Aurélien Esnard

Nicolas Bonichon

ENSEIGNEMENT •••••••• Retour d'expérience sur une UE Projet en licence informatique

Introduction

Cet article présente un retour d'expérience sur une unité d'enseignement (UE) projet en licence informatique à l'université de Bordeaux. Dans le cadre de cette UE, nous avons mis en place plusieurs stratégies pour atteindre efficacement nos objectifs pédagogiques. Nous ne prétendons pas que notre approche est la meilleure, mais nous pensons néanmoins que ce retour d'expérience pourra nourrir la réflexion d'autres collègues.

La suite de l'article est organisée de la manière suivante. Dans un premier temps, nous rappellerons le contexte de cette UE et pourquoi nous avons évolué vers la réalisation d'un projet sur l'année. Ensuite, nous verrons comment nous avons organisé cette UE projet. Enfin, nous présenterons les outils techniques que nous avons utilisés pour mettre en place cette UE projet.

Contexte

Positionnement de l'UE dans le cursus L'UE considérée ici est une UE à 6 crédits (ECTS), qui se déroule sur toute l'année, soit 40 heures de présentiel au total, avec 3 cours et 12 séances de TD (sur machine) de 1h20 chaque semestre. Au final, c'est un temps très court chaque semaine, ce qui implique beaucoup de travail des étudiants en dehors des séances encadrées. Nous avons un effectif assez important, avec environ 250 étudiants en licence informatique à gérer. Nous nous retrouvons ainsi avec 12 groupes de TD et une dizaine de chargés de TD qui se répartissent ces groupes. Dans chaque groupe de TD, les étudiants se répartissent en équipe de trois. Ainsi, nous avons environ 75 équipes à gérer.

Cette UE se trouve en deuxième année de licence informatique (L2). Elle a quelques prérequis en première année (L1) en algorithmique élémentaire, en programmation C, et un peu en programmation web. Notons que lors du semestre d'automne (S3), les étudiants suivent en parallèle une UE de Programmation C, qui fait suite à l'UE Initiation à la programmation C (S2). Après leur L2, nos étudiants suivent en L3 une autre UE projet de développement logiciel.

Objectifs pédagogiques

L'objectif pédagogique principal est de former nos étudiants à des méthodes et des bonnes pratiques de développement logiciel, et de leur apporter une certaine maîtrise des outils techniques, afin qu'ils puissent participer à des projets logiciels en entreprise. Cela se décline donc en une liste de compétences assez génériques :

-renforcer le niveau en programmation et en algorithmique ; -apprendre à travailler en équipe ; -savoir faire des tests unitaires ; -savoir évaluer la couverture de ses tests ; -savoir écrire du code propre ; -savoir documenter son code ; -savoir déboguer efficacement son code ; -savoir rendre son code maintenable ; -comprendre l'importance du découpage modulaire et de l'interopérabilité ; -respecter un cahier des charges. Adossés à ces premiers objectifs, on a également des objectifs plus techniques, liés à des outils :

-maîtriser un IDE (VS Code) ; -maîtriser le processus de compilation (gcc, make) ; -maîtriser un outil de gestion de version (Git) et les fonctionnalités de base d'une forge logicielle (GitLab) ; -maîtriser un système de construction logicielle (CMake) ;

-savoir s'approprier une bibliothèque logicielle externe (SDL) ; -maîtriser quelques technologies Web (HTML, CSS, JS, WASM) ; -rédiger un rapport en LaTeX.

Pourquoi un projet sur toute l'année ?

Historiquement, il s'agissait d'une UE qui avait à peu près le même contenu pédagogique, mais avec des modalités un peu plus classiques, c'est-à-dire avec 1h20 de cours et 2h40 de TD chaque semaine, pendant un semestre. On présentait essentiellement la même liste de méthodes et de technologies à maîtriser. La mise en oeuvre de tout cela se faisait sous la forme de TD indépendants les uns des autres et d'un mini-projet à rendre en fin du semestre (puisque cette UE se déroulait sur un seul semestre). Malheureusement, nous avons remarqué que les étudiants avaient du mal à s'approprier ces méthodes et ces technologies. Une des causes principales était, selon nous, que les étudiants ne voyaient pas l'intérêt de ces méthodes et de ces technologies lorsqu'elles étaient présentées en cours et manipulées en TD. En effet, les réticences des étudiants étaient les suivantes :

-« Monsieur, moi quand je code ma petite bidouille, je fais du quick and dirty et ça marche très bien comme ça » ; -« Je n'ai pas besoin d'apprendre tous vos outils. Pour compiler, je fais simplement gcc * .c et ça marche bien » ; -« Pour debugger, pas besoin de gdb, je rajoute des printf de temps en temps, ça suffit ! » ;

Et pour le reste, c'est un peu la même chose. Ces remarques sont certes caricaturales, mais elles sont néanmoins tout à fait légitimes. Pour de tout petits programmes, c'est une méthode suffisamment efficace de développement. Et comme nos étudiants ont principalement développé des petits programmes, principalement seuls, leur expérience personnelle leur donnait raison. C'est pourquoi nous avons décidé de migrer vers un projet plus conséquent se déroulant sur toute l'année. L'idée était de mettre les étudiants dans une situation où il devient utile (sinon nécessaire) d'utiliser les méthodes et les outils présentés. Le fait que le projet se déroule sur toute l'année nous permet de travailler sur un temps de développement plus long, qui permet d'atteindre une taille du logiciel suffisante pour rendre nos objectifs pédagogiques pertinents.

Lorsque le projet avance, la maîtrise des outils n'est plus simplement utile, elle devient nécessaire du fait de la montée en complexité du logiciel. Ici, le timing est assez difficile à trouver. Car, si on avance trop vite, les étudiants n'ont pas le temps d'acquérir les compétences associées et ils s'enlisent dans le projet. Chaque année, nous ajustons ce timing en fonction de la difficulté intrinsèque du projet, mais aussi de l'avancement de la promotion.

Organisation pédagogique

Au fil des années, nous avons convergé vers une organisation et un scénario qui se veut motivant pour les étudiants et qui permet d'introduire progressivement les méthodes et les outils associés.

Sujet du projet

Le projet à réaliser est en fait un prétexte (un fil rouge) pour introduire les outils et méthodes de développement. Il s'agit d'un petit jeu de logique (type Sudoku), qui change chaque année. L'important est que le projet soit suffisamment simple pour que les étudiants puissent le réaliser en autonomie, mais suffisamment complexe pour qu'ils aient besoin d'utiliser les outils et méthodes de développement présentés dans cette UE.

Nous avons choisi comme thématique un petit jeu, mais cela pourrait être tout autre chose, tant qu'il est possible de faire varier le choix du projet chaque année tout en gardant la même structure. Ce dernier point est particulièrement important si l'on souhaite pouvoir réutiliser au maximum les supports pédagogiques d'une année sur l'autre. Dans notre cas, il s'agit d'un puzzle logique, qui se joue à un seul joueur sur une grille 2D. Notons par ailleurs que dans le contexte de notre UE, le sujet du projet est le même pour toutes les équipes. Ces dernières années, nous avons choisi des jeux parmi ceux présentés dans la collection de Simon Tatham2 . Cette année, nous avons choisi le jeu Takuzu (également connu sous le nom Unruly dans cette collection). Dans ce jeu, le joueur part d'une grille où se trouvent déjà des cases noires et blanches fixes. Le joueur doit compléter la grille en respectant les règles suivantes : chaque ligne et chaque colonne doit contenir autant de cases noires que de cases blanches et il ne doit pas y avoir plus de deux cases blanches ou noires consécutives. La figure 1 illustre plusieurs exemples de jeux réalisés ces dernières années avec différents types d'interface utilisateur que les étudiants devront implémenter au cours de l'année : mode texte, mode graphique, Android, Web.

Le scénario pédagogique

Le scénario pédagogique que nous avons mis au point au fil des années est décrit dans ce qui suit (voir figure 2).

Étape a. Au début, nous fournissons aux étudiants le noyau fonctionnel du jeu déjà implémenté sous forme d'une bibliothèque compilée (un fichier game.a, sans le code source) avec une API documentée (un fichier game.h), ainsi que la documentation complète générée par Doxygen. La première étape consiste simplement à implémenter le jeu en mode texte. Cette première étape, qui ne comporte aucune difficulté algorithmique, permet aux étudiants de se familiariser avec le jeu et de se remettre dans la programmation en langage C. C'est également le prétexte pour parler de Une fois cela établi, nous leur demandons d'écrire des tests unitaires de la bibliothèque fournie. C'est la première fois qu'ils ont à développer des tests et ils sont un peu « frileux » à ce sujet. Pour les motiver, nous leur donnons des versions buggées de notre bibliothèque et ils doivent trouver ces différents bugs avec leurs tests, ce qui les encourage à les améliorer. Comme nous avons un peu d'expérience, les bugs que nous introduisons sont à peu près ceux que nous retrouvons régulièrement dans les projets précédents. Donc, s'ils arrivent à trouver nos bugs, ils vont probablement trouver les bugs qu'ils vont faire par la suite.

