Le processus ancestral est appliqué pour étudier la variabilité génétique et la mesure de déséquilibre de liaison de séquences d’ADN, et faire de l’inférence statistique sur les divers facteurs responsables de cette variabilité. En tenant compte, en premier lieu, des facteurs de dérive génétique, de mutation, et de recombinaison, les calculs exacts de la mesure de déséquilibre de liaison de deux loci sont retrouvés. De plus, une approximation du processus exact, SMC (sequentially Markov chain), est utilisée pour trouver la mesure d’association à deux loci, et une formule de covariance pour calculer cette mesure est corrigée. En intégrant le facteur de conversion dans le modèle de Moran, on trouve l’espérance des mesures de polymorphisme exprimées par les espérances des mesures de variation intra-locus et inter-locus. Celles-ci sont calculées à l’aide de temps espérés dans les états ancestraux. De plus, l’espérance du déséquilibre de liaison est trouvée et il est montré qu’elle diminue quand le taux de recombinaison augmente. En utilisant ces résultats théoriques, on présente une méthode pour estimer les paramètres de mutation, de recombinaison, et de conversion. / The ancestral process is applied to investigate the amount of DNA variation and the amount of linkage disequilibrium ; it is also applied to make statistical inference about the multiple factors responsible for this variation. Considering genetic drift, mutation, and recombination events, the exact solutions for linkage disequilibrium between two loci are obtained. Furthermore, the association measure between two loci is obtained by using an approximation of the exact process, SMC (sequentially Markov chain), and correcting a covariance formula. After introducing intrachromosomal gene conversion under the Moran model, the expected amounts of variation within and between two loci are obtained using expected times spent in the ancestral states. Furthermore, the expectation of linkage disequilibrium is obtained and it is shown to decrease as the recombination rate is increased. Using these theoretical results, a method for estimating the mutation, recombination and gene conversion parameters is presented. / Les diagrammes de transitions d'états ont été réalisés avec le logiciel Latex.

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Les diagrammes de transitions d'états ont été réalisés avec le logiciel Latex. / Le processus ancestral est appliqué pour étudier la variabilité génétique et la mesure de déséquilibre de liaison de séquences d’ADN, et faire de l’inférence statistique sur les divers facteurs responsables de cette variabilité. En tenant compte, en premier lieu, des facteurs de dérive génétique, de mutation, et de recombinaison, les calculs exacts de la mesure de déséquilibre de liaison de deux loci sont retrouvés. De plus, une approximation du processus exact, SMC (sequentially Markov chain), est utilisée pour trouver la mesure d’association à deux loci, et une formule de covariance pour calculer cette mesure est corrigée. En intégrant le facteur de conversion dans le modèle de Moran, on trouve l’espérance des mesures de polymorphisme exprimées par les espérances des mesures de variation intra-locus et inter-locus. Celles-ci sont calculées à l’aide de temps espérés dans les états ancestraux. De plus, l’espérance du déséquilibre de liaison est trouvée et il est montré qu’elle diminue quand le taux de recombinaison augmente. En utilisant ces résultats théoriques, on présente une méthode pour estimer les paramètres de mutation, de recombinaison, et de conversion. / The ancestral process is applied to investigate the amount of DNA variation and the amount of linkage disequilibrium ; it is also applied to make statistical inference about the multiple factors responsible for this variation. Considering genetic drift, mutation, and recombination events, the exact solutions for linkage disequilibrium between two loci are obtained. Furthermore, the association measure between two loci is obtained by using an approximation of the exact process, SMC (sequentially Markov chain), and correcting a covariance formula. After introducing intrachromosomal gene conversion under the Moran model, the expected amounts of variation within and between two loci are obtained using expected times spent in the ancestral states. Furthermore, the expectation of linkage disequilibrium is obtained and it is shown to decrease as the recombination rate is increased. Using these theoretical results, a method for estimating the mutation, recombination and gene conversion parameters is presented.

