The rapid accumulation of numerous sequenced genomes has provided a golden opportunity for ancestral state reconstruction studies, especially in the whole genome reconstruction area. However, most ancestral genome reconstruction methods developed so far only focus on gene or replicon sequences instead of whole genomes. They rely largely on either detailed modeling of evolutionary events or edit distance computation, both of which can be computationally prohibitive for large data sets. Hence, most of these methods can only be applied to a small number of features and species. In this dissertation, we describe the design, implementation, and evaluation of an ancestral genome reconstruction system (REGEN) for bacteria. It is the first bacterial genome reconstruction tool that focuses on ancestral state reconstruction at the genome scale instead of the gene scale. It not only reconstructs ancestral gene content and contiguous gene runs using either a maximum parsimony or a maximum likelihood criterion but also replicon structures of each ancestor. Based on the reconstructed genomes, it can infer all major events at both the gene scale, such as insertion, deletion, and translocation, and the replicon scale, such as replicon gain, loss, and merge. REGEN finishes by producing a visual representation of the entire evolutionary history of all genomes in the study. With a model-free reconstruction method at its core, the computational requirement for ancestral genome reconstruction is reduced sufficiently for the tool to be applied to large data sets with dozens of genomes and thousands of features. To achieve as accurate a reconstruction as possible, we also develop a homologous gene family prediction tool for preprocessing. Furthermore, we build our in-house Prokaryote Genome Evolution simulator (PEGsim) for evaluation purposes. The homologous gene family prediction refinement module can refine homologous gene family predictions generated by third party de novo prediction programs by combining phylogeny and local gene synteny. We show that such refinement can be accomplished for up to 80% of homologous gene family predictions with ambiguity (mixed families). The genome evolution simulator, PEGsim, is the first random events based high level bacteria genome evolution simulator with models for all common evolutionary events at the gene, replicon, and genome scales. The concepts of conserved gene runs and horizontal gene transfer (HGT) are also built in. We show the validation of PEGsim itself and the evaluation of the last reconstruction component with simulated data produced by it. REGEN, REconstruction of GENomes, is an ancestral genome reconstruction tool based on the concept of neighboring gene pairs (NGPs). Although it does not cover the reconstruction of actual nucleotide sequences, it is capable of reconstructing gene content, contiguous genes runs, and replicon structure of each ancestor using either a maximum parsimony or a maximum likelihood criterion. Based on the reconstructed genomes, it can infer all major events at both the gene scale, such as insertion, deletion, and translocation, and the replicon scale, such as replicon gain, loss, and merge. REGEN finishes by producing a visual representation of the entire evolutionary history of all genomes in the study. / Ph. D.

Com o intuito de contribuir para a compreensão da evolução cariotípica em mamíferos, realizamos estudos comparativos, utilizando a pintura cromossômica, em dois grupos basais de mamíferos, as preguiças e os marsupiais. Realizamos comparações entre os cromossomos humanos e os cromossomos das preguiças de três dedos Bradypus torquatus e Bradypus variegatus, estabelecendo as homologias. A análise conjunta de nossos dados e daqueles da literatura sobre pintura cromossômica em outras espécies de Xenarthra permitiu identificar ou confirmar sinapomorfias cromossômicas dos grupos assim como características ancestrais. Também realizamos comparações entre os cromossomos X das duas espécies de preguiça e entre os cromossomos X dos marsupiais americanos Marmosops incanus e Metachirus nudicaudatus. Os principais resultados e conclusões estão resumidos a seguir. 1. Os cariótipos de B. torquatus e B. variegatus são semelhantes quanto à correspondência com os cromossomos humanos. As duas espécies apresentaram em comum (a) a presença das associações dos cromossomos humanos (HSA) 4/8, 7/10, 7/16, 12/22, 14/15 e 17/19, (b) a conservação de HSA 5, 6, 9, 11, 13, 14, 15, 17, 18, 20 e X, (c) dois pares compartilhando homologia com HSA 2, 7, 10, 12, 19 e 22, (d) três pares, com segmentos homólogos a HSA 8 e (e) a ausência da associação ancestral de Eutheria HSA 16/19. 