Au sein de chaque équipe, les étudiants se répartissent les fonctions à tester. Ils commencent à se rendre compte de l'intérêt d'utiliser un outil de gestion de version. Comme ils sont encore en phase de rodage avec Git, il leur arrive également de perdre du temps à cause de Git. C'est pourquoi la charge de travail est relativement faible à ce moment-là.

Étape b. Une fois que tout cela est mis en place, nous enlevons notre bibliothèque compilée et c'est aux équipes étudiantes d'implémenter leur propre version de la bibliothèque. L'API est fixée, mais c'est à eux de choisir leurs structures de données (type opaque) et les algorithmes de chaque fonction. Assez rapidement, ils perçoivent l'intérêt des tests unitaires développés précédemment. C'est aussi l'occasion de mettre en application les techniques de debugging présentées en parallèle.

Étape c. Lorsque cette première version (V1) est complètement implémentée, nous faisons évoluer le cahier des charges en considérant une variante un peu plus générale du jeu à implémenter. Cette évolution du cahier des charges est annoncée dès le début de l'année : on l'appelle le caprice du client ! L'objectif de cette évolution est de leur faire sentir concrètement l'importance d'avoir du code propre et maintenable.

Étape d. Une fois arrivé là, il est demandé à chaque équipe de livrer une version propre de leur projet. On rentre alors dans une phase de relecture de code où chaque étudiant doit récupérer le code d'une autre équipe et le lire, l'évaluer, le tester et puis vérifier l'interopérabilité entre son code et celui de l'autre équipe en faisant travailler sa bibliothèque avec l'interface texte et les tests de l'autre équipe, et inversement. C'est la première fois où ils sont confrontés au code d'autres étudiants. Ils se disent : « J'avais fait des choix qui me paraissaient évidents, mais finalement il y a d'autres choix possibles, tout aussi pertinents ». Ils sont également confrontés à du code soit meilleur, soit moins bon que le leur. Dans les deux cas, c'est très formateur. Cette relecture croisée est ensuite évaluée par l'équipe enseignante, qui note d'une part le code livré et d'autre part les relectures croisées. C'est un travail assez chronophage pour l'équipe enseignante, mais que l'on estime « payante » pour nos étudiants.

Étape e. Cette étape débute généralement un peu après le début du second semestre. Nos étudiants sont maintenant à l'aise avec la programmation C, et les outils de base du développement logiciel (CMake, Git, debugging...) intégrés à leur IDE. On commence alors à aborder des étapes du projet un peu plus sophistiquées. Comme certaines équipes commencent à rencontrer des difficultés avec des bugs dans leur bibliothèque, nous leur fournissons une version corrigée de la bibliothèque afin que chacun puisse repartir sur des bases saines. C'est également l'occasion pour les étudiants de relire le code des enseignants, et de comprendre ce que nous appelons un code propre. Le premier jalon de cette étape consiste à implémenter un solveur pour ce jeu. Nous avons à cet endroit deux niveaux d'exigences. Un niveau standard pour les étudiants moins à l'aise où il suffit d'implémenter un algorithme de type « brute force ». Puis un deuxième niveau avec un algorithme plus sophistiqué de type branch and cut pour aller plus loin. Pour les équipes les plus fortes, capables de produire du code optimisé, nous présentons sur une page web un classement automatique des performances des différents solveurs. Ce challenge permet de stimuler les meilleurs étudiants tout en laissant aux autres le temps de consolider leurs apprentissages plus essentiels. Il faut noter que pour debugger le solveur, les outils de debugging présentés ne sont plus simplement utiles, ils deviennent indispensables.

Jusqu'à présent, les sujets étaient très guidés, mais pour le jalon suivant, nous leur offrons plus de liberté, nous leur demandons également plus d'autonomie. En effet, dans cette partie, ils doivent implémenter une interface graphique pour leur jeu en utilisant la bibliothèque graphique SDL et pour cela, ils doivent apprendre par eux-mêmes à utiliser cette bibliothèque. En ce qui concerne l'interface graphique, ils ont toute latitude pour faire ce qu'ils veulent, du moment que le jeu soit jouable et convivial (voir figure 3).

Enfin, pour conclure, selon les années, nous ajoutons une partie de portage Android ou Web (en se basant sur WASM). C'est l'occasion de leur faire découvrir d'autres technologies plus modernes. L'autre intérêt de cette partie vient du fait qu'ils peuvent montrer à leur famille ou à leurs amis ce qu'ils ont réalisé pendant l'année. Ils sont souvent très fiers de ce qu'ils ont accompli et ils ont raison de l'être.

Déroulement sur l'année

Le scénario présenté ci-dessus s'articule autour d'une quinzaine de TD qui durent 1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023 de une à deux semaines environ. À chaque fois, des évaluations sont réalisées, mélangeant des évaluations individuelles et en équipe (voir figure 4). La plupart des évaluations individuelles concernent les exercices préliminaires des feuilles de TD, qui présentent les méthodes et outils nécessaires à la réalisation du nouveau jalon. Ce mélange permet d'éviter que certains étudiants ne se laissent porter par l'équipe et ne travaillent pas suffisamment les acquis essentiels au travail du projet en équipe. En marge de ce dispositif pédagogique, nous accompagnons nos étudiants tout au long de l'année avec des séances supplémentaires de soutien, la mise à disposition d'une FAQ sur les erreurs classiques (que nous complétons chaque année), ou encore l'animation d'un forum de discussion sur RocketChat. Ce forum permet aux enseignants de répondre aux questions des étudiants, en précisant certains points de détail sur le sujet du projet ou encore aux étudiants de s'entraider (sans divulguer de solution évidemment).

Mise en oeuvre et aspects techniques

1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023

Organisation d'un TD avec Moodle

Chaque TD s'organise de la même manière sur Moodle. Pour illustrer notre propos, nous allons examiner plus en détail l'exemple du TD 5. L'objectif pédagogique de ce TD est de savoir implémenter des tests unitaires (voir figure 5). Au début de la page, on trouve des informations de base sur la durée du TD (ici deux semaines), ainsi que des informations sur les rendus à effectuer avec leurs coefficients. Vous noterez que le premier rendu (le rendu initial) est individuel, tandis que le rendu final s'effectue en équipe. Nous reviendrons plus tard sur la notion de « passes ». On trouve ensuite un certain nombre de ressources préliminaires, telles que des vidéos ou des supports de cours (nous n'avons que 6 séances de cours sur l'année). Ces ressources doivent être consultées « à la maison » avant la séance de TD. Ensuite vient la feuille de TD à proprement parler (ou plutôt un lien vers une page web qui contient le sujet du TD). Dans cette feuille de TD, les étudiants trouvent le plus souvent une activité préliminaire présentant les méthodes et les outils à utiliser, puis une activité principale consistant à mettre en oeuvre ces nouveaux acquis pour le projet. Immédiatement après, on trouve des activités Moodle pour effectuer les rendus demandés dans le sujet, qui feront l'objet d'une ou plusieurs évaluations. Enfin, nous effectuons un petit sondage pour recueillir auprès des étudiants des retours sur le TD : combien de temps cela vous a-t-il pris ?trouvez-vous que c'était difficile ou facile ? Ces retours sont très précieux, car ils nous permettent d'améliorer nos sujets et d'adapter la charge de travail (pour les prochaines séances ou pour l'année suivante).

Pour réaliser cette feuille de TD, nous disposons de deux séances de 1h20 en présentiel (une par semaine). C'est un temps très court finalement qu'il faut optimiser. Pour l'enseignant, il s'agit essentiellement d'un travail de coordination, de synchronisation et de motivation des équipes. Notons qu'un chargé de TD gère en moyenne 5 ou 6 équipes de 3 étudiants. Il commence généralement sa séance par faire un debriefing sur le dernier rendu. En général, les étudiants ont des doléances à nous faire remonter, dont nous discutons. Quand il s'agit de l'activité préliminaire, nous donnons le plus souvent une correction. Puis, nous lançons l'activité suivante, typiquement celle concernant le projet. Il faut alors expliquer le sujet, coordonner les équipes et les encourager à se répartir le travail pour les semaines à venir.