Les écosystèmes sub-Antarctiques sont particulièrement vulnérables aux perturbations environnementales et notamment aux invasions biologiques. L'introduction du Chat (Felis silvestris catus) sur la Grande Terre de l'archipel des Kerguelen a eu des effets désastreux sur les communautés d'oiseaux marins. Ce prédateur doit sa survie dans cet environnement à la présence d'une proie introduite, le Lapin (Oryctolagus cuniculus), qui constitue sa ressource principale pendant l'hiver lorsque les oiseaux marins sont repartis en mer. L'éradication du chat n'apparaît pas être une solution réaliste compte tenu de la taille de l'île (6675 km2) et son inaccessibilité. De plus elle serait susceptible de conduire à des résultats non souhaités comme par exemple une explosion démographique des populations de lapins. La mise en place d'une politique de gestion adaptée nécessite d'améliorer notre connaissance des facteurs qui conditionnent la dynamique spatio-temporelle des populations de chats. Au cours de cette thèse, j'ai cherché à identi_er les mécanismes des interactions entre le chat, le lapin et la végétation, car elles sont attendues conditionner celles existantes entre le chat et les oiseaux marins. J'ai analysé la dynamique spatio-temporelle de quatre populations de chats sur la Grande Terre et j'ai en particulier recherché si des conditions environnementales spatialement corrélées (effet Moran) pouvaient, en se propageant dans la chaine alimentaire, synchroniser les variations temporelles d'abondance des populations de chats. Enfin, j'ai étudié l'impact des variations spatio-temporelles d'abondance des populations de chats sur les variations spatio-temporelles de la structure génétique des populations de chats. / Sub-Antarctic ecosystems are particularly vulnerable to environmental perturbations including biological invasions. The introduction of the feral cat (Felis silvestris catus) on the Grande TerreIsland of the Kerguelen archipelago has lead to detrimental effects on seabird's communities. Cat survival in this environment is possible because of the presence of the introduced rabbit (Oryctolagus cuniculus), which constitute the main prey of the cat during winter when most seabirds are offshore. Cat eradication is not a realistic solution given the size and inaccessibility of the island (6675 km2). Moreover it can lead to unwanted results such as the demographic explosion of rabbit populations. The design of appropriate management policy needs to improve our understanding of the factors that influence the spatio-temporal dynamics of cat populations. In this thesis, I explored the mechanisms of cat-rabbit-vegetation interactions, as they are expected to determine interactions existing between cats and seabirds. I analyzed the spatio-temporal dynamics of four cat populations on Grande Terre Island and I especially sought whether environmental conditions spatially correlated (Moran effect) could synchronize cat through their effect on the trophic web pathways. Finally, I studied the impact of spatio-temporal

<img src="http://vg00.met.vgwort.de/na/806c85cec18906a64e06" width="1" height="1" alt=""> Subject of this work is the possibility to synchronize nonlinear systems via correlated noise and automatic control. The thesis is divided into two parts.<br> The first part is motivated by field studies on feral sheep populations on two islands of the St. Kilda archipelago, which revealed strong correlations due to environmental noise. For a linear system the population correlation equals the noise correlation (Moran effect). But there exists no systematic examination of the properties of nonlinear maps under the influence of correlated noise. Therefore, in the first part of this thesis the noise-induced correlation of logistic maps is systematically examined. For small noise intensities it can be shown analytically that the correlation of quadratic maps in the fixed-point regime is always smaller than or equal to the noise correlation. In the period-2 regime a Markov model explains qualitatively the main dynamical characteristics. Furthermore, two different mechanisms are introduced which lead to a higher correlation of the systems than the environmental correlation. The new effect of "correlation resonance" is described, i. e. the correlation yields a maximum depending on the noise intensity. <br> In the second part of the thesis an automatic control method is presented which synchronizes different systems in a robust way. This method is inspired by phase-locked loops and is based on a feedback loop with a differential control scheme, which allows to change the phases of the controlled systems. The effectiveness of the approach is demonstrated for controlled phase synchronization of regular oscillators and foodweb models. / Gegenstand der Arbeit ist die Möglichkeit der Synchronisierung von nichtlinearen Systemen durch korreliertes Rauschen und automatische Kontrolle. Die Arbeit gliedert sich in zwei Teile.