Le fil conducteur de cette thèse, composée de trois parties, est la notion de branchement.Le premier chapitre est consacré à l'arbre de Yule et à l'arbre binaire de recherche. Nous obtenons des résultats d'oscillations asymptotiques de l'espérance, de la variance et de la distribution de la hauteur de ces arbres, confirmant ainsi une conjecture de Drmota. Par ailleurs, l'arbre de Yule pouvant être vu comme une marche aléatoire branchante évoluant sur un réseau, nos résultats permettent de mieux comprendre ce genre de processus.Dans le second chapitre, nous étudions le nombre de particules tuées en 0 d'un mouvement brownien branchant avec dérive surcritique conditionné à s'éteindre. Nous ferons enfin apparaître une nouvelle phase de transition pour la queue de distribution de ces variables.L'objet du dernier chapitre est le graphe d'Erdős–Rényi dans le cas critique : $G(n,1/n)$. En introduisant un couplage et un changement d'échelle, nous montrerons que, lorsque $n$ augmente les composantes de ce graphe évoluent asymptotiquement selon un processus de coalescence-fragmentation qui agit sur des graphes réels. La partie coalescence sera de type multiplicatif et les fragmentations se produiront selon un processus ponctuel de Poisson sur ces objets. / This thesis is composed by three chapters and its main theme is branching processes.The first chapter is devoted to the study of the Yule tree and the binary search tree. We obtain oscillation results on the expectation, the variance and the distribution of the height of these trees and confirm a Drmota's conjecture. Moreover, the Yule tree can be seen as a particular instance of lattice branching random walk, our results thus allow a better understanding of these processes.In the second chapter, we study the number of particles killed at 0 for a Brownian motion with supercritical drift conditioned to extinction. We finally highlight a new phase transition in terms of the drift for the tail of the distributions of these variables.The main object of the last chapter is the Erdős–Rényi graph in the critical case: $G(n,1/n)$. By using coupling and scaling, we show that, when $n$ grows, the scaling process is asymptotically a coalescence-fragmentation process which acts on real graphs. The coalescent part is of multiplicative type and the fragmentations happen according a certain Poisson point process.

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Die vorliegende Arbeit behandelt das biologische Phänomen der Dormanz mit Hilfe mathematischer Modellierung. Dormanz beschreibt dabei einen reversiblen Zustand von Individuen, in dem die metabolische Aktivität reduziert wird und die Resistenz gegen Natureinflüsse erhöht ist. Der erste Teil der Arbeit widmet sich den ökologischen Eigenschaften. Hier wird zunächst ein Moranmodell vorgestellt, welches verschiedene Modellierungsarten von Dormanz aus der Populationsgenetik vereint und unter verschiedenen Skalierungen den schwachen seed-bank Koaleszenten und den starken seed-bank Koaleszenten als anzestralen Prozess innehat. Dadurch werden die Parameter der Koaleszenten vergleichbar. Als Anwendung betrachten wir die sogenannte species abundance distribution, welche mithilfe von Koaleszenten beschrieben werden kann. Der zweite Teil beschäftigt sich mit den Auswirkungen von Dormanz auf evolutionäre Eigenschaften und beginnt mit einer Einführung in die Theorie von adaptive dynamics. Dort werden auch verschiedene Möglichkeiten der Modellierung von Dormanz in individuenbasierten Modellen besprochen. Danach befassen wir uns mit der Erweiterung eines Modells für sympatrische Speziation um den Aspekt der Dormanz. Die canonical equation of adaptive dynamics wird - motiviert durch ein Modell mit Dormanz - für schnellere Mutationsraten aus dem sogenannten power-law Mutationsregime für einen Grenzfall hergeleitet. Die Arbeit schließt mit dem dritten Teil, in welchem ein individuenbasiertes Modell für die Entwicklung von Krebs unter dem Einfluss von Chemotherapie und unter Berücksichtigung von Dormanz vorgestellt wird. In Simulationsstudien wird untersucht, inwiefern Dormanz zu Misserfolg einer Therapie beiträgt. Ein weiteres Ziel ist die Analyse von Kombinationsbehandlung mit einem Medikament welches mit dormanten Zellen interagieren kann insbesondere unter Betrachtung verschiedener Therapieansätze zur Behandlung von dormanten Krebszellen. / The present thesis uses mathematical modelling to investigate the consequences of dormancy. Dormancy describes a reversible and protected state of reduced metabolic activity which enhances an individual's resilience to hazardous conditions. In this sense, dormancy acts as a protection mechanism against habitats with unfavourable environments. The thesis considers the impact of dormancy on ecological, evolutionary and in its broadest sense pathogenic properties of microbial populations. The first part is concerned with studying the impact of dormancy on ecology. For this, a Moran model is presented which unifies different models of dormancy from population genetics and exhibits the weak seed-bank coalescent and the strong seed-bank coalescent as the scaling limit of the ancestral process. As an application we consider the species abundance distribution which can be described using coalescent theory. In the second part we consider the influence of dormancy on evolutionary properties. The modelling framework for this is the theory of adaptive dynamics. We then show that competition-induced dormancy may favour sympatric speciation. A key aspect in the derivation of this result is the canonical equation of adaptive dynamics. We extend this equation - motivated by a model including dormancy - to power-law mutations in a limiting case. We conclude the thesis with the third part where we provide an individual-based model for the treatment of cancer with chemotherapy under consideration of dormant cancer cells. Using simulation studies, we investigate how dormancy may contribute to treatment failure. Another goal of this chapter is to analyse combination treatment with a drug which directly targets dormant cancer cells and to formulate general observations regarding various strategies to counter cancer cell dormancy.