Stratégie d'évaluation (automatique)

Comme expliqué auparavant, chaque TD se découpe typiquement en deux activités : une activité préliminaire avec un rendu initial (plutôt individuel) et une activité principale sur le projet avec un rendu final (en équipe). Concernant le rendu de l'activité principale, nous utilisons généralement une évaluation en deux passes selon les principes suivants :

-une première passe « à l'aveugle » (ou presque) avec des retours partiels à volonté avant la deadline, puis un retour complet qui sera délivré aux étudiants (avec une note) après la deadline ; -une deuxième passe avec cette fois-ci un retour complet (à volonté) jusqu'à la seconde deadline, généralement une semaine après la première. La plupart de ces rendus sont évalués automatiquement sur Moodle grâce au plugin VPL (cf. la section suivante), ce qui nous permet de maintenir un rythme soutenu d'évaluation tout au long de l'année. L'avantage principal de ces évaluations automatiques, c'est que cela nous permet de fournir plus de retours aux étudiants, et plus rapidement. Cela garantit également une évaluation très équitable. En revanche, ces évaluations peuvent sembler assez rigides pour nos étudiants. Cette rigidité est à la fois un avantage et un inconvénient. L'avantage, c'est que cela enseigne une certaine rigueur à nos étudiants. L'inconvénient, c'est que certains étudiants pourraient se retrouver avec un zéro parce qu'ils n'ont pas respecté les consignes, alors qu'ils ont fourni un travail qui ne mérite pas une telle note, ce qui est très frustrant. Pour remédier à cela, nous avons mis en place un système d'évaluation avec des retours à deux niveaux, plus ou moins détaillés. Le premier niveau de retour est accessible à volonté dès la première passe. À chaque fois qu'un étudiant dépose ou modifie un rendu, il reçoit un retour partiel sur son rendu, qui lui indique si ce qu'il a remis est bien ce qui était attendu. (Exemples : le fichier porte-t-il le bon nom ? est-ce qu'il compile correctement ? est-ce que cela répond aux premières questions ?). Ainsi, l'étudiant qui se serait fourvoyé peut rectifier le tir avant la date limite de rendu. Généralement, un étudiant (ou une équipe) qui n'a aucun avertissement à ce stade a la garantie d'avoir au minimum entre 30 % et 50 % des points selon les rendus. À l'inverse, si son rendu n'est pas conforme (par exemple, s'il ne compile pas), alors il n'a pas d'excuse et nous ne négocions pas, ce qui économise pas mal d'énergie à l'équipe pédagogique ! Une fois la date limite passée, l'évaluation complète de tous les rendus est lancée par l'enseignant. À l'issue de cette première passe, les étudiants ont une note ainsi qu'un retour complet sur leur rendu. Le fait de ne pas rendre accessible à volonté les retours complets est là pour trois raisons. Il permet de limiter la triche. En effet, si les étudiants avaient accès à l'évaluation complète, ils pourraient se contenter de copier le code d'un autre étudiant et de le soumettre jusqu'à ce que le système leur donne un retour positif. Ensuite, les étudiants pourraient optimiser leur note sans comprendre le fond de l'exercice. Enfin, cela incite également les étudiants à vérifier leurs rendus avant de les soumettre.

Une fois la première passe terminée, on va débloquer une seconde passe qui va se dérouler en général à cheval sur la prochaine séance. Dans cette seconde passe, les étudiants ont accès à une évaluation complète de leur travail à chaque modification. Soient N 1 et N 2 les notes respectives de la première et de la seconde passe. La note finale (N f ) de cette activité sera calculée comme le maximum entre la première passe et la moyenne des deux passes : N f = max(N 1 , avg(N 1 , N 2 )). Avec cette formule, on privilégie quand même la première passe, mais on en encourage les étudiants à se rattraper ou à se perfectionner. En effet, la seconde passe permet aux étudiants en retard (ou en difficulté) de continuer à améliorer leurs rendus même après la date limite de la première passe. Ceci est d'autant plus important que, dans le cadre de cette UE, les compétences s'empilent. Cette stratégie d'évaluation « non punitive » est très motivante pour les étudiants qui peuvent continuer à améliorer leur code (et leur note), même après la fin de la première passe. De notre point de vue, cela les encourage à travailler encore davantage !

Mise en oeuvre dans Moodle avec VPL

Rentrons un peu plus dans la partie technique. Pour implémenter cette stratégie d'évaluation, nous avons utilisé l'activité Virtual Programming Lab3 (VPL) dans Moodle (voir figure 6). VPL est un plugin de Moodle qui offre un environnement pour l'enseignement et l'évaluation de la programmation, accessible depuis son navigateur Web. Il permet aux étudiants d'écrire du code dans différents langages de programmation (dans un éditeur de texte intégré à VPL), de le compiler et de l'exécuter directement dans Moodle (via le bouton Run). VPL facilite également l'évaluation automatisée des exercices de programmation (via le bouton Eval), fournissant un retour immédiat aux étudiants. Les avantages de cette approche sont doubles. Toute l'équipe pédagogique s'approprie et contribue activement aux supports de cours. De plus, au lieu de restreindre l'accès aux cours avec des authentifications (intrinsèques à Moodle), nous pouvons rendre les ressources accessibles en dehors de Moodle, ce qui nous permet de partager notre travail avec le reste de la communauté universitaire 6 .

Conclusion

Nous trouvons cette approche très motivante pour les étudiants, et nous avons de très bons retours 7 . C'est une UE qui demande beaucoup de travail et nous l'annonçons dès le début aux étudiants : « Attention, c'est difficile, il va falloir travailler ! ». Ils le comprennent bien. C'est également une UE qui demande beaucoup de travail pour les enseignants et notamment pour le responsable qui coordonne tout cela. Mais c'est également une UE qui apporte beaucoup de satisfaction.

À la fin de l'année, les étudiants sont souvent très fiers du travail accompli, et de l'ensemble des compétences acquises. Pour l'équipe enseignante, c'est également agréable d'avoir ces retours très positifs des étudiants, et cela nous conforte dans le choix des modalités pédagogiques que nous avons présentées dans cet article. En 6. https://pt2.gitlabpages.inria.fr/support/site. 7. Taux de satisfaction de 78 % sur ces quatre dernières années d'après nos propres enquêtes (anonymes) auprès des étudiants.

1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023 effet, nous avons dépensé beaucoup d'énergie pour mettre en place ces systèmes d'évaluation automatique qui permettent de gérer de grosses cohortes. Un effort a également été fait sur les supports pour gérer une grande équipe pédagogique. Notons que ces efforts, étalés sur plusieurs années, ont été rentabilisés assez rapidement du fait du nombre important d'étudiants à gérer et d'enseignants à coordonner.

Malgré tout, il y a des difficultés intrinsèques. L'écriture de ces scripts et leur maintenance restent des activités fastidieuses et chronophages. Les retours des scripts ne sont pas toujours suffisamment clairs pour les étudiants. De plus, il est difficile d'être exhaustif en anticipant tous les cas possibles. Par ailleurs, il y a toujours des ambiguïtés, des flous qui restent et qui doivent être levés en TD par les enseignants. La gestion des équipes et la configuration de Moodle restent également une charge de travail importante qu'il ne faut pas sous-estimer.

La mise en place au sein de l'équipe pédagogique de toute cette chaîne d'intégration continue facilite grandement la mise à jour collaborative des supports de TD. Cette fluidité est un ingrédient important qui nous encourage à toujours améliorer nos supports.

Pour finir, il faut noter qu'il y a aussi des bénéfices cachés au système de correction automatique. D'abord, il est plus satisfaisant pour l'enseignant de programmer des scripts (même en bash) plutôt que de lire n fois le même code avec les mêmes erreurs. Il y a également un changement de posture intéressant de l'enseignant visà-vis de l'étudiant. En effet, il n'est plus celui qui pointe du doigt les erreurs. Il se trouve du côté des « gentils » qui aident les étudiants à affronter ce « méchant » script pour que les étudiants puissent finalement avoir de bonnes notes. Notons toutefois, que ces scripts aussi sophistiqués soient-ils, ne sont qu'une aide à la notation, et qu'il est toujours possible à l'enseignant « humain » d'amender manuellement une note si cela se justifie, ce que nous faisons régulièrement pour prendre en compte les situations particulières des différentes équipes.

FIGURE 1 .

 1 FIGURE 1. Différents exemples de jeux réalisés ces dernières années : Takuzu, Bridges, Light Up.

FIGURE 2 .

 2 FIGURE 2. Scenario pédagogique, illustrant les principales étapes dans la réalisation du projet par les étudiants.

FIGURE 3 .

 3 FIGURE 3. Ensemble des interfaces graphiques produites cette année par les équipes étudiantes pour le jeu Takuzu.

FIGURE 4 .

 4 FIGURE 4. Découpage des jalons sur l'année.

FIGURE 5 .

 5 FIGURE 5. Supports pour un TD type sur Moodle.

FIGURE 6 .

 6 FIGURE 6. Utilisation du plugin VPL dans Moodle.

FIGURE 7 .

