Soit G un groupe dénombrable, qui se scinde en un produit libre de la forme G=G_1*...*G_k*F, où F est un groupe libre de type fini, et les G_i sont librement indécomposables et non isomorphes à Z. Nous montrons que le groupe Out(G) des automorphismes extérieurs de G satisfait l'alternative de Tits, dès lors que chacun des groupes G_i et Out(G_i) la satisfait. Par des méthodes similaires, nous montrons aussi l'alternative suivante pour tout sous-groupe H de Out(F_N), due à Handel et Mosher lorsque H est de type fini : soit H fixe virtuellement la classe de conjugaison d'un facteur libre propre de F_N, soit H contient un automorphisme complètement irréductible. Nos méthodes, géométriques, utilisent l'étude de la dynamique de l'action de certains sous-groupes de Out(G) sur des espaces hyperboliques. Nous décrivons notamment l'adhérence de l'outre-espace de G relatif aux G_i, et le bord de Gromov du complexe (hyperbolique) des scindements cycliques relatifs associé. Nous étudions par ailleurs les marches aléatoires sur Out(F_N). Sous un certain nombre de conditions sur la mesure de probabilité mu, nous montrons que presque toute trajectoire de la marche aléatoire sur (Out(F_N),mu) converge vers un point du bord de Gromov du complexe des facteurs libres de F_N, que nous identifions au bord de Poisson de (Out(F_N),mu). Par ailleurs, nous décrivons l'horofrontière de l'outre-espace. Ceci a des applications à l'étude de la croissance des classes de conjugaison de F_N sous l'effet de produits aléatoires d'automorphismes extérieurs. / Let G be a countable group that splits as a free product of the form G=G_1*...*G_k*F, where F is a finitely generated free group, and the groups G_i are freely indecomposable and not isomorphic to Z. We show that Out(G) satisfies the Tits alternative, as soon as all the groups G_i and Out(G_i) do. Similar techniques also yield another alternative for subgroups H of Out(F_N), due to Handel and Mosher when H is finitely generated, namely: either H virtually fixes the conjugacy class of some proper free factor of F_N, or H contains a fully irreducible automorphism. Our methods are geometric, and require understanding the dynamics of the action of some subgroups of Out(G) on Gromov hyperbolic spaces. In particular, we determine the closure of the outer space of G relative to the G_i's, as well as the Gromov boundary of the (hyperbolic) complex of relative cyclic splittings of G. We also study random walks on Out(F_N). Given a probability measure mu on Out(F_N) (satisfying some conditions), we prove that almost every sample path of the random walk on (Out(F_N),mu) converges to a point of the Gromov boundary of the free factor complex of F_N, which we identify with the Poisson boundary of (Out(F_N),mu). We also describe the horoboundary of outer space, and give applications to growth of conjugacy classes of F_N under random products of outer automorphisms.

Dans son preprint, M. Bruno Kahn a construit une suite spectrale par rang en utilisant la méthode catégorique. Cette suite spectrale est construit par une filtration de la catégorie des modules sans-torsion de type fini d'un anneau intègre A ce qui explique le nom : suite spectrale par rangs. Cette suite spectrale converge vers les groupes d'homologies de la Q-construction de la catégorie de A-modules sans torsion de type fini et elle été utilisé par Quillen pour prouver que les K-groupes sont de génération finie pour anneau d'intègres d'un corps de nombres. Notre but de cette thèse est de calculer le différentiel de la suite spectrale par rangs qui peut servit comme une première étape d'une idée générale d'unifier les calculs de rangs des K-groupes de la courbe sur un corps fini (G. Harder) et la courbe arithmétique (A. Borel). Pour gagner ça, nous étudions le foncteur cellulaire (connexe) et les constructions de Grothendieck en détail, en particulier ses propriétés homotopiques. En utilisant ça, nous pouvons mettre le différentiel dans certain triangles distingués de foncteurs sur une catégorie, puis nous réalisons ces foncteurs explicits en langages d'immeuble de Tits, module de Steinberg et symbole modulaire au sens d'Ash-Rudolph. Nous avons aussi obliger de fabriquer un autre symbole : le symbole étendu pour étudier l'homologie de la suspension d'immeuble de Tits, mais nous montons que ce symbole est équivalent que symbole modulaire. / Bruno Kahn has constructed a rank spectral sequence by using a purely categorical approach. This spectral sequence was derived by using a filtration of the category of torsion-free modules over integral domain by ranks and hence the name: rank spectral sequence. This spectral sequence converges to the homology groups of the Q-construction over the category of finitely generated torsion-free modules over an integral ring. Quillen used it in the proof of the finite generation of K-groups of rings of integers. Our goal in this thesis is to calculate the differential of the rank spectral sequence. We believe that this is a first step towards a much bigger project, that is, to unify the calculation of the ranks of K-groups of curves over a finite field (result of G. Harder) and of arithmetic curves (result of A. Borel).To achieve our goal, we put the differential in certain distinguished triangles of coefficients/functors over some categories, and make these functors explicit in terms of Tits building and Ash-Rudolph's modular symbols. To accomplish this, we shall use Quillen's categorical homotopy theory intensively and introduce the notion of extended (modular) symbols which is equivalent to Ash-Rudolph's via the suspension of Tits buildings.