Phylogenetics is the research of ancestor-descendant relationships among different groups of organisms, for example, species or populations of interest. The datasets involved are usually sequence alignments of various subsets of taxa for various genes. A major task of phylogenetics is often to combine estimated gene trees from many loci sampled from the genes into an overall estimate species tree topology. Eventually, one can construct the tree of life that depicts the ancestor-descendant relationships for all known species around the world. If there is missing data or incomplete sampling in the datasets, then supertree methods can be used to assemble gene trees with different subsets of taxa into an estimated overall species tree topology. In this study, we assume that gene tree discordance is solely due to incomplete lineage sorting under the multispecies coalescent model (Degnan and Rosenberg, 2009). If there is missing data or incomplete sampling in the datasets, then supertree methods can be used to assemble gene trees with different subsets of taxa into an estimated species tree topology. In addition, we examine the performance of the most commonly used supertree method (Wilkinson et al., 2009), namely matrix representation with parsimony (MRP), to explore its statistical properties in this setting. In particular, we show that MRP is not statistically consistent. That is, an estimated species tree topology other than the true species tree topology is more likely to be returned by MRP as the number of gene trees increases. For some situations, using longer branch lengths, randomly deleting taxa or even introducing mutation can improve the performance of MRP so that the matching species tree topology is recovered more often. In conclusion, MRP is a supertree method that is able to handle large amounts of conflict in the input gene trees. However, MRP is not statistically consistent, when using gene trees arise from the multispecies coalescent model to estimate species trees.

Performing inference on contemporary samples of homologous DNA sequence data is an important task. By assuming a stochastic model for ancestry, one can make full use of observed data by sampling from the distribution of genealogies conditional upon the sample configuration. A natural such model is Kingman's coalescent, with numerous extensions to account for additional biological phenomena. However, in this model the distribution of interest cannot be written down analytically, and so one solution is to utilize importance sampling. In this context, importance sampling (IS) simulates genealogies from an artificial proposal distribution, and corrects for this by weighting each resulting genealogy. In this thesis I investigate in detail approaches for developing efficient proposal distributions on coalescent histories, with a particular focus on a two-locus model mutating under the infinite-sites assumption and in which the loci are separated by a region of recombination. This model was originally studied by Griffiths (1981), and is a useful simplification for considering the correlated ancestries of two linked loci. I show that my proposal distribution generally outperforms an existing IS method which could be recruited to this model. Given today's sequencing technologies it is not difficult to find volumes of data for which even the most efficient proposal distributions might struggle. I therefore appropriate resampling mechanisms from the theory of sequential Monte Carlo in order to effect substantial improvements in IS applications. In particular, I propose a new resampling scheme and confirm that it ensures a significant gain in the accuracy of likelihood estimates. It outperforms an existing scheme which can actually diminish the quality of an IS simulation unless it is applied to coalescent models with care. Finally, I apply the methods developed here to an example dataset, and discuss a new measure for the way in which two gene trees are correlated.

