour. This link between intentions and behavior was only of moderate magnitude and is due to the fact that dropout behavior is not fully under the control of the athletes. In some cases, the decision to withdraw is externally controlled [START_REF] Gould | Understanding attrition in children's sport[END_REF]. For example, athletes who are cut from teams, or suffer from such severe injuries that they are no longer able to participate, have no choice but to withdraw from the activity. It is thus possible that 8 month earlier some athletes did not express a desire to leave the activity but nevertheless did due to factors outside of their control (e.g., an injury). Future studies should check if the final decision to drop out is within the control of the individual athlete or not.

On the cost/benefit analysis One of the main postulates of the social exchange model is that people participate in an activity if the balance between rewards and costs is favorable [START_REF] Thibaut | The social psychology of groups[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF]. In the majority of the studies on engagement, the costs/benefits analysis is expressed by a global rating of positive affect like satisfaction (e.g., [START_REF] Rusbult | Commitment and satisfaction in romantic associations: A test of the investment model[END_REF][START_REF] Rusbult | A longitudinal test of the investment model: The development (and deterioration) of satisfaction and commitment in heterosexual involvement[END_REF] or enjoyment (e.g., Scanlan, Carpenter, Schmidt, et al., 1993). Enjoyment has been consistently found to be one of the strongest predictors of commitment. However, a global measure of affect provides little information on the sources of enjoyment and the process of the cost-benefit analysis. By undertaking a cost-benefit analysis we have sought to better understand the variables taken into account in the cost/benefit analysis by female handballers.

We conceptualised the balance between rewards and costs as a latent variable subjacent to individual perceptions of realizing the most desired consequences of sport participation. The higher these perceptions, the greater the perceived benefits. Costs are the negative side of benefit because the higher the benefits are, the lower the costs [START_REF] Rusbult | A longitudinal test of the investment model: The impact of job satisfaction, job commitment, and turnover of variations in rewards, costs, alternatives and investments[END_REF]. A review of the extant literature on youth sport motivation (e.g., [START_REF] Gill | Participation motivation in youth sports[END_REF][START_REF] Gould | Understanding attrition in children's sport[END_REF][START_REF] Gould | Motives for participating in competitive youth swimming[END_REF][START_REF] Harter | The self-perception profile for adolescents[END_REF][START_REF] Nicholls | The competitive ethos and democratic education[END_REF][START_REF] Petlichkoff | Coaching children: understanding the motivational process[END_REF][START_REF] Ryckman | Male and Female Adolescents' motives related to involvement in organized team sports[END_REF][START_REF] Smith | Toward a cognitive-affective model of athletic burnout[END_REF][START_REF] Vallerand | Toward a hierarchical model of intrinsic and extrinsic motivation[END_REF][START_REF] Wankel | Factors underlying enjoyment of youth sports: sport and age group comparisons[END_REF][START_REF] Weiss | Children's motivation for participation in and withdrawal from sport: Identifying the missing links[END_REF], on the sources of sport enjoyment (e.g., [START_REF] Scanlan | Social psychological aspects of the competitive sport experience for male youth sport participants: IV. Predictors of enjoyment[END_REF][START_REF] Scanlan | The construct of sport enjoyment[END_REF]Scanlan et al., 1993;[START_REF] Wankel | Factors underlying enjoyment of youth sports: sport and age group comparisons[END_REF], and a pilot study with Female handballers [START_REF] Guillet | Abandon et investissement chez les joueuses de handball[END_REF] emphasized six important dimensions for sport among this population, namely, competence, autonomy, relatedness, progress, coach's support and the amount of playing time.

Results showed that players who dropped out perceived themselves as significantly less competent, less autonomous, less related to their team, lower in progress, less supported by their coach and cited a lower time of play in matches than players who persisted. Moreover, these perceptions were interrelated and the results corroborated the existence of a latent variablenamed 'perceived benefit'-subjacent to these perceptions. This construct strongly predicted enjoyment (β = .95, study 1) and commitment (β = .76, study 2). Moreover, study 2 showed a Dropout in Female Handballers difference in the magnitude of the latent variables which predicted commitment with perceived benefits the predominant predictor of commitment.