 7 FIGURE 7. Vue d'ensemble de notre infrastructure technique pour VPL. Par rapport à ce scénario standard, nous avons apporté quelques ajustements. Tout d'abord, nos scripts d'évaluation ne sont pas codés et hébergés dans la plateforme Moodle, mais dans un dépôt Git à part. Cela permet de les versionner et de faire un peu d'intégration continue sur nos scripts. Enfin, par rapport à l'infrastructure classique, nous avons mis en place un système de Docker 4 pour contrôler précisément l'environnement d'exécution et garantir qu'il soit vraiment similaire aux conditions de travail en TD. Tous ces ajustements, ainsi que le développement d'une boîte à outils 5 , nous ont permis d'avoir assez de flexibilité pour mettre en place de nombreuses

-Bulletin de la Société informatique de France -numéro 22, novembre 2023

https://www.chiark.greenend.org.uk/~sgtatham/puzzles.1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023••••••••

https://vpl.dis.ulpgc.es.1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023

https://github.com/GuillaumeBlin/vplbdx, développé par Guillaume Blin.

https://github.com/orel33/vpltoolkit développé par Aurélien Esnard.1024 -Bulletin de la Société informatique de France -numéro 22, novembre 2023

Remerciements

Merci à tous ceux qui sont intervenus dans cette UE et qui ont participé à son amélioration au cours de ces 10 dernières années, en particulier Guillaume Blin, Pierre-André Wacrenier, Paul Dorbec, Abdou Guermouche et Vincent Penelle. Merci également à tous les enseignants qui ont pris courageusement l'aventure en chemin. Merci également à l'équipe technique du CREMI, et plus particulièrement Christophe Delmon, pour leur soutien permanent.


Cécile Vanpé

MALE MATING SYSTEMS AND SEXUAL SELECTION IN UNGULATES

Strong reciprocal relationships have long been suspected between mating systems and sexual selection, and so different angles of discussion can be pursued to investigate these relationships. In this essay, mating systems are regarded as one of the factors that may influence the strength and consequences of sexual selection. The ungulates show a wide variety of mating systems, and though most ungulate species are polygynous, male mating tactics range from non-territorial males courting individual estrous females, to both female-defense harem systems and resource-defense territorial systems, and to leks. It is thus interesting to focus on this group to investigate the scope for development of sexual selection in relation to various mating tactics. Based on behavioural ecology and sexual selection theories, it is possible to propose several predictions concerning mechanisms of competition over mates and sexually selected traits favoured by each ungulate mating tactic. The aim of this essay is to review the main sexually selected traits reported in ungulate studies, with special reference to the Cervidae, the Bovidae and the Antilocapridae, and to discuss the fit of them with the theoretical predictions.

Contents

Introduction

Mating systems are defined by the reproductive strategies adopted by individuals of both sexes in order to mate [START_REF] Clutton-Brock | Mammalian mating systems[END_REF]. The ultimate aim of these behaviors can be viewed as the maximization of the relative genetic contribution to subsequent generations. According to general theories of the behavioral ecology, optimal mating strategies tend to be different for the two sexes, because of the size difference between male and female gametes: females produce few large macrogametes rich in energy, whereas males produce a lot of small, highly mobile microgametes [START_REF] Trivers | Parental investment and sexual selection[END_REF]. According to [START_REF] Trivers | Parental investment and sexual selection[END_REF], this difference in the size of the gametes can be expressed as a difference in parental investment between the sexes. Females usually allocate more energy in parental investment (including investment in the production of gametes, in the nourishing of the embryo and in the care of offspring) than males. The consequence of this difference in parental investment between the sexes is that males can make many more gametes than females and have the capacity to fertilize a number of females and father a number of young. They should thus attempt to mate with as many fecund females as possible [START_REF] Trivers | Parental investment and sexual selection[END_REF]. Females, on the other hand, need only one male to be fertilized. Their investment in fewer but larger gametes should make them more careful in their choice of mating partner.

As a consequence, many sexually active males will be searching at a given moment for relatively few receptive females, leading to competition among males for mates, while providing opportunity for females to choose among potential mates. These processes lead to Sexual Selection [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF], which concerns variation among individual traits of one sex that affect success in competition over mates and fertilizations. If the differences in the traits are hereditary, sexual selection will lead to the spread of those attributes that enhance reproductive success. The sexual selection of a trait can then be viewed as the differences in reproductive success, caused by competition over mates, and related to the expression of the trait [START_REF] Andersson | Sexual selection[END_REF]. [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF] proposed two main mechanisms of mating competition leading to sexual selection of a trait. First, via contest competition (leading to intrasexual selection), which consists of fighting between males to gain access to females. This type of competition over mates creates a selection pressure favoring the development of male traits that enhance their ability to fight and dominate (e.g., increase of body size ; elaboration of organs used as weapons). Second, via mate choice (leading to intersexual selection), which consists of competition between males to attract the females. It leads to the elaboration of structures or behavior patterns that attract females, and that could be reliable indicators of male phenotypic quality. Different signals such as body size, secondary sexual characteristics (e.g., antler size), or behaviors reflecting vigor (e.g., vocalization, display, status) can be used to show male quality. The type of competition over mates favored by sexual selection and the expression of secondary sex traits will differ between the various mating systems. In fact, the mating system can be viewed as one of the main factors that influence the strength and consequences of sexual selection (for a review see [START_REF] Andersson | Sexual selection[END_REF]. The purpose of this essay is to investigate the relation between male mating systems and sexual selection in ungulates.

The ungulate group consists of medium sized and large herbivorous mammals. It is classified into five orders: i.e., Artiodactyla (e.g., donkeys, camels, pigs, hippopotamus, peccaries, deer, musk deer, bovids, giraffes), Perissodactyla (e.g., horses, zebras, tapirs, rhinoceroses), and the three primitive orders Hyracoidea, Tubulidentata and Proboscidea (e.g., elephants). The ungulates show a wide variation in morphology, behavior, and social organization among species. The following mating systems have been reported: harem defense, lekking, roving, territoriality [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF]. It could be thus interesting to focus on ungulates to investigate the differential scope for development of sexual selection in relation to variation in mating systems. I will focus mainly on the case of territoriality, which is very common in ungulates but with a varying incidence among the different families: though territoriality is prevalent among most of the antelope of the subfamily Bovinae, appearing also in some equids, rhinoceros, camelids and antilocaprids, it is generally absent with few exceptions in the wild cattle tribe (Bovini), in sheep and goat (Caprinae), and in deer (Cervidae) [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF].

In my essay, I will thus first review the various mating tactics occurring in ungulates in relation to the ecological factors (environmental and sociological) that promote their evolution. I will then expose the potentiality for sexual selection associated with each mating tactic, with special reference to territorial ungulates. Finally, I will give a background to the main sexually selected traits that have been reported in male ungulates, before discussing their fit to our expectations.

VARIABILITY OF MALE MATING SYSTEMS IN MAMMALS a) From monogamy to promiscuity

The ideal way for a male to maximize his reproductive success may be to mate with as many females as possible, leaving the females to provide for all parental care. For a female, the ideal may be to mate and then leave the male to care for the offspring while she accumulates reserves for a future litter [START_REF] Krebs | Parental care and mating systems[END_REF]. In practice, the apparent conflict of interest in the optimal mating strategies of the two sexes will be resolved according to two factors. First, different species have different physiological and life history constraints which predispose one sex to provide more parental care than the other. Second, ecological factors will influence the costs and benefits associated with parental care and mating tactics [START_REF] Krebs | Parental care and mating systems[END_REF]. Depending on the parental care constraints, different mating tactics should then be favored.

Although different mating systems have long been recognized in evolutionary biology, there is no strict agreement on their classification [START_REF] Andersson | Sexual selection[END_REF]. The number of mating partners per male and female is one of the main criteria. Monogamy (a male and a female form a pair bond) should be favored mainly when males and females share parental care for the young after birth and in some cases for the eggs. This is the case in the great majority of bird species, but in very few mammals [START_REF] Krebs | Parental care and mating systems[END_REF]. Polygyny (a male mates with several females, while each female mate with only one male) should be favored particularly when females are strongly predisposed to care for the young (for example because of the prolonged period of gestation and the lactation constraints). This is the case in most mammals, in which males usually provide little parental care after birth, and so females take sole responsibility for the care for the young in order to improve the odds that the offspring will reach reproductive age and transmit the parent's genes. Two other cases occur, but are more infrequent: polyandry (a female mates with several males, while each male mate with only one female) and promiscuity (both male and female mate several times with different individuals so there is a mixture of polygyny and polyandry). In the first case, it is often the male who provides most parental care, whereas in the second case, either sex may care for the eggs or young [START_REF] Krebs | Parental care and mating systems[END_REF].