A major goal in evolutionary biology is to understand how ecological factors shape the phenotypic and genetic variation that we observe in natural populations and in this thesis I examine how rapid changes in temperature have influenced phenotypic and genetic variation in morphological and life history traits in long-term studies of great tits. In Chapter 1 I review what is known about the effects of environmental change on natural populations, and outline the quantitative genetic framework that is available to study genetic variation in natural populations. Much focus on the effects of climate change has concerned species’ phenology, far less attention has been given to other traits. In Chapter 2 I examine the effects changing environmental conditions have had on the proportion of females that produce second broods. Temperature operates mainly through indirect effects (such as food abundance) but may also have more direct effects. In Chapter 3 I show that over a 36 year period body size have declined in line with predictions from Bergmann’s rule and I explore the genetic basis of this decline and the environmental factors involved. Although we can learn much from population level responses, there is a great deal of additional information to be gained by studying between-individual responses. In Chapter 4 I therefore compare the multivariate pattern of between-individual variation in phenotypic plasticity and its genetic basis for laying date and clutch size, in two great tit populations. Environmental changes may also directly affect the expression of genetic variance as well as the strength of selection acting on a trait, and in Chapter 5 I show that, for laying date, the environment induces a positive covariance between strength of selection and the expression of additive genetic variance, something that may enhance the rate of adaptation. Finally, in Chapter 6 I discuss and summarise the wider implications of the findings from this thesis.

Este projeto de mestrado tem por objetivo dar uma prova elementar do seguinte teorema de Tits, conhecido como Teorema da Alternativa de Tits: Seja G um grupo linear finitamente gerado sobre um corpo. Então G é solúvel por finito ou G contém um grupo livre não cíclico. Este teorema, que foi provado por J. Tits em 1972 [4], foi considerado pelo matemático J.P. Serre como um dos mais importantes resultados de álgebra do século XX. Quando dizemos uma prova elementar, não queremos absolutamente te dizer uma prova simples. Seguiremos a prova simplificada de John D. Dixon / This masters project aims to give an elementary proof of the following theorem of Tits, known as the Alternative Tits Theorem: Let G be a finitely generated linear group over a field. Then either G is solvable by finite or G contains a noncyclic free subgroup. This theorem was proved by J. Tits in 1972 [4], was considered by the mathematician J.P. Serre, as one of the most important algebra results of the XX century. When we say an elementary proof, we absolutely not mean a simple proof. We will follow the simplified proof of John D. Dixon

Dans cette thèse, nous utilisons et contribuons à la théorie des produits de matrices aléatoires afin d'étudier des propriétés génériques des éléments et des sous-groupes des groupes linéaires. Notre premier résultat donne une version probabiliste de l'alternative de Tits : nous montrons que si M_n et M'_n sont deux marches aléatoires indépendantes sur un groupe linéaire de type fini non virtuellement résoluble alors presque sûrement les deux marches finiront par engendrer un sous-groupe libre non abélien à deux générateurs. Cela répond par l'affirmative à une question de Guivarc'h et de Gilman, Miasnikov et Osin. Plus précisément, nous montrons que la probabilité que M_n et M'_n n'engendrent pas un sous-groupe libre décroit exponentiellement vite vers zéro. Notre outil principal est la théorie des produits de matrices aléatoires. Durant la preuve, nous établissons de nouveaux théorèmes limites dans cette théorie, d'une part en généralisant des résultats connus dans le cadre des produits de matrices à valeurs dans les corps archimédiens à tout corps local, d'autre part en donnant des résultats qui sont nouveaux même sur R. Par exemple, nous montrons que sous des hypothèses naturelles sur la marche aléatoire, les composantes suivant K de M_n dans la décomposition KAK deviennent asymptotiquement indépendantes avec vitesse exponentielle. Dans la deuxième partie de la thèse, nous utilisons ces résultats pour étudier la transience des sous-variétés des groupes algébriques. Un de nos résultats peut être formulé comme suit: soient H un sous-groupe non élémentaire de SL_2(R), une probabilité adaptée sur H ayant un moment exponentiel, alors pour toute sous-variété algébrique propre V de SL_2(R), la probabilité que la marche aléatoire appartienne à V décroit exponentiellement vite vers zéro. Par conséquent, la sous-variété algébrique V est transiente pour la marche aléatoire. Nous généralisons cet énoncé au cas ou la marche aléatoire est adaptée sur un groupe Zariski dense des points réels d'un groupe algébrique défini et déployé sur R. Ces résultats sont à comparer avec des travaux récents de Kowalski et de Rivin.