2. O cariótipo de B. variegatus (2n=54) é mais rearranjado em relação ao humano do que o de B. torquatus (2n=50), principalmente devido a fissões de cromossomos ancestrais, que levaram ao maior número diplóide dessa espécie. 3. Reunindo os dados para as preguiças B. variegatus e B. torquatus aos das demais espécies de Xenarthra que tiveram estabelecidas as correlações entre seus cromossomos e os cromossomos humanos, confirmamos como características presentes em todas as espécies dessa supraordem (a) a conservação de HSA 9, 13, 17, 18, 20 e X, (b) a presença de dois pares cromossômicos compartilhando homologia com HSA 19 e 22 e (c) a presença das associações HSA 4/8, 7/16, 12/22 e 14/15. 4. Confirmamos a associação HSA 7/10 e a divisão de HSA 8 em três blocos como assinaturas cromossômicas da supraordem Xenarthra, o que concorda com a monofilia do grupo. 5. Mostramos que a associação HSA 17/19, presente nos cariótipos de B. variegatus, B. torquatus e B. tridactylus, parece ser assinatura cromossômica do gênero Bradypus, apoiando a monofilia do grupo. 6. Mostramos que a associação HSA 12/22/16 parece ser uma sinapomorfia cromossômica, unindo as espécies B. variegatus e B. tridactylus. 7. Considerando a correspondência com os cromossomos humanos, verificamos que os cariótipos de B. variegatus e B. tridactylus são os mais semelhantes, no gênero Bradypus. 8. A análise das correspondências entre as sequências dos cromossomos humanos e as sequências dos cromossomos de grupos externos de mamíferos placentários (marsupial e galinha) disponíveis no banco de dados Ensembl, mostrou que a associação HSA 7/10 presente na supraordem Xenarthra também ocorre nesses grupos externos. Confirmando-se a homologia dessa associação entre os grupos, ela deveria ser classificada como ancestral de Eutheria, apoiando a posição basal dos Xenarthra na árvore filogenética dos mamíferos placentários. 9. Nossas análises comparativas permitiram propor um cariótipo ancestral de Xenarthra com número diplóide de 48 cromossomos, incluindo (a) as associações HSA 3/21, 4/8, 7/10, 7/16, 12/22 (2x), 14/15 e 16/19, (b) a conservação dos cromossomos HSA 1, 3, 4, 5, 6, 9, 11, 13, 14, 15, 17, 18, 20, 21 e X, (c) dois pares cromossômicos com homologia a HSA 2, 7, 10, 12, 16, 19 e 22 e (d) três pares com homologia a HSA 8. 10. Entre os Xenarthra, B. torquatus e C. hoffmanni, com os menores números diplóides da supraordem, apresentam os cariótipos mais conservados em relação ao cariótipo que propusemos como ancestral de Xenarthra e também em relação ao mais recente cariótipo proposto como ancestral de Eutheria. 11. A conservação da eucromatina do cromossomo X foi evidenciada nos experimentos de pintura cromossômica interespecífica, entre as preguiças B. torquatus e B. variegatus e entre os marsupiais M. incanus e M. nudicaudatus. Os segmentos heterocromáticos desses cromossomos se mostraram divergentes, não permitindo a hibridação in situ interespecífica. / In an attempt to shed additional light on mammalian karyotype evolution, we studied, by chromosome painting, the chromosomes of species from two mammalian basal groups, sloths and marsupials. We compared human chromosomes with the chromosomes of two species of three-toed sloths, Bradypus torquatus and Bradypus variegatus, establishing homologies. Analyzing together ours and published data on chromosome painting in Xenarthra species allowed us to identify or confirm chromosome synapomorphies and ancestral characteristics. We also used chromosome painting to compare the X chromosomes of Bradypus torquatus and Bradypus variegatus as well as the X chromosomes of two American marsupials, Marmosops incanus and Metachirus nudicaudatus. Our main results and conclusions are summarized below. 1. The karyotypes of both B. torquatus and B. variegatus include (a) the human chromosomes associations HSA 4/8, 7/10, 7/16, 12/22, 14/15 and 17/19, (b) the conservation of HSA 5, 6, 9, 11, 13, 14, 15, 17, 18, 20 and X, (c) the disruption into two blocks of HSA 2, 7, 10, 12, 19 and 22, (d) three pairs sharing homologous segments with HSA 8, and (e) the absence of the ancestral eutherian association HSA 16/19. 2. B. variegatus (2n=54) presents a more rearranged karyotype, in relation to the human karyotype, than B. torquatus (2n=50), in particular due to fissions of ancestral chromosomes, which account for its higher diploid number. 3. Our data on B. variegatus and B. torquatus together with the previously published comparisons between human and Xenarthra chromosomes confirm, as characteristics common to the species of this super-order (a) the conservation of HSA 9, 13, 17, 18, 20 and X, (b) the disruption of HSA 19 and 22 into two blocks, and (c) the presence of the human chromosome associations HSA 4/8, 7/16, 12/22 and 14/15. 