What is interesting to note it is that the different perceived benefits which emerged in studies 1 and 2 have resonance with self-determination theory. Self-determination theory developed by Deci andRyan (1991, 2000) assumes that people initiate and persist at behaviors to the extent that they believe the behaviors will lead to desired outcomes or goals. More specifically, [START_REF] Deci | The What and Why of goal pursuits: humans needs and the self-determination of behavior[END_REF] postulated that satisfying the fundamental needs of autonomy, competence, and relatedness are linked directly to well-being and increased satisfaction. People are more likely to engage in activities that social groups relevant to them value, especially when they feel efficacious with respect to those activities. Secondly, the experience of autonomy is also a critical element for increased satisfaction. Finally, one of the reasons people initially engage in particular activities is because the behaviors are prompted, modeled, or valued by significant others to whom they feel attached or related. A recent study (Sheldon, Elliot, Kim, & Kasser, 2001) showed that when people are asked to bring to mind deeply satisfying experiences, they think of experiences in which they felt strongly autonomous, competent, or related to others.

In the research described here, the benefits to emerge as important are consistent with the basic psychological needs -competence, autonomy, and relatedness -argued within selfdetermination theory. These results suggest that integrating self-determination theory and social exchange theory represents a potentially promising new line of research that warrants further scientific scrutiny, particularly to identify the perceived benefits in a specific domain such as sport. It is possible that some important benefits have been missed in this research and that the list of perceived benefits described in this work is not exhaustive. Future studies need to determine if the six perceptions of the cost/benefit analysis underlined in the studies reported here are found with other populations (e.g., high level athletes or male athletes) or if they must be supplemented by other perceptions.

On the other antecedents of commitment In addition to the positive impact of perceived benefits on sport commitment, the structural equation modeling results of study 2 revealed a negative influence for social constraints (β = -.14) and involvement alternatives (β = -.19). The involvement alternatives finding is in line with model predictions and sport attrition studies which have found that conflicts of interest and/or interest in other activities were the most consistently cited motives for sport withdrawal [START_REF] Gould | Understanding attrition in children's sport[END_REF]. This situation is more pertinent during adolescence, a period characterized by emergence of a need for independence and changes of interests [START_REF] Lindner | Construction et validation de l'échelle des perceptions de compétence dans les domaines de vie (Construction and validation of the perceived competence toward life domains scale)[END_REF]. These changes lead to an attraction for other activities in which many of the athlete's peers are deeply involved (e.g., hanging out with friends, developing a relationship with a boy friend). [START_REF] Maehr | The motivation factor/A theory of personal investment[END_REF] speak of "perceived options," defined as behavioral alternatives or action possibilities that a person perceives to be available to him or her in any given situation. Such individuals may still enjoy their sport but favor the alternative; that is, they weigh the costs/benefits of being involved and choose to withdraw because the alternatives are more attractive (Petlichkoff, 1993a). Nevertheless, the involvement alternative construct was a non-significant factor in past studies (e.g., [START_REF] Carpenter | A test of the Sport Commitment Model using structural equation modeling[END_REF][START_REF] Carpenter | A longitudinal study of elite youth cricketers' commitment[END_REF].

Further research is necessary to evaluate if it is a specificity of the female population of this study or measurement problem noted in prior studies. More generally, the impact of this variable among girls and boys at various stages of the athlete's development and on different levels of practice requires further investigation.

Contrary to social exchange hypothesis and the sport commitment model, social constraints negatively predicted commitment (β = -.14). [START_REF] Carpenter | A test of the Sport Commitment Model using structural equation modeling[END_REF] also reported a positive relationship and argued in part that the positive relationship between commitment and social constraints revealed in close relationships studies (e. g., [START_REF] Kelley | Love and commitment[END_REF] may indicate that the nature of adult close relationships may be very different from youth sport involvement. In close relationships, the positive relationship between social constraints and commitment is based on the assumption that pressure to continue is a function of the perceived negative sanctions from others the individual would experience if he or she were to terminate involvement. Further, it also is assumed that the individual is motivated to comply with these perceived sanctions [START_REF] Rusbult | Commitment in close relationships: the investment model[END_REF]. Typically, youth sport is viewed as a voluntary free-choice activity that is enjoyable to most continuing participants (see [START_REF] Scanlan | The construct of sport enjoyment[END_REF]. Accordingly, most athletes participate because they want to, not because they have to [START_REF] Csikszentmihayli | Talent and enjoyment: Findings from a longitudinal study[END_REF]. This negative relation between social constraints and commitment suggests that stress can occur when young athletes feel pressure to participate (Scanlan & Lewthewaite, 1984). This aversive state of stress may lower commitment. Moreover, feelings of obligatory participation, in what is generally viewed as a voluntary activity, also may undermine feelings of personal control and self-determination (see Ryan & Deci, 2000[START_REF] Vallerand | Toward a hierarchical model of intrinsic and extrinsic motivation[END_REF], and work to lower the desire and resolve to continue. Finally, contrary to past studies, personal investment was not significantly related to commitment. However, examining the differences between players who persisted and those who dropped out did show that persistent players had more invested in terms of years of practice than dropout players, although the two populations were not different in terms of hours of training per week. In addition, personal investment was correlated with commitment (r = .22, cf. figure 3).