Este projeto de mestrado tem por objetivo dar uma prova elementar do seguinte teorema de Tits, conhecido como Teorema da Alternativa de Tits: Seja G um grupo linear finitamente gerado sobre um corpo. Então G é solúvel por finito ou G contém um grupo livre não cíclico. Este teorema, que foi provado por J. Tits em 1972 [4], foi considerado pelo matemático J.P. Serre como um dos mais importantes resultados de álgebra do século XX. Quando dizemos uma prova elementar, não queremos absolutamente te dizer uma prova simples. Seguiremos a prova simplificada de John D. Dixon / This masters project aims to give an elementary proof of the following theorem of Tits, known as the Alternative Tits Theorem: Let G be a finitely generated linear group over a field. Then either G is solvable by finite or G contains a noncyclic free subgroup. This theorem was proved by J. Tits in 1972 [4], was considered by the mathematician J.P. Serre, as one of the most important algebra results of the XX century. When we say an elementary proof, we absolutely not mean a simple proof. We will follow the simplified proof of John D. Dixon

L’urbanisation des milieux est un phénomène croissant induisant des changements importants des habitats naturels auxquels doit faire face la biodiversité. Ces modifications rapides et profondes de l’environnement vont créer de nouvelles conditions potentiellement contraignantes pour les individus. En effet, le cocktail de paramètres artificiels (par exemple : lumière, bruit, pollution chimique) couplé à une présence humaine ainsi qu’une ressource alimentaire souvent modifiée et/ou peu disponible peuvent contraindre la survie et la reproduction des espèces ayant colonisées les milieux urbains. Par ailleurs, les modifications profondes des habitats urbains sont susceptibles d’amener les individus à mal décrypter les indices communément utilisés dans les milieux non perturbés conduisant ces derniers à des réponses maladaptatives, et les populations associées jusqu’à des situations de trappe écologique. C’est dans ce contexte que s’inscrivent ces travaux de thèse chez la Mésange charbonnière, Parus major. Ces oiseaux ont été suivis en reproduction dans des nichoirs placés sur des sites présentant des niveaux d’artificialisation variables, que nous avons quantifiés, au sein de la ville de Montpellier. La taille de la cavité de reproduction a été également manipulée expérimentalement (manipulation de l’indice). Nous avons pu observer une préférence pour les cavités les plus grandes ainsi qu’un investissement dans la ponte plus important mais un nombre de jeunes envolés plus faible relativement aux cavités de taille plus petite. Cette réponse maladaptative associée à la taille de la cavité nous a amené à nous questionner plus précisément sur le rôle des ressources alimentaires associées au milieu urbain et sur le potentiel adaptatif de nos oiseaux urbains. Les expériences menées, en lien avec les ressources alimentaires, ont mis en évidence qu’effectivement la ressource est un facteur clé contraignant la reproduction des mésanges urbaines. Par ailleurs, grâce à un dispositif forestier historique situé à une vingtaine de kilomètres de notre site d’étude urbain, nous avons testé la présence de deux écotypes urbains et ruraux. Nous avons pu mettre en évidence des différences de morphologies entre habitats, sans détecter pour autant de différence de condition physique. Pourtant, à l’échelle plus fine du gradient d’urbanisation, ces différences apparaissent. De plus, l’étude des personnalités des oiseaux a mis également en évidence un différentiel de personnalités inter-habitat mais aussi intra-habitat, qui soulève encore à l’heure actuelle des questions d’adaptation autour de ces phénotypes particuliers. Ces travaux soulignent la complexité des questions écologiques et évolutives dans les environnements fortement perturbés que sont les milieux urbains et nécessitent de continuer à approfondir nos connaissances afin d’apporter au mieux des solutions pour la gestion de la biodiversité urbaine. / Urbanization is an increasing phenomenon inducing dramatic modifications of natural habitats facing biodiversity. These rapid and drastic environmental changes create new conditions, potentially constraining individuals. Indeed, artificial parameters, such as light, noise and chemical pollution, coupled with human presence and food resources which are often modified and less available, should constrain survival and reproduction of urban species. Moreover, urban habitat changes could lead individuals to misinterpret natural environmental cues, inducing maladaptive responses and populations into an ecological trap. In this context, we developed this research project on great tits, Parus major to improve our understanding of avian adaptation in cities. We monitored great tit reproduction breeding in nest-boxes within an urbanization gradient, which has been quantified, in the city of Montpellier. We experimentally manipulated nesting-cavity size using different types of nest-boxes. We found that the birds preferred the largest artificial cavities for breeding when they could choose between small, medium-sized and large cavities. Individuals from the largest cavities also invested more in egg production, yet had a lower fledging success than those from medium-sized cavities. These results are an experimental demonstration of a trap mechanism in free-living animals. To test our hypothesis that food resources are an environmental key factor limiting reproductive performance in our urban great tit population, we conducted experiments modulating constraints on food resources. The conclusion of these experiments is that food is a limiting factor for reproduction. In addition, in a local adaptation framework, we examined if urban great tits possess particular phenotypic traits that differ from great tits that live in more natural conditions. We found that urban and rural great tits expressed differences in morphology and personality profiles both at the inter-habitat and intra-habitat level. Additional studies will be required to better understand the underlying mechanisms that link phenotypic and reproductive performance in individuals that face rapid environmental change and increased urbanization, also to improve biodiversity conservation programs in these environments.