Among ungulate species, while polygyny is widespread, monogamy [START_REF] Kleiman | Monogamy in mammals[END_REF]) and promiscuity [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF] have been also reported.

b) Male mating tactics among polygynous mammals

In mammals, most species have a polygynous mating system. The reproductive success of females is mainly limited by access to resources necessary to breed and to meet the energy requirements of gestation and lactation (e.g., food, breeding sites), whereas the reproductive success of males is limited more by access to females [START_REF] Trivers | Parental investment and sexual selection[END_REF]. As a consequence, while the distribution of females should depend primarily on resource dispersion (modified by predation pressure and the costs and benefits of associating with other individuals), males should distribute themselves in relation to female dispersion in order to gain access to as many mates as possible [START_REF] Krebs | Parental care and mating systems[END_REF]. [START_REF] Clutton-Brock | Mammalian mating systems[END_REF] concludes that the variation in mating behavior of male mammals depends mainly on the defensibility of females, that is directly related to the density and distribution of females, female range size and female group size and stability, and indirectly to the distribution of resources.

Yet males in mammals may have two main options to maximize the number of matings: they could compete for females either directly in male-male contest or indirectly by anticipating how resources will influence female dispersion and competing for resource-rich sites.

The first strategy, named « female defence polygyny » (Elmen & Oring 1977), should be favored when the possibility of finding a receptive female in any one location is low, e.g., at low population densities or when food is unpredictable and females range over large areas. In this case, males gain access to females by following and defending directly one or a group of females against rivals, instead of waiting for the females.

-Where females live in small groups, males can rove and try to associate with individuals in oestrus [START_REF] Krebs | Parental care and mating systems[END_REF]: this is the « roaming » or « roving » strategy. This mating system is represented among various ungulate species: e.g., white-tailed deer Odocoileus virginianus [START_REF] Hirth | Social behavior of white-tailed deer in relation to habitat[END_REF], moose Alces alces [START_REF] Whitehead | Deer of the world[END_REF], bighorn sheep Ovis canadensis [START_REF] Hogg | Intrasexual competition and mate choice in Rocky Mountain sheep[END_REF], Soay sheep Ovies aries [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF], greater kudu Tragelaphus imberbis [START_REF] Owen-Smith | Age, size, dominance and reproduction among male kudus: mating enhancement by attrition of rivals[END_REF].

-Where female groups are larger, the most dominant males may attempt to defend these groups, constituting some « harems » [START_REF] Krebs | Parental care and mating systems[END_REF]. This is the mating system of red deer Cervus elaphus (Clutton-Brock et al. 1979, 1982), Burchell's zebra Equus burchelli [START_REF] Klingel | A comparison of the social behaviour of the Equidae. Pp. 124-132[END_REF], African buffalo Syncerus caffer [START_REF] Sinclair | The African buffalo -A study of resource limitation of populations[END_REF], or reindeer Rangifer tarandus [START_REF] Barrette | Sparring, relative antler size, and assessment in male caribou[END_REF], etc.

The second strategy, named « resource defense polygyny » (Elmen & Oring 1977), should be favored when females are spatially predictable, e.g., when females occupy small ranges containing clumped and high-quality food resources. In this case, males gain access to females indirectly by defending a space against other males and controlling an area with certain vital resources that females require (food, birth sites) and where females can occupy small ranges. This strategy is characterized by « territoriality », which is usually defined in terms of defence, exclusion and site-specific dominance [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF]. This strategy is particularly common among African antelopes (e.g., impala, Aepyceros melampus ; defassa waterbuck, Kobus defassa: see Owen-Smith 1977) ; but it also exists in various ungulate family groups: Cervidae (e.g., roe deer Capreolus capreolus: Bramley 1970, Sika deer Cervus nippon: Miura 1984, Reeves's muntjac Muntiacus reevesis: [START_REF] Barrette | Fighting behavior of muntjac and the evolution of antlers[END_REF], Bovidae (e.g., American pronghorn Antilocarpa americana: [START_REF] Kitchen | Social behavior and ecology of the pronghorn[END_REF], Suidae and Hippopotomidae (see review in [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF].

Lastly, when neither females nor their home range are defensible, males may aggregate into groups on a communal display area where each male defends a tiny mating territory containing no resources at all and attempts to attract and court females which visit the lek solely for mating [START_REF] Clutton-Brock | Mammalian mating systems[END_REF][START_REF] Höglund | Leks[END_REF]. Males in this case provide no material resources, only genes. These mating systems are known as « leks » or « male dominance polygyny » (e.g., Grevy's zebra Equus grevii, Uganda kob Kobus kob, Clutton-Brock 1989 ; fallow deer Dama dama, [START_REF] Apollonio | Lekking in fallow deer: just a matter of density?[END_REF]).

It should be noted that mating tactics do not only vary between species, but also within species, depending on environmental factors such as population density, habitat, climate, predation pressure (e.g., [START_REF] Lott | Intraspecific variation in the social systems of wild vertebrates[END_REF][START_REF] Thirgood | Intraspecific variation in ungulate mating strategies: The case of the flexible fallow deer[END_REF]. This seems to be particularly marked for the fallow deer, for which mating systems range from non-territorial males courting individual estrous females (roaming), to both resource-defense polygyny and femaledefense harem systems and to leks [START_REF] Langbein | Variation in mating systems of fallow deer in relation to ecology[END_REF]).

POTENTIALITY FOR SEXUAL SELECTION IN VARIOUS MATING SYSTEMS

The strength of sexual selection and the type of competition over mates favored by sexual selection will differ between the various mating systems.

a) Influence of mating system on sexual selection strength

Intuitively, it seems likely that the opportunity for sexual selection should increase with party size [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF]. Previous studies on ungulates (e.g., Jarman 1983) described a continuum of sexual selection intensity with at one extreme, monogamous and monomorphic species, exhibiting similar life-history traits in both sexes, and at the other, highly polygynous and dimorphic species, with differential life-history traits between sexes. In polygynous species, where some males mate with several females and others with none, success in competition over mates is indeed crucial for the fitness of males, the variance in male mating success is usually high and sexual selection is often strong [START_REF] Andersson | Sexual selection[END_REF]). However, although there is little scope for competition leading to sexual selection in monogamous species when each individuals mate with only one other individual during each breeding cycle and when pair bonds are generally stable, sexual selection might also act in these species (e.g., [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF]. Indeed, under strict monogamy, no individual has more than one mate, but some males may have none in the case of skewed sex ratios [START_REF] Andersson | Sexual selection[END_REF]). In addition, mates vary in fecundity or parental ability depending on age, condition, and other aspects. Such differences in quality among mates can lead to sexual selection [START_REF] Andersson | Sexual selection[END_REF], favoring for example ever-earlier preparedness to breed [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF]. Lastly, in many species especially in birds, monogamy is not complete, in the sense that some males achieve higher reproductive success through extra-pair copulations [START_REF] Andersson | Sexual selection[END_REF].

b) Mechanisms of mate competition favored by the various male mating tactics

In lekking, males establish dominance relationships among themselves and female then choose between them, largely on the basis of their status and probably independently of direct material benefits. Sexual selection tends therefore to be inter-sexual and this favors the evolution of some very extreme male epigamic characters and elaborate male behaviors (Krebs & Davies 1978) ; however male contest competition may also be involved [START_REF] Andersson | Sexual selection[END_REF]. Moreover, as females are usually not synchronized in their periods of sexual activity, and only a small proportion of them will visit the male aggregation at any time, inter-male competition for mates is thus intense and mating success often varies greatly among the males on a lek [START_REF] Andersson | Sexual selection[END_REF]. Sexual selection and dimorphism are thus expected to be stronger in lekking than in other related species [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF].

In the case of resource defence polygyny (territoriality), male behavioral interactions readily interpreted as active defence (advertisement, threat, and attack) of the territory may be infrequent and several authors have emphasized the importance of a subjective boundary modifying behavior inside and outside the delineated area, or talked about a dominance depending on location with a reciprocity of dominance among neighboring territory holders (see [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF][START_REF] Geiger | Rank order of roe deer at artificial winter feeding sites in a Swiss hunting district[END_REF][START_REF] Kitchen | Social behavior and ecology of the pronghorn[END_REF]. Territorial systems should thus provide the conditions in which intrasexual selection will favor the enhancement of characters needed mainly for assessing male dominance, status and fighting ability, and for successfully defending the territory without involving fights (Krebs & Davies 1978). Moreover, female choice should be mainly directed not towards the males themselves but towards the quantity or quality of the resources that the males are defending. Mating systems of this type will thus generally not lead to the evolution of male epigamic characters through intersexual selection.