4. The human chromosome association HSA 7/10 and the disruption of HAS 8 into three blocks were confirmed as chromosome signatures for the super-order Xenarthra, supporting the monophyly of the group. 76 5. The HSA 17/19 association, which we demonstrated to be shared by B. variegatus, B. torquatus and B. tridactylus karyotypes, appears as a chromosome signature for the genus Bradypus, supporting the monophyly of the group. 6. The HSA 12/22/16 association seems to be a chromosome synapomorphic trait linking the species B. variegatus e B. tridactylus. 7. Take into account the correspondence between human and Bradypus chromosomes we observed that B. variegatus and B. tridactylus karyotypes are the most similar in the genus. 8. Based on the comparison of the human chromosomes sequences to the chromosomes sequences of the chicken and a marsupial species (outgroups to placental mammals), available in Ensembl database, we showed that a HSA 7/10 association, which is present in the super-order Xenarthra, is also present in the karyotype of the two outgroup species. As the homology between this chromosome association in Xenarthra and the outgroups are demonstrated, strong support for the classifications of this association as ancestral to Eutheria and of Xenarthra as a basal group in the eutherian phylogenetic tree will be given. 9. Our comparative analysis allow us to propose an ancestral Xenarthra karyotype with 2n=48, including (a) the human chromosome associations HSA 3/21, 4/8, 7/10, 7/16, 12/22 (2x), 14/15 and 16/19, (b) the conservation of HSA 1, 3, 4, 5, 6, 9, 11, 13, 14, 15, 17, 18, 20, 21 and X, (c) the disruption into two blocks of HSA 2, 7, 10, 12, 16, 19 and 22, and (d) three pairs sharing homologous segments with HSA 8. 10. Among Xenarthra species, B. torquatus and C. hoffmanni, with the lowest diploid number of the super-order, show the most conserved karyotypes in relation to our proposed ancestral Xenarthra karyotype as well as to the most recently proposed ancestral eutherian karyotype. 11. The conservation of the X chromosome euchromatin was demonstrated by interspecific chromosome painting between the sloths, B. torquatus and B. variegatus, and between the marsupials, M. incanus and M. nudicaudatus. The X chromosome heterochromatic segments were shown to be divergent in the extent to prevent in situ hybridization between species.

Orientador: Silvia Rodrigues Machado / Resumo: Leguminosae é a terceira maior família dentre as Angiospermas, é cosmopolita, podendo ocorrer em florestas tropicais úmidas, florestas secas, savanas, regiões mediterrâneas e desérticas. Papilionoideae, subfamília com maior riqueza de espécies de Leguminosae, apresenta Phaseoleae como uma de suas tribos de maior importância econômica e alto número de espécies. Cajaninae, por sua vez, é a maior subtribo de Phaseoleae, destacando-se por apresentar aproximadamente 490 espécies distribuídas em 10 gêneros. Os representantes desta subtribo possuem distribuição pantropical, com apenas Rhynchosia e Eriosema ocorrendo nos neotrópicos. De modo geral, as espécies desta subtribo ocorrem em campos graminosos, florestas tropicais secas, regiões semiáridas, áreas degradadas e ambientes propensos à passagem do fogo. A ocorrência das espécies de Cajaninae nestes diferentes ambientes pode estar relacionada à presença de estruturas secretoras, como glândulas vesiculares e tricomas de base bulbosa. Apesar do conhecimento sobre a existência destas estruturas peculiares neste grupo desde o século 19, nenhum estudo detalhado de anatomia, ultraestrutura ou estudos com enfoque evolutivo haviam sido realizados. A subtribo tem sido considerada monofilética, porém os poucos trabalhos filogenéticos existentes abordam Phaseoleae como um todo, possuindo uma amostragem muito baixa dos representantes de Cajaninae, o que não esclarece sua monofilia. Considerando o pouco conhecimento sobre as relações filogené... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Leguminosae is the third largest family among Angiosperms, is cosmopolitan, occurring in humid tropical forests, dry forests, savannas, Mediterranean and desert regions. Papilionoideae, a subfamily with the highest species richness of Leguminosae, presents Phaseoleae as one of its tribes of major economic importance and high number of species. Cajaninae, in turn, is the largest subtribe of Phaseoleae, standing out to present approximately 490 species distributed in 10 genera. The representatives of this subtribe have pantropical distribution, with only Rhynchosia and Eriosema occurring in the neotropics. The species of this subtribe occur in greenfields, dry tropical forests, semi-arid