Delimitar espécies e reconstruir a história evolutiva em complexos de espécies pode demandar grandes esforços uma vez que grupos taxonomicamente problemáticos são muitas vezes consequência de eventos de especiação recente ou de rápida especiação. O complexo \'Cattleya coccinea\', da família Orchidaceae, é composto por orquídeas com alto valor ornamental, epifíticas e rupícolas de porte pequeno. Apesar de estarem descritas com caracteres morfológicos diagnósticos claros que permitem sua identificação, a delimitação das espécies atualmente reconhecidas é problemática. Portanto, os objetivos dessa pesquisa foram revisar a delimitação de espécies do complexo e a relação entre as espécies, além de avaliar a diversidade e estrutura genética, aliadas às análises filogeográficas para testar a ocorrência de eventos demográficos históricos. Para responder tais questões foram utilizadas regiões de sequência de cpDNA e nrDNA, 11 locos microssatélites, além de inferência bayesiana e modelo coalescente somadas às estatísticas tradicionais como metodologia. Os resultados suportam o monofiletismo para o clado para as regiões de cpDNA concatenadas. Indicam também quatro grandes eventos de reticulação das espécies do clado C. coccinea com outras espécies do gênero Cattleya. Adicionalmente, suportam o reconhecimento de sete diferentes espécies para o clado C. coccinea, composto por duas principais linhagens evolutivas mais ao norte da região Sudeste: C. brevipedunculata predominante da Serra do Espinhaço e C. wittigiana do norte da Serra do Mar. E cinco espécies distribuídas ao longo da Serra do Mar e Serra da Mantiqueira (C. coccinea, C. mantiqueirae, e mais três espécies correspondentes às populações de DMES; SJPSP e CSRS/JOSC/PMPR. As análises de diversidade mostraram de moderados a altos níveis de diversidade genética e apontam que as espécies C. coccinea e C. brevipedunculata apresentam os maiores níveis de diversidade comparadas a outras espécies do clado. A estruturação genética entre populações dentro de espécies mostrou variação entre níveis baixos a altos. A análise de atribuição de indivíduos a partir de inferência bayesiana mostrou a formação de oito grupos geneticamente distintos. A análise de taxa de dispersão de fluxo gênico pólen x semente mostrou que a dispersão via pólen é aproximadamente oito vezes mais eficiente que a dispersão via sementes somente para C. coccinea. Além disso, a rede de haplótipos indicou que as espécies raramente compartilham haplótipos e que C. coccinea e C. brevipedunculata apresentam maior diversidade com eventos de expansão. A análise de estimativa de tempo de divergência demonstrou que C. brevipedunculata e C. wittigiana provavelmente se originaram entre o Plioceno e o Pleistoceno. As outras espécies do clado se diversificaram no Pleistoceno. Eventos de expansão populacional foram observados para todas as espécies em eras glaciais do Pleistoceno. Por se tratarem de espécies ameaçadas, esse estudo recomenda a conservação \"in situ\" como também a conservação \"ex situ\" de todas as espécies do clado, com atenção especial às duas espécies do Espírito Santo: C. wittigiana e a espécie da localidade DMES, além da espécie da localidade SJPSP em São Paulo. / Species delimitation and reconstruction of the evolutionary history of species complexes may require great efforts since taxonomically problematic groups are often a result of recent speciation events or rapid speciation. The \'Cattleya coccinea\' complex, of the orchid family, consists of epiphytic and small rupicolous orchids with high ornamental value. Despite being described with clear diagnostic morphological characters that allow their identification, delimitation of the currently recognized species is problematic. Therefore, the objectives of this study were to review the species delimitation of the complex and the relationship between species, and to evaluate the genetic diversity and structure, combined with phylogeographic analyzes to test the occurrence of historical demographic events. To answer such questions, cpDNA and nrDNA sequence regions, 11 microsatellite loci, and Bayesian inference and coalescent model were used, combined with traditional statistics and methodology. The results support the monophyly for the clade for concatenated cpDNA regions. They also indicate four major reticulation events of C. coccinea species clade with other species of the genus Cattleya. Additionally, results support the recognition of seven different species for C. coccinea clade, composed of two main evolutionary lineages further north in the Southeast: C. brevipedunculata predominant in the Serra do Espinhaço and C. wittigiana from northern Serra do Mar. And five species distributed along the Serra do Mar and Serra da Mantiqueira (C. coccinea, C. mantiqueirae, and three other species of the populations DMES; SJPSP and CSRS/JOSC/PMPR. The diversity analyzes showed moderate to high levels of genetic diversity and point out that the species C. coccinea and C. brevipedunculata have the highest levels of diversity compared to other species of the clade. The genetic structure of populations within species showed variation from low to high. Assigning individuals analysis from Bayesian inference showed the formation of eight genetically distinct groups. The dispersal rate analysis of pollen x seed gene flow showed that dispersal through pollen is approximately eight times more efficient than the dispersal through seeds only for C. coccinea. Furthermore, the haplotype network indicated that the species rarely share haplotypes and that C.coccinea and C. brevipedunculata present greater diversity with expansion events. The divergence time estimation analysis showed that C. brevipedunculata and C. wittigiana probably originated between the Pliocene and the Pleistocene. The other clade species have diversified in the Pleistocene. Population expansion events were observed for all species in the Pleistocene ice ages. Because they are endangered species, this study recommends the \"in situ\" conservation as well as \"ex situ\" conservation for all species of clade, with special attention for two species of Espírito Santo: C. wittigiana and the species of DMES locality, in addition to the species of SJPSP location in São Paulo.