Female defence polygyny (harem and roving) may arise as an extension of resource defence polygyny, male aggressive behaviors not being directed mainly to the defense of an area but of the females attracted to that area. In this case, direct male-male interactions are common and sexual selection should be primarily intrasexual, favoring the development of characters that enhance male strength and fighting ability (Krebs & Davies 1978), while female choice may not be important.

c) Potentiality for sexual selection in territorial ungulates

In territorial ungulate species, the number of resident females present in the various male territories can vary widely. Such differences in number of potential mates seems to contribute to variability of reproductive success of individual males and the number of female ranges overlapping the territory seems to limit seasonal mating success for a territorial male (e.g., in roe deer: [START_REF] Liberg | Mating tactics and success in male roe deer -effects of age and territory[END_REF]. According to sexual selection theory, neighboring territorial males should thus attempt to enhance their access to receptive females still further by maximizing the number of female ranges overlapping their territory. This could be done in two different, but not exclusive, ways: either by enlarging their zone of dominance, or by occupying territories in areas particularly favored by females during the main breeding period [START_REF] Owen-Smith | On territoriality in ungulates and an evolutionary model[END_REF], since the distribution of receptive females is influenced by variation in resource distribution in mammals. This is expected in resource defence polygyny where, by definition, males defend a resource that is attractive to females. We can thus expect that male territory size and/or habitat quality in male territory might be sexual selected traits in territorial ungulates.

But as pointed out by Balmford et al. (1992), male quality and territory quality are often intercorrelated, and it is often not possible to disentangle them. Indeed, intrasexual competition among males is likely to produce a situation where the most competitive males occupy the largest territories or the territories preferred by females. If characters of males that allow success in intrasexual competition are those that are sought after by females, there would be no need for females to choose among males according to male phenotypic quality. Females can simply choose the best territories, and male-male competition would ensure that those territories were occupied by the best males [START_REF] Apollonio | Site-specific asymmetries in male copulatory success in a fallow deer lek[END_REF]). However, it is possible that females would gain by choosing males according to characteristics (structures or behavior patterns) other than those important in intrasexual competition that could be reliable indicators of male phenotypic quality. A conflict may then exist because the preferred males would not necessarily be in the preferred territories. In this case, females should also select territories partly because of the characteristics of defending males [START_REF] Apollonio | Site-specific asymmetries in male copulatory success in a fallow deer lek[END_REF]). When males defend mating territories, females can therefore be attracted to them by the area itself because it contains some resources (e.g., food, shelter from predators), the males, or some component of both. In conclusion, we can expect that sexual selection in territorial species may act on male individual characteristics that enhance the fighting ability/dominance ranks of males and/or their attraction for females (e.g., body size/weight/condition and weapon/ornament size).

SEXUALLY SELECTED TRAITS IN MALE UNGULATES

In this section, I will attempt to give a background to the main sexually selected traits that have been reported in male ungulates, focusing mainly on territorial ungulates and with special reference to Cervidae, Bovidae and Antilocapridae (see appendice 1). The main criteria for the inclusion of a study in this review was that it demonstrates a statistically significant relationship between the quantitative variation in a character and mating success. In a few cases however, despite the lack of such a demonstration, some studies, for which results strongly suggest a role of a character in male contests or female choice, have also been included.

a) Body size, body mass and body condition

Larger male than female size, typical of most birds, mammals (especially in ungulates), and some reptiles, amphibians, beetles, crustaceans, and certain other groups, has usually been explained by a size advantage in contests over females (e.g., [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF].

Studies of a wide variety of vertebrate species, in which fights are decided by contests involving pushing, have thus found that larger male size often gives an advantage in dominance contests and fights over females. However, few of them have clearly shown that dominance also leads to higher production of offspring (reviewed by [START_REF] Clutton-Brock | Reproductive success[END_REF]. For instance, Mc Elligott et al. (2001) have shown in fallow deer that male mating success was directly related to body size and that there is an indirect relationship between mating success and male body mass via prerut dominance rank. In Soay sheep too, body size is influential in determining access to females and should be a significant predictor of siring success, regardless of the size of their testes and horns [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF]. In bighorn sheep, [START_REF] Coltman | Age-dependent sexual selection in bighorn rams[END_REF] showed that mating success is positively correlated with body weight within and across years. In red deer finally, body size and body weight also affect reproductive success. Stags that were considerably lighter than their opponents usually lost contests. Though not all large stags were good fighters, individuals that were consistently successful in fights and held large numbers of hinds in several seasons were almost always of more than average size [START_REF] Clutton-Brock | Red deer -Behavior and ecology of two sexes[END_REF]. Evidence for a relationship between body size and reproductive success was also provided by the fact that lifetime reproductive success among stags was well correlated with mean antler weight, which is known to be related to body size and weight in red deer (e.g., Clutton-Brock et al. 1979).

But large size may also give an advantage in endurance rivalry, permitting a male to spend longer time especially at a breeding site and compete for females [START_REF] Bartholomew | A model for the evolution of pinniped polygyny[END_REF]. In Soay sheep for instance, [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF] suggested that body condition is important in determining mating success. Indeed, before gaining access to receptive females, males spend a lot of time roving, trying to locate females, and examining ewes for signs of oestrus. This time is particularly costly in terms of energy: males are estimated to lose 30% of their body weight by the end of the rut. Thus, physical exhaustion may limit the success of males in poor condition to find receptive females. In red deer too, stags in poor condition seldom rutted successfully since they often failed to secure harems, and Clutton-Brock et al. (1982) suggested that body condition determines male reproductive success.

Furthermore, male body size has been reported to be related to mating success, via sequestering of females and forced copulation, or sperm competition if large size leads to higher sperm production (Wedell 1997, cited in Mc Elligott et al. 2001). Sperm competition has been noted for instance in Soay sheep [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF]. The authors found that larger testes are independently associated with both higher copulation rates and increased siring success.

Finally, another advantage would be female preferences for large males, for example because larger males may provide more resources than smaller males or because body size may be a honest signal of genetic quality of the male (see Andersson 1994 for review). A study of genetic variability in the major histocompatibility complex in white-tailed deer suggested thus that body size may provide an advertisement of heritable male quality (Ditchkoff et al. 2001) and so females may act on this cue to select mates (Ditchkoff et al. 2001).

b) Weapon size and asymmetry

Ungulate antlers and horns have received enormous attention since [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF] developed his theory of sexual selection, and several hypotheses have been proposed to explain their evolution (e.g., [START_REF] Clutton-Brock | The function of antlers[END_REF][START_REF] Geist | The evolution of horn-like organs[END_REF][START_REF] Lincoln | Biology of antlers[END_REF] for reviews), in the framework of male competition over females.

A widespread idea is that horns and antlers in ungulates are used as weapons against rival males during the mating season (e.g., [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF][START_REF] Geist | The evolution of horn-like organs[END_REF]. Large horn and antler size (irrespective of age, body size, condition and testes size) is often associated with increased access to receptive females due to the advantage that they confer in intrasexual combat. Death and high levels of damage due to fighting have been reported several times among ungulates (e.g., in red deer: Clutton-Brock et al. 1979). But horns and antlers could also function defensively, acting as shield (e.g., [START_REF] Geist | The evolution of horn-like organs[END_REF][START_REF] Clutton-Brock | The function of antlers[END_REF]. The behavioral advantage of large horns and antlers should translate into reproductive success, with larger-horned and larger-antlered males siring more offspring. [START_REF] Clutton-Brock | The function of antlers[END_REF] demonstrated that in red deer the antler's weight was well correlated with reproductive success. But mean antler weight is known to be related to body size and weight in red deer (Clutton-Brock et al. 1979). However, [START_REF] Kruuk | Antler size in red deer: heritability and selection but no evolution[END_REF] showed that antler size, which are used by males as weapons in fights over access to females, was significantly correlated with male breeding success in red deer, in a given year but also across an individual's lifetime, and both before and after correcting for body size. Besides, experimental removal of antlers reduces reproductive success in male red deer and reindeer via a reduction of their fighting ability and dominance status [START_REF] Espmark | Studies in dominance-subordination relationship in a group of semi-domestic reindeer (Rangifer tarandus L.)[END_REF][START_REF] Lincoln | The role of antlers in the behaviour of red deer[END_REF], Clutton-Brock et al. 1982). This indicates that antlers are important in competition among males, even if other factors such as age, body size, and condition also play a role. It has also been shown that the number of offspring sired in a given year increases with male horn size in bighorn sheep [START_REF] Coltman | Age-dependent sexual selection in bighorn rams[END_REF] and in Soay sheep [START_REF] Preston | Overt and covert competition in a promiscuous mammal: the importance of weaponry and testes size to male reproductive success[END_REF]. In muntjac, [START_REF] Barrette | Fighting behavior of muntjac and the evolution of antlers[END_REF] demonstrated that antlers clearly play a role as weapons in intrasexual competition over female access. In roe deer finally, a positive correlation has been found between antler size and yearling dispersal tendency, due to male-male aggression, which is directed mainly against the most sexually mature yearlings, as antler size is also correlated with testicle size [START_REF] Wahlström | The significance of male-male aggression for yearling dispersal in roe deer (Capreolus capreolus)[END_REF]. Subadults with well developed antlers are more frequently harassed by territorial males than subadults with poorly developed antlers, supposing that the former are a bigger threat in terms of mating competition.