Combined, these results do suggest that personal investment may play an important role even though the results of structural equation modeling did not support the hypothesis that the higher personal investment is related to higher commitment. The non-significant result seems related to two reasons. First, the sample represented a sub-district or district area competition level. At this level the frequency of training is not very high (the majority of players only train for four hours per week) and one can suppose that personal investments are less relevant. In addition, the girls of this population had not invested many years of practice in their sport (cf. Table 2).

Accordingly in this population, personal investments would have had a negligible influence on commitment. Second, the way in which personal investments were measured in this study may have led to the non-significant result. We employed more "objective" variables (e.g., number of year of practice) whereas in the past studies the measures were more "subjective" (e.g., "how much of (1) your time, (2) effort, (3) money have you put into playing this season?"). It is possible that "perceptions" of personal investments counts more than objective reality. Future research needs to address this supposition.

The results of these studies support the application of the sport commitment model to predicting those French female handball players who dropout versus those who persist. The model explained 75% of the commitment variance and the important determinants of commitment were consistent with extant research. Moreover, these studies highlighted the principal variables taken into account in the cost/benefit analysis. However, the generalizability of these results to, for example, male athletes or high level athletes, remains to be tested.

Practical implications

The results of these studies have at least one major practical implication. This research indicates that when major participation motives or major psychological needs (e.g., developing skill, being with friends) are not achieved, the costs of involvement exceed the benefits. It is recommended that the coach takes into account these various reasons when working with his or her athletes. Gould and Horn (1984) have suggested that adult leaders structure the sport environment so that theses motives are fulfilled. Special emphasis should be placed on skill instruction for children of all ability levels. Excitement and fun must be maintained in practices and competitions by keeping athletes active and by allowing all adolescents the opportunity to participate. Special efforts should be made to meet the affiliation needs of athletes. Finally, success should be more broadly defined as personal improvement, in contrast to winning.

In summary, this study suggests that one of the priorities of the coach and other sports leaders (e.g., parents, administrators) is to create a social environment that allows players to achieve their motives for participation. Specifically, we should seek to ensure that players'expectations related to progress, relatedness, competence, sport enjoyment, significant others'support, should be met if we wish enjoyment to be high and correspondingly commitment and actual continued involvement. Footnote 1. It appears that less than 10% of the current sample dropped out. This figure is significantly lower than the 50% dropout rate cited in the literature review to this research. The discrepancy is explained when it is noted that the 50% rate corresponds to dropout over several years (3 to 4 years) whereas the rate reported in this study is for approximately one year. If the same attrition rate was maintained over the next three years, the number of players to dropout of the program would approach the 50% rate cited.

Figure 1

 1 Figure 1 using structural equation modeling analyses and a prospective design over 8 months to predict actual dropout behaviour.

STUDY 2 :

 2 Predicting withdrawal in female handballers with Social Exchange postulates

  French handball females between the ages of 14 and 16 years (M = 15 years, SD = 0.81). These athletes came from 50 different teams located in the South East of France. All players competed in either sub-district area (n = 115) or district area (n = 138) competition level.

Figure 1 .

 1 Figure 1. Main variables in the Social Exchange framework to explain the process of dropping out of sport.

Figure 2 .

 2 Figure 2. Structural model with Generally Weighted Least Squares estimates for the relations between perceived benefits and sport enjoyment.

Figure 3 .

 3 Figure 3. Measurement model: Generally Weighted Least Squares estimates for five-factor model. Circles represent latent constructs and squares represent measured variables.

Figure 4 .

 4 Figure 4. Structural model with Generally Weighted Least Squares estimates for the relations among main variables of the Social Exchange model to explain the process of dropping out of sport.

Table 1

 1 Means and Standard Deviations of the personal perceptions for Dropout and Persistent players Means and standard deviations of the commitment, social constraints, involvement alternatives, and personal investments scores for dropout and persistent players.

	Personal perceptions	M	Dropout players (n = 23)	SD	M	Persistent players (n = 230) SD	F(1, 251) p
	Competence Relatedness Progress Autonomy Coach's support Time of play	3.13 4.02 3.52 3.04 3.45 4.65	1.22 1.92 1.66 1.38 1.65 1.64	4.17 5.70 4.73 4.41 4.39 5.70	1.23 1.16 1.49 1.36 1.51 1.23	<.001 <.001 <.001 <.001 <.001 <.001

Author's note Acknowledgements:

Preparation of this article was facilitated through a grant from the French Federation of Handball to the first author.

The plus (+) and minus (-) signs presented in this figure represent the hypothesized direction of influence of each variable.