This thesis focuses on phylogenetic relationships among some of the major lineages in Silene subgenus Behenantha (Caryophyllaceae) using DNA sequences from multiple, potentially unlinked gene regions from a large taxonomic and geographic sample. Both traditional phylogenetic analyses and a strategy to infer species trees and gene trees in a joint approach are used. A new strategy to optimize species classifications, based on the likelihoods of the observed gene trees, is presented. Silene latifolia, S. dioica and the other dioecious species previously classified in section Elisanthe are not closely related to the type of the section (S. noctiflora). The correct name for the group of dioecious species is section Melandrium. The chloroplast DNA data presented indicate a geographic, rather than a taxonomic, structure in section Melandrium. The nuclear genes investigated correlate more to the current taxonomy, although hybridization has likely been influencing the relationships within section Melandrium. Incongruence between different parts of the gene SlXY1 in two Silene lineages is investigated, using phylogenetic methods and a novel probabilistic, multiple primer-pair PCR approach. The incongruence is best explained by ancient hybridization and recombination events. A survey of mitochondrial substitution rate variation in Sileneae is presented. Silene section Conoimorpha, S. noctiflora and the closely related S. turkestanica have elevated synonymous substitution rates in the mitochondrial genes investigated. Morphological and phylogenetic data reject that the Californian S. multinervia should be treated as a synonym to the Asian S. coniflora, as has previously been suggested. Furthermore, none of the genes investigated, or a chromosome count, support the inclusion of S. multinervia in section Conoimorpha. Data from multiple genes suggest that S. noctiflora and S. turkestanica form a sister group to section Conoimorpha. The calyx nervature, which is a potential synapomorphy for S. multinervia and section Conoimorpha, may be explained either by parallelism or by sorting effects.

Dans la majeure partie de cette thèse, nous nous sommes consacrés à l'étude de la forme des arbres phylogénétiques et plus particulièrement à leur déséquilibre. Une phylogénie est dite déséquilibrée, si la plupart des noeuds internes (les ancêtres communs) séparent l'arbre en deux sous-arbres de tailles sensiblement différentes. Les deux modèles de phylogénies aléatoires les plus classiques sont le modèle de Yule qui suppose que toutes les espèces ont la même probabilité de spéciation, et le modèle uniforme qui suppose que toutes les phylogénies de même taille sont équiprobables. Dans ces deux modèles, nous avons pu identifier les distributions limites des mesures de déséquilibre les plus utilisées par les biologistes. Les démonstrations sont inspirées de méthodes apparues récemment dans l'analyse des algorithmes. En génétique des populations, nous avons montré que le déséquilibre des généalogies de gènes est le signal d'un phénomène culturel : l'héritage de la fertilité. Nous avons mis en évidence la présence de ce trait culturel dans les populations de chasseurs-cueilleurs en utilisant le déséquilibre de généalogies reconstruites à partir d'ADN mitochondrial. Dans une dernière partie, la théorie de la coalescence a été appliquée à la génétique spatiale. Trois méthodes d'inférence d'un paramètre de dispersion spatiale ont été proposées. La vitesse de dispersion des ours bruns de Scandinavie a été estimée par une de ces trois méthodes.