While large horns and antlers are efficient weapons in fights between males, they may also be used in display for intimidating opponents (e.g., [START_REF] Geist | The evolution of horn-like organs[END_REF][START_REF] Lincoln | The role of antlers in the behaviour of red deer[END_REF], functioning as indicators of male strength and fighting ability for other males. Horn and antler size is correlated with body size and nutritional condition, and hence probably also with strength (e.g., [START_REF] Clutton-Brock | Red deer -Behavior and ecology of two sexes[END_REF]. Males might therefore assess each other in part by the size of horns and antlers, avoiding fights with superior competitors (e.g., [START_REF] Geist | The evolution of horn-like organs[END_REF], Clutton-Brock et al. 1982). [START_REF] Geist | The evolution of horn-like organs[END_REF] put forward that this may be the case in bighorn sheep. In reindeer, [START_REF] Barrette | Sparring, relative antler size, and assessment in male caribou[END_REF] distinguished between fighting (which is very violent, occurs between matched males, can cause injury and death, and is quite rare) and sparing (which usually starts slowly and is gentle, the animals carefully adjusting their antlers before pushing and twisting). In sparring, the animals with the smallest antlers initiated about half of the matches, but withdrew in almost 90% of them. The authors suggested therefore that frequent sparring could be a form of tactile assessment of fighting ability, which might later permit visual assessment of other males based on their antler size. So antlers in reindeer may play a role in male assessment of competitors. In roe deer finally, [START_REF] Liberg | Mating tactics and success in male roe deer -effects of age and territory[END_REF] found a correlation between a measurement of dominance and mating success in roe bucks, indicating the importance of male quality; but they found no correlation between mating success and conflict frequency, i.e. bucks that were involved in many conflicts irrespective of outcome, were not better or worse than bucks that lived more peacefully. In fact, one of the most successful bucks, that had three consecutive mating seasons, with a high number of overlapping females, and high tending and copulation scores, was never seen to interact with any competitor, simply because the author never saw any other bucks in or near his territory. His territory must have been very attractive, and the only reason for the absence of intruders may be that this male was so superior in strength that no competitors bothered or dared even to approach him. The antler size could so play a major role in the dominance hierarchy between males, acting as intimidation weaponry: males with small antlers could remain subordinate to males with larger antlers during interactions.

Finally, large weaponry in ungulates may be preferred by females, as an indicator of male quality, sexual vigor or condition (e.g., Darwin 1871) and cervid females would selectively breed with large-antlered males. Choosing a male with large weapons might thus lead to immediate benefits for females, such as a reduced risk of being courted by young, inexperienced males with inept mating behavior that may harm the females [START_REF] Clutton-Brock | The function of antlers[END_REF]. By responding only to males who have fully developed epigamic characters and who display vigorously and persistently, females ensure that they mate with fully mature and sexually competent males. Choosing a male with large antlers that reflect good condition, a female might also make it more likely that her offspring will be of high quality, to the extent that it is heritable. But there is, however, few evidence in mammals that females choose a mate in relation to the size of his weapons [START_REF] Clutton-Brock | The function of antlers[END_REF]. According to [START_REF] Clutton-Brock | Mate choice on fallow deer leks[END_REF], females, in fallow deer, may choose mates on the base of male antler size. A study of genetic variability in the major histocompatibility complex in white-tailed deer suggests also that antler development may provide an advertisement of heritable male quality (Ditchkoff et al. 2001a) and so females may act on this cue to select mates. [START_REF] Geist | The evolution of horn-like organs[END_REF] also suggested that horn size in bighorn sheep serves in intersexual selection. But there is no evidence that antlers are subject of female choice in red deer [START_REF] Clutton-Brock | The function of antlers[END_REF].

Sexual selection is, moreover, often associated with asymmetry, with symmetric individuals enjoying improved mating success (Møller & Thornhill 1998), and this effect seems greater than that for size of the same characters (Thornhill & Møller 1998). Fluctuating asymmetry (FA) refers to small random deviations from perfect bilateral symmetry in the development of a morphological trait (such as weapons and ornaments), normally distributed around a mean of zero [START_REF] Van Valen | A study of fluctuating asymmetry[END_REF]. Under the hypothesis that the degree of FA in secondary sex traits reflects the ability of males to cope adequately with environmental stress or physical damage during the development of the character, FA should reflect male quality and so might be used by females in intersexual selection to select mates, or by males in intrasexual selection to infer competitor quality. If the trait development (e.g., antler size) reflects individual quality, a negative relationship is expected between this trait development and the degree of FA [START_REF] Møller | Patterns of fluctuating asymmetry in weapons: evidence for reliable signaling of quality in beetle horns and birds spurs[END_REF]. Several studies have thus found a negative relationship between FA and weapon size, showing thus that the degree of FA in antler or horn size can reflect individual quality, but few of them controlled for age and body mass [START_REF] Kruuk | Fluctuating asymmetry in a secondary sexual trait: no associations with individual fitness, environmental stress or inbreeding, and no heritability[END_REF]. Examination of FA in moose antlers reveals that asymmetry is less and number of antler points is greater in large-antlered males, which presumably do most of the breeding [START_REF] Solberg | Fluctuating asymmetry in the antlers of moose (Alces alces)does it signal male quality[END_REF][START_REF] Bowyer | Fluctuating asymmetry in antlers of Alaskan moose: size matters[END_REF], but there was a negative relationship between FA and the carcass mass of an individual after correcting for antler size and this relationship changed with age. In reindeer too, the degree of FA antlers is negatively related with antler size and is positively correlated with parasite burden, so antlers could be visual indicators of individual quality [START_REF] Markusson | Reindeer antlers: visual indicators of individual quality?[END_REF]. In roe deer, absolute FA significantly decreased with age. It also tended to decrease with antler size at constant carcass mass and within age classes. Antler development could therefore represent a reliable signaling of individual quality [START_REF] Pélabon | Asymmetry in antler size in roe deer (Capreolus capreolus): an index of individual and population conditions[END_REF]. According to Ditchkoff et al. (2001b), FA of antlers of white-tailed deer follows patterns predicted for sexually selected traits, so may be reliable signals of male quality and, as such, may be important in maintaining honesty in intrasexual advertisements during breeding. Yet some studies have reached opposite conclusion, for instance in mountain goat and bighorn sheep, in which asymmetry in horn size did not reflect individual quality in males (Côté & Festa-Bianchet 2001, Fitzsimmons et al. 1995). Besides, almost no studies have tested for a direct association between FA in male weaponry and mating success in ungulates or have investigated whether females select mates based on FA [START_REF] Kruuk | Fluctuating asymmetry in a secondary sexual trait: no associations with individual fitness, environmental stress or inbreeding, and no heritability[END_REF]. While [START_REF] Malyon | Fluctuating asymmetry in antlers of fallow deer, Dama dama, indicates dominance[END_REF] report a negative association between measures of FA and dominance rank in eight farmed fallow deer, [START_REF] Pélabon | What, if anything, does visual asymmetry in fallow deer antlers reveal?[END_REF] found no association between levels of asymmetry and dominance rank in a sample of 45 male fallow deer in a zoo population. [START_REF] Miura | Social behavior and territoriality in male sika deer (Cervus nippon Temminck 1838) during the rut[END_REF] found that the rank of sika deer males was directly related to the configuration of the antlers. In red deer, it seems on the contrary that FA in male antler size did not predict either annual or lifetime breeding success [START_REF] Kruuk | Fluctuating asymmetry in a secondary sexual trait: no associations with individual fitness, environmental stress or inbreeding, and no heritability[END_REF].