regions, degraded areas and environments prone to fire. The occurrence of Cajaninae species in these different environments may be related to the presence of secretory structures, such as vesicular glands and bulbous based-trichomes. Despite the knowledge about the existence of these peculiar structures in this group since the 19th century, no detailed study of anatomy, ultrastructure or evolutionary approach studies had been performed. The subtribe has been considered monophyletic, but the few existing phylogenetic works address Phaseoleae as a whole, having a very low sampling of Cajaninae representatives, which does not clarify its monophyly. Considering the little knowledge about the phylogenetic relationships in Cajaninae, on the secretory structures that are peculiar to this group and the... (Complete abstract click electronic access below) / Doutor

Com o intuito de contribuir para a compreensão da evolução cariotípica em mamíferos, realizamos estudos comparativos, utilizando a pintura cromossômica, em dois grupos basais de mamíferos, as preguiças e os marsupiais. Realizamos comparações entre os cromossomos humanos e os cromossomos das preguiças de três dedos Bradypus torquatus e Bradypus variegatus, estabelecendo as homologias. A análise conjunta de nossos dados e daqueles da literatura sobre pintura cromossômica em outras espécies de Xenarthra permitiu identificar ou confirmar sinapomorfias cromossômicas dos grupos assim como características ancestrais. Também realizamos comparações entre os cromossomos X das duas espécies de preguiça e entre os cromossomos X dos marsupiais americanos Marmosops incanus e Metachirus nudicaudatus. Os principais resultados e conclusões estão resumidos a seguir. 1. Os cariótipos de B. torquatus e B. variegatus são semelhantes quanto à correspondência com os cromossomos humanos. As duas espécies apresentaram em comum (a) a presença das associações dos cromossomos humanos (HSA) 4/8, 7/10, 7/16, 12/22, 14/15 e 17/19, (b) a conservação de HSA 5, 6, 9, 11, 13, 14, 15, 17, 18, 20 e X, (c) dois pares compartilhando homologia com HSA 2, 7, 10, 12, 19 e 22, (d) três pares, com segmentos homólogos a HSA 8 e (e) a ausência da associação ancestral de Eutheria HSA 16/19. 2. O cariótipo de B. variegatus (2n=54) é mais rearranjado em relação ao humano do que o de B. torquatus (2n=50), principalmente devido a fissões de cromossomos ancestrais, que levaram ao maior número diplóide dessa espécie. 3. Reunindo os dados para as preguiças B. variegatus e B. torquatus aos das demais espécies de Xenarthra que tiveram estabelecidas as correlações entre seus cromossomos e os cromossomos humanos, confirmamos como características presentes em todas as espécies dessa supraordem (a) a conservação de HSA 9, 13, 17, 18, 20 e X, (b) a presença de dois pares cromossômicos compartilhando homologia com HSA 19 e 22 e (c) a presença das associações HSA 4/8, 7/16, 12/22 e 14/15. 4. Confirmamos a associação HSA 7/10 e a divisão de HSA 8 em três blocos como assinaturas cromossômicas da supraordem Xenarthra, o que concorda com a monofilia do grupo. 5. Mostramos que a associação HSA 17/19, presente nos cariótipos de B. variegatus, B. torquatus e B. tridactylus, parece ser assinatura cromossômica do gênero Bradypus, apoiando a monofilia do grupo. 6. Mostramos que a associação HSA 12/22/16 parece ser uma sinapomorfia cromossômica, unindo as espécies B. variegatus e B. tridactylus. 7. Considerando a correspondência com os cromossomos humanos, verificamos que os cariótipos de B. variegatus e B. tridactylus são os mais semelhantes, no gênero Bradypus. 8. A análise das correspondências entre as sequências dos cromossomos humanos e as sequências dos cromossomos de grupos externos de mamíferos placentários (marsupial e galinha) disponíveis no banco de dados Ensembl, mostrou que a associação HSA 7/10 presente na supraordem Xenarthra também ocorre nesses grupos externos. Confirmando-se a homologia dessa associação entre os grupos, ela deveria ser classificada como ancestral de Eutheria, apoiando a posição basal dos Xenarthra na árvore filogenética dos mamíferos placentários. 9. Nossas análises comparativas permitiram propor um cariótipo ancestral de Xenarthra com número diplóide de 48 cromossomos, incluindo (a) as associações HSA 3/21, 4/8, 7/10, 7/16, 12/22 (2x), 14/15 e 16/19, (b) a conservação dos cromossomos HSA 1, 3, 4, 5, 6, 9, 11, 13, 14, 15, 17, 18, 20, 21 e X, (c) dois pares cromossômicos com homologia a HSA 2, 7, 10, 12, 16, 19 e 22 e (d) três pares com homologia a HSA 8. 10. Entre os Xenarthra, B. torquatus e C. hoffmanni, com os menores números diplóides da supraordem, apresentam os cariótipos mais conservados em relação ao cariótipo que propusemos como