<br> Der erste Teil ist motiviert durch Feldstudien an wilden Schafspopulationen auf zwei Inseln des St. Kilda Archipels, die starke Korrelationen aufgrund von Umwelteinflüssen zeigen. In einem linearen System entspricht die Korrelation der beiden Populationen genau der Rauschkorrelation (Moran-Effekt). Es existiert aber noch keine systematische Untersuchung des Verhaltens nichtlinearer Abbildungen unter dem Einfluss korrelierten Rauschens. Deshalb wird im ersten Teils dieser Arbeit systematisch die rauschinduzierte Korrelation zweier logistischer Abbildungen in den verschiedenen dynamischen Bereichen untersucht. Für kleine Rauschintensitäten wird analytisch gezeigt, dass die Korrelation von quadratischen Abbildungen im Fixpunktbereich immer kleiner oder gleich der Rauschkorrelation ist. Im Periode-2 Bereich beschreibt ein Markov-Modell qualitativ die wichtigsten dynamischen Eigenschaften. Weiterhin werden zwei unterschiedliche Mechanismen vorgestellt, die dazu führen, dass die beiden ungekoppelten Systeme stärker als ihre Umwelt korreliert sein können. Dabei wird der neue Effekt der "correlation resonance" aufgezeigt, d. h. es ergibt sich eine Resonanzkurve der Korrelation in Abbhängkeit von der Rauschstärke. <br> Im zweiten Teil der Arbeit wird eine automatische Kontroll-Methode präsentiert, die es ermöglicht sehr unterschiedliche Systeme auf robuste Weise in Phase zu synchronisieren. Die Methode ist angelehnt an Phase-locked-Loops und basiert auf einer Rückkopplungsschleife durch einen speziellen Regler, der es erlaubt die Phasen der kontrollierten Systeme zu ändern. Die Effektivität dieser Methode zur Kontrolle der Phasensynchronisierung wird an regulären Oszillatoren und an Nahrungskettenmodellen demonstriert.

The aim of this thesis is to describe and analyze the geographical distribution of everyday criminality in the town of Borlänge during the year 2002 and to analyze which measures to be taken in the physical social planning to decrease this everyday criminality there. The term everyday criminality is here to be understood as those categories of crime that appear most frequently in the records of reports to the police every year. Here two kinds of crime have been in focus, thefts from cars and office burglary.In fulfilling this aim two main questions have been answered. The first one is how the everyday criminality was distributed geographically in the town of Borlänge during the year 2002. The second one is which measures to be taken in the physical social planning to decrease this everyday criminality in the town of Borlänge.In order to answer the first question a spatial autocorrelation analysis, Local Moran LISA has been used. This method is based on the measurement Moran´s I and shows the spatial autocorrelation for every single location. To answer the second question three different theories of crime prevention through environmental design have been studied and applied in the analysis. These are Jane Jacobs’ ideas about ”the living city”, Oscar Newman´s ideas about ”defensible space” and Ronald V. Clarke´s theories about crime prevention.The major conclusions that can be drawn from this thesis are that the risk of being exposed to thefts from cars, during the analyzed time period, was highest in Centrum and Hagalund and their surroundings. The lowest risk of being exposed to this type of crime was found in Domnarvet and Islingby, during the year 2002. The highest risk of being a victim of the crime office burglary was found in Hagalund and its surroundings and in the single area of Kvarnsveden. The corresponding lowest risk was found in Lergärdet and its surroundings and in Norra Backa and Kupolen. The measures that should be taken in order to decrease these types of criminality can be divided into overall changes and place-specific changes. When it comes to the crime thefts from cars a more attractive central business district, a better view of parking lots from nearby buildings, dividing of larger parking lot zones into smaller ones, migration of hidden parking lots and stronger access control to parking lots where problems with this kind of crime have occurred have been suggested as overall changes. The corresponding place-specific changes are to remove vegetation that is blocking the view, better lighting and to put up signs with information about increased risk of exposure to crime at parking lots with the most problems. To decrease the amount of office burglaries overall changes as to create a better view of the area from nearby surroundings, move bigger office compartments or divide them into smaller units, rebuild characteristic buildings and increase security by strengthening the access control to offices with these kinds of problems could be useful. Finally there are possibilities to decrease office burglary by using place-specific measures as surveillance cameras combined with signs containing information about these, high fences and better lighting around the buildings where a higher risk of being exposed to this kind of criminality is present.