c) Territory size, location, and habitat quality

The importance of habitat quality and territory size for male reproductive success is well documented in birds (e.g., [START_REF] Verner | The influence of habitats on mating systems of North American passerine birds[END_REF], see also Anderson 1994). It has also been suggested in a few ungulates, but data on male lifetime reproductive success are lacking in most of these studies to demonstrate the relationship between territory size, location or habitat quality, and male fitness. For pronghorns, in which males defend feeding territories, [START_REF] Kitchen | Social behavior and ecology of the pronghorn[END_REF] demonstrated thus a positive correlation between forage quality in a territory and the mean number of females present or male mating success. In a fallow deer lek in Italy, females appear to choose mates partly on the basis of location, and thus males should compete for ownership of territories preferred by females [START_REF] Apollonio | Site-specific asymmetries in male copulatory success in a fallow deer lek[END_REF]. In a population of red deer with harem mating system, male reproductive success was affected by the area where the stag rutted [START_REF] Clutton-Brock | Red deer -Behavior and ecology of two sexes[END_REF]. At Kilmory and Samhnan Insir, where large numbers of hinds gathered on the greens, the reproductive success and harem size of stags was higher than in the Intermediate Area or the Upper Glen, where there were fewer hinds. In a population of red deer with resource defence polygyny, [START_REF] Carranza | Female attraction by males versus sites in territorial rutting red deer[END_REF] fenced territories so that the territorial males had to defend a new territory at a different site. He showed that females are attracted by the area rather than by the male, and therefore the success of a territorial male largely depends on the location of his territory. In roe deer finally, the quality of the territory, but not territory size, seems to influence male mating success according to [START_REF] Liberg | Mating tactics and success in male roe deer -effects of age and territory[END_REF], and males with clover fields in their range had the highest success .

d) Other potential sexually selected traits

• Chemical signals

It has long been known that scent is used for mate attraction in insects, and for territorial marking in mammals (e.g., [START_REF] Gosling | A reassessment of the function of scent marking in territories[END_REF]. Many male mammals scent-mark their home range or defended territory. Territorial scent marking might play a role in attraction or physiological priming of mates, especially in some small mammals, which could play important roles in reproductive competition and sexual selection. Females might discriminate among males in relation to their odors (for example between dominant and subordinate males). Odors from adult males may also accelerate puberty in juvenile females, induce oestrus and ovulation and facilitate pregnancy in adult females, delay puberty in juvenile males, and perhaps reduce testosterone levels in other adult males [START_REF] Andersson | Sexual selection[END_REF]. For the male, such effects on females should often increase his mating and fertilization success. Several aspects suggests that male scent marking may also be related to contest competition over mates [START_REF] Andersson | Sexual selection[END_REF]. Males mark more than females, dominant males and territory holders mark more than others, and males often mark conspicuously during contests with others [START_REF] Ralls | Mammalian scent marking[END_REF]. Scent marks may thus function in competitor assessment (e.g., [START_REF] Gosling | A reassessment of the function of scent marking in territories[END_REF]. In moose, males dig rutting pits where they deposit odorous urine and females are strongly attracted to and often wallow in those pits. Moreover, mating and parturition are highly synchronized in this species. [START_REF] Whittle | Putative pheromones in urine of rutting male moose (Alces alces): Evolution of honest advertisement[END_REF] suggested that male urine may play an important role in the mating system and in synchronizing reproduction in moose. The authors analyzed male urine, and found potential pheromones. They suggested that these compounds are related to hypophagia and catabolism of body reserves by rutting males, and thereby provide an honest advertisement of body condition by male moose during the mating season. In white-tailed deer, [START_REF] Miller | Putative chemical signals from white-tailed deer (Odocoileus virginianus): Social and seasonal effects on urine volatile excretion in males[END_REF] found some differences in compound presence and concentration of volatiles in urine between dominant and subordinate males and suggested that these differences may produce a rank-specific odor and may serve in the identification of social status in this species.

• Acoustic signals

Song and other acoustic signals are the traits most often shown to be sexually selected, especially in insects, frogs, and birds (see review in [START_REF] Andersson | Sexual selection[END_REF], but also in some mammals. Acoustic signals may be used in contests between males but also for attracting females [START_REF] Darwin | The Descent of Man, and Selection in Relation to Sex[END_REF], as the territory is important for mating success. In wild red deer, male roaring rates reflects male condition and is positively correlated with fighting ability and reproductive success through contest competition (Clutton-Brock & Albon 1979, Clutton-Brock et al. 1979) and also with female choice. In two-choice loudspeaker tests with farmed red deer, females were attracted to high roaring rates and to leading bouts of roars [START_REF] Mc Comb | Female choice for high roaring rates in red deer, Cervus elaphus[END_REF]. In another experiment, females exposed to playback of roaring ovulated earlier than control females [START_REF] Mc Comb | Roaring by red deer stags advances the date of ooestrus in hinds[END_REF]. This suggests that roaring may enhance male success both by attracting hinds and by making them more likely to ovulate and mate before being taken over by another stag. [START_REF] Reby | Red deer (Cervus elaphus) hinds discriminate between the roars of their current harem-holder stag and those of neighbouring stags[END_REF] have also shown, by conducting playback experiments, that hinds are able to discriminate between roars of their current harem-holder stag and those of other neighboring stags and suggested that this ability may be important in female mate choice in red deer. In roe deer finally, [START_REF] Reby | Contexts and possible function of barking in roe deer[END_REF] suggested that barking is linked in part to the expression of territoriality among bucks, and may enable them to identify and locate each other, and perhaps to assess dominance status, particularly during barking / counterbarking sessions involving several animals. It seems indeed that individual differences in propensity to bark are related to dominance.

Discussion / Conclusion

I have identified several traits that may be subject to sexual selection in ungulates (see section 3). A difficulty in such an exercise is to isolate indirectly selected traits from directly selected traits: a trait correlated with mating success may indeed be indirectly selected through correlation with some other, directly selected trait [START_REF] Andersson | Sexual selection[END_REF]. It is also often difficult to separate the roles of mate choice and contests over mates in sexual selection of a trait [START_REF] Andersson | Sexual selection[END_REF]. For example, antlers and horns in ungulates can be used both as weapons and/or as ornaments, and both roles can lead to the selection of their size and symmetry. It seems however that some traits are favored mainly by one of the two mechanisms of competition over mates (see appendice 1). In ungulates, large body size in males seems thus to be usually selected by male contests (e.g., in red deer, fallow deer, Soay sheep and bighorn sheep), and seldom by female choice (e.g., in white-tailed deer). Acoustic and chemical signals are often selected by female choice, sometimes by both female choice and male contests, but seldom just by male contests (e.g., barking in roe deer). Finally, male territory size, location and quality are selected by only female choice.

Is it at this stage of the essay, possible to distinguish a pattern in the favored sexually selected traits and the mechanisms acting behind, according to mating tactics in ungulates? If so, do the found pattern fit to the predictions based on sexual selection theories (see section 2)? To answer to these questions, I will compare the results of three cervid species with contrasting mating tactics: red deer (female defence polygyny), fallow deer (lek) and roe deer (resource defence polygyny).

In the harem defence red deer, male contests seem to be the main mechanism of sexual selection, whereas in the lekking fallow deer and the territorial roe deer, both mechanisms of competition over mate (intra and intersexual selection) seem to coexist. These results therefore fit well with the predictions. Moreover, in the harem species (i.e., red deer), the traits that are reported to be selected by intrasexual selection are body size/weight/condition and antler size, which may enhance male strength and fighting ability. This is actually expected for female defence polygyny species. However, female choice may also play a role in competition over mates, via roaring rate and rut location. In the territorial species (i.e., roe deer), antler size/symmetry and barking seem to be selected and are favored by male contests. These traits are known to be important in the defence of the territory by allowing the assessment of male dominance, status or fighting ability by other males without direct interactions. Besides, territory quality in roe deer is selected by female choice, whereas male traits (e.g., body size) seem not to be subject to intersexual selection. This is also expected in resource defence polygyny species. Finally, for the lekking species (i.e., fallow deer), male ornament development seems to be selected by intersexual selection, but intrasexual selection may also play a role in this development. Besides, male contest competition over mates may also be involved in the selection of body size, while male position on the lek could play a role in male attractiveness, with a preference for central males as noted in many lekking species (see [START_REF] Andersson | Sexual selection[END_REF] for a review).

The results in these three contrasting species seem therefore to fit on the whole with theoretical predictions. But more empirical data are required in order to generalize to the whole ungulate taxa. Further, we need more studies on a whole variety of potentially selected traits, in different species within a range of mating tactics to better understand the influence of sexual selection on male mating systems in mammals in general and in ungulates more specifically.

Appendice 1. Sexually selected traits reported in ungulate species mentioned in this essay.

Mating system

Trait selected

Selective mechanism Reference

Body size/weight Male contests [START_REF] Clutton-Brock | Red deer -Behavior and ecology of two sexes[END_REF] Body condition Endurance rivalry [START_REF] Clutton-Brock | Red deer -Behavior and ecology of two sexes[END_REF] Roaring (rate) Female choice/Male contests Clutton-Brock et al. 1979, Clutton-Brock & Albon 1979[START_REF] Mc Comb | Roaring by red deer stags advances the date of ooestrus in hinds[END_REF], 1991[START_REF] Reby | Red deer (Cervus elaphus) hinds discriminate between the roars of their current harem-holder stag and those of neighbouring stags[END_REF] Antler