Delimitar espécies e reconstruir a história evolutiva em complexos de espécies pode demandar grandes esforços uma vez que grupos taxonomicamente problemáticos são muitas vezes consequência de eventos de especiação recente ou de rápida especiação. O complexo \'Cattleya coccinea\', da família Orchidaceae, é composto por orquídeas com alto valor ornamental, epifíticas e rupícolas de porte pequeno. Apesar de estarem descritas com caracteres morfológicos diagnósticos claros que permitem sua identificação, a delimitação das espécies atualmente reconhecidas é problemática. Portanto, os objetivos dessa pesquisa foram revisar a delimitação de espécies do complexo e a relação entre as espécies, além de avaliar a diversidade e estrutura genética, aliadas às análises filogeográficas para testar a ocorrência de eventos demográficos históricos. Para responder tais questões foram utilizadas regiões de sequência de cpDNA e nrDNA, 11 locos microssatélites, além de inferência bayesiana e modelo coalescente somadas às estatísticas tradicionais como metodologia. Os resultados suportam o monofiletismo para o clado para as regiões de cpDNA concatenadas. Indicam também quatro grandes eventos de reticulação das espécies do clado C. coccinea com outras espécies do gênero Cattleya. Adicionalmente, suportam o reconhecimento de sete diferentes espécies para o clado C. coccinea, composto por duas principais linhagens evolutivas mais ao norte da região Sudeste: C. brevipedunculata predominante da Serra do Espinhaço e C. wittigiana do norte da Serra do Mar. E cinco espécies distribuídas ao longo da Serra do Mar e Serra da Mantiqueira (C. coccinea, C. mantiqueirae, e mais três espécies correspondentes às populações de DMES; SJPSP e CSRS/JOSC/PMPR. As análises de diversidade mostraram de moderados a altos níveis de diversidade genética e apontam que as espécies C. coccinea e C. brevipedunculata apresentam os maiores níveis de diversidade comparadas a outras espécies do clado. A estruturação genética entre populações dentro de espécies mostrou variação entre níveis baixos a altos. A análise de atribuição de indivíduos a partir de inferência bayesiana mostrou a formação de oito grupos geneticamente distintos. A análise de taxa de dispersão de fluxo gênico pólen x semente mostrou que a dispersão via pólen é aproximadamente oito vezes mais eficiente que a dispersão via sementes somente para C. coccinea. Além disso, a rede de haplótipos indicou que as espécies raramente compartilham haplótipos e que C. coccinea e C. brevipedunculata apresentam maior diversidade com eventos de expansão. A análise de estimativa de tempo de divergência demonstrou que C. brevipedunculata e C. wittigiana provavelmente se originaram entre o Plioceno e o Pleistoceno. As outras espécies do clado se diversificaram no Pleistoceno. Eventos de expansão populacional foram observados para todas as espécies em eras glaciais do Pleistoceno. Por se tratarem de espécies ameaçadas, esse estudo recomenda a conservação \"in situ\" como também a conservação \"ex situ\" de todas as espécies do clado, com atenção especial às duas espécies do Espírito Santo: C. wittigiana e a espécie da localidade DMES, além da espécie da localidade SJPSP em São Paulo. / Species delimitation and reconstruction of the evolutionary history of species complexes may require great efforts since taxonomically problematic groups are often a result of recent speciation events or rapid speciation. The \'Cattleya coccinea\' complex, of the orchid family, consists of epiphytic and small rupicolous orchids with high ornamental value. Despite being described with clear diagnostic morphological characters that allow their identification, delimitation of the currently recognized species is problematic. Therefore, the objectives of this study were to review the species delimitation of the complex and the relationship between species, and to evaluate the genetic diversity and structure, combined with phylogeographic analyzes to test the occurrence of historical demographic events. To answer such questions, cpDNA and nrDNA sequence regions, 11 microsatellite loci, and Bayesian inference and coalescent model were used, combined with traditional statistics and methodology. The results support the monophyly for the clade for concatenated cpDNA regions. They also indicate four major reticulation events of C. coccinea species clade with other species of the genus Cattleya. Additionally, results support the recognition of seven different species for C. coccinea clade, composed of two main evolutionary lineages further north in the Southeast: C. brevipedunculata predominant in the Serra do Espinhaço and C. wittigiana from northern Serra do Mar. And five species distributed along the Serra do Mar and Serra da Mantiqueira (C. coccinea, C. mantiqueirae, and three other species of the populations DMES; SJPSP and CSRS/JOSC/PMPR. The diversity analyzes showed moderate to high levels of genetic diversity and point out that the species C. coccinea and C. brevipedunculata have the highest levels of diversity compared to other species of the clade. The genetic structure of populations within species showed variation from low to high. Assigning individuals analysis from Bayesian inference showed the formation of eight genetically distinct groups. The dispersal rate analysis of pollen x seed gene flow showed that dispersal through pollen is approximately eight times more efficient than the dispersal through seeds only for C. coccinea. Furthermore, the haplotype network indicated that the species rarely share haplotypes and that C.coccinea and C. brevipedunculata present greater diversity with expansion events. The divergence time estimation analysis showed that C. brevipedunculata and C. wittigiana probably originated between the Pliocene and the Pleistocene. The other clade species have diversified in the Pleistocene. Population expansion events were observed for all species in the Pleistocene ice ages. Because they are endangered species, this study recommends the \"in situ\" conservation as well as \"ex situ\" conservation for all species of clade, with special attention for two species of Espírito Santo: C. wittigiana and the species of DMES locality, in addition to the species of SJPSP location in São Paulo.

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