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Cette thèse concerne l’étude de grandes déviations précises pour deux statistiques de test:le coefficient de corrélation empirique de Pearson et la statistique de Moran.Les deux premiers chapitres sont consacrés à des rappels sur les grandes déviations précises et sur la méthode de Laplace qui seront utilisés par la suite. Par la suite, nous étudions les grandes déviations précises pour des coefficients de Pearson empiriques qui sont définis par:$r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ ou, quand les espérances sont connues, $\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$. Notre cadre est celui d’échantillons (Xi, Yi) ayant une distribution sphérique ou une distribution gaussienne. Dans chaque cas, le schéma de preuve suit celui de Bercu et al.Par la suite, nous considérons la statistique de Moran $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$, où γ est la constante d’ Euler. Enfin l’appendice est consacré aux preuves de résultats techniques. / This thesis focuses on the study of Sharp large deviations (SLD) for two test statistics:the Pearson’s empirical correlation coefficient and the Moran statistic.The two first chapters aim to recall general results on SLD principles and Laplace’s methodsused in the sequel. Then we study the SLD of empirical Pearson coefficients, name $r_n=\sum_{i=1}^n(X_i-\bar X_n)(Y_i-\bar Y_n)/\sqrt{\sum_{i=1}(X_i-\bar X_n)^2 \sum_{i=1}(Y_i-\bar Y_n)^2}$ and when the meansare known,$\tilde r_n=\sum_{i=1}^n(X_i-\mathbb E(X))(Y_i-\mathbb E(Y))/\sqrt{\sum_{i=1}(X_i-\mathbb E(X))^2 \sum_{i=1}(Y_i-\mathbb E(Y))^2} \, .$ .Our framework takes place in two cases of random sample (Xi, Yi): spherical distributionand Gaussian distribution. In each case, we follow the scheme of Bercu et al. Next, westate SLD for the Moran statistic $T_n=\frac{1}{n}\sum_{k=1}^n\log\frac{X_i}{\bar X_n}+\gamma \, ,$o\`u $\gamma$ , where γ is the Euler constant.Finally the appendix is devoted to some technical results.