LIPANSKÁ, B. 2011: Effect of alarm calls on tit's behavior on feeder. MSc Thesis. Faculty of Science, Charles University in Prague. Alarm calls of the Great tit (Parus major) used in the context of ground-predators or perching-raptors consist of high-frequency tonal syllables and of series of churring syllables with broad-frequency range. The function of some acoustical parametres of these complex calls was tested in playback experiment on feeder. As the most effective appeared to be alarm calling of two birds simultaneously. More important for warning function of the calls were broad-frequency range syllables. The length of series of these syllables had an opposite impact than in some north-American chickadees (genus Poecile). The Blue tit (Cyanistes caeruleus) responds to Great tit's alarm calls, but its reactions are weaker. This difference can be caused by its lower competition ability against the Great tit. Key words: antipredation behavior, alarm calls, tits, playback experiment

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The drivers of fidelity and divorce of pair-bonded individuals, along with their fitness consequences, are of great interest as they influence mating systems, population structure and productivity, and gene flow. Socially monogamous birds offer an ideal opportunity to study divorce since they show great variability in the extent to which pair bonds are maintained. However, there has been little consensus as to whether divorce is a behavioural adaptation to improve a mating situation, or a consequence of other processes. Moreover, the biological and ecological correlates of fidelity are difficult to address because previous work has been based on indirect and potentially biased methods. Finally, in terms of process, the link between the process of mate choice and subsequent mating decisions has been largely inaccessible to study. My doctoral thesis addressed these significant gaps in our understanding of cause, process and consequence in the formation and dissolution of pair bonds in socially monogamous birds. I accomplished this in three principal ways. First, I conducted a robust phylogenetic meta-analysis on 84 studies across 64 species to assess the existing empirical evidence that divorce in socially monogamous birds is adaptive (in terms of breeding success). This analysis revealed that divorce is, in general, adaptive as it is both triggered by relatively low breeding success and leads to improvement in success. Next, I developed a novel probabilistic multievent capture–mark–recapture framework that provides joint estimates of survival and fidelity while explicitly accounting for imperfect detection, capture heterogeneity, and uncertainty in pair status. By applying this model to breeding data on a wild great tit population I showed that birds that remain faithful to their partner exhibit higher survival rates and are more likely to remain faithful in the next breeding season than do birds that change partners. Subsequently, I confirmed the generality of a survival benefit by applying the model to breeding data on other tit populations. Then, by applying the model to data from a population of mute swans, I showed that fidelity decreases the likelihood of skipping breeding and mortality in this long-lived species, and that these effects depended on age, individual quality, and immigration status. Finally, I investigated how the timing of pair formation influences breeding success and divorce probability using five years of data on the over-winter social behaviour of great tits. I showed that early pair formation had a positive effect on fitness components, influencing the likelihood of divorce only indirectly, through breeding success. Further, my work revealed that males, but not females, with higher numbers of the female associates in winter, and males whose future breeding partners were ranked low amongst these, divorced more often. My research makes a significant contribution to our understanding of divorce and fidelity, and generates a number of important implications for future studies. First, my work establishes that divorce is adaptive for breeding success. Second, my results highlight that survival is an important (and likely, widespread) fitness consequence of pairing decisions. Third, I provide a novel statistically rigorous modelling framework for estimating fidelity-rates and testing hypothesis about fidelity that overcomes many of the inherent biases in traditional estimates. Fourth, it provides the first evidence for a selective advantage of early pair formation in wild, thus highlighting that there are benefits to pair familiarity that manifest via social associations of individuals prior to breeding. Finally, my work reveals the selective pressures operating via the social environment can ultimately influence the mating strategies individuals adopt.