Cancer as a disease causes about 8.8 million deaths worldwide per year, a number that will largely increase in the next decades. Although the cellular processes involved in tumor emergence are more and more understood, the implications of specific changes at the cellular scale on tumor emergence at the tissue scale remain elusive. Main reasons for this lack of understanding are that the cellular processes are often hardly observable especially in the early phase of tumor development and that the interplay between cellular and tissue scale is difficult to deduce. Cell-based mathematical models provide a valuable tool to investigate in which way observable phenomena on the tissue scale develop by cellular processes. The implications of these models can elucidate underlying mechanisms and generate quantitative predictions that can be experimentally validated. In this thesis, we infer the role of genetic and phenotypic cell changes on tumor development with the help of cell-based Markov chain models which are calibrated by tissue-scale data. In the first part, we utilize data on the diagnosed fractions of benign and malignant tumor subtypes to unravel the consequences of genetic cell changes on tumor development. We introduce extensions of Moran models to investigate two specific biological questions. First, we evaluate the tumor regression behavior of pilocytic astrocytoma which represents the most common brain tumor in children and young adults. We formulate a Moran model with two absorbing states representing different subtypes of this tumor, derive the absorption probabilities in these states and calculate the tumor regression probability within the model. This analysis allows to predict the chance for tumor regression in dependency of the remaining tumor size and implies a different clinical resection strategy for pilocytic astrocytoma compared to other brain tumors. Second, we shed light on the hardly observable early cellular dynamics of tumor development and its consequences on the emergence of different tumor subtypes on the tissue scale. For this purpose, we utilize spatial and non-spatial Moran models with two absorbing states which describe both benign and malignant tumor subtypes and estimate lower and upper bounds for the range of cellular competition in different tissues. Our results suggest the existence of small and tissue-specific tumor-originating niches in which the fate of tumor development is decided long before a tumor manifests. These findings might help to identify the tumor-originating cell types for different cancer types. From a theoretical point of view, the novel analytical results regarding the absorption behavior of our extended Moran models contribute to a better understanding of this model class and have several applications also beyond the scope of this thesis. The second part is devoted to the investigation of the role of phenotypic plasticity of cancer cells in tumor development. In order to understand how phenotypic heterogeneity in tumors arises we describe cell state changes by a Markov chain model. This model allows to quantify the cell state transitions leading to the observed heterogeneity from experimental tissue-scale data on the evolution of cell state proportions. In order to bridge the gap between mathematical modeling and the analysis of such data, we developed an R package called CellTrans which is freely available. This package automatizes the whole process of mathematical modeling and can be utilized to (i) infer the transition probabilities between different cell states, (ii) predict cell line compositions at a certain time, (iii) predict equilibrium cell state compositions and (iv) estimate the time needed to reach this equilibrium. We utilize publicly available data on the evolution of cell compositions to demonstrate the applicability of CellTrans. Moreover, we apply CellTrans to investigate the observed cellular phenotypic heterogeneity in glioblastoma. For this purpose, we use data on the evolution of glioblastoma cell line compositions to infer to which extent the heterogeneity in these tumors can be explained by hierarchical phenotypic transitions. We also demonstrate in which way our newly developed R package can be utilized to analyze the influence of different micro-environmental conditions on cell state proportions. Summarized, this thesis contributes to gain a better understanding of the consequences of both genetic and phenotypic cell changes on tumor development with the help of Markov chain models which are motivated by the specific underlying biological questions. Moreover, the analysis of the novel Moran models provides new theoretical results, in particular regarding the absorption behavior of the underlying stochastic processes.

The distribution of species in space is determined by the species dispersal capacity, adaptation to environmental conditions, and response to predators and competitors. To determine the importance of dispersal limitation, environmental filtering, and species interactions on the distribution of species in the Brazilian Amazonian forest, I sampled termites in a large area of Brazil. I investigated patterns in species occurrence that could indicate competition and predation structuring termite communities, and analyzed the association of termite abundance and species richness with the density of ant predators. The spatial distribution of termites, and their association with climatic and edaphic conditions were also used to infer about the effects of dispersal limitation and environmental filtering. A total of 271 termite species and 4,389 colonies was found in the 148 transects sampled. Predator density was the strongest predictor of termite abundance and species richness at small spatial scales, but the turnover in termite species composition was mostly associated with measures of soil texture. At broad spatial scales, soil chemistry, climate, and isolation by distance were associated with termite abundance, species richness, and species composition. These results suggest that both species interactions, their association with the environment, and their dispersal capacity determine their distribution. Nevertheless, dispersal limitation seem to be stronger over large areas, whereas environmental filtering can act both at small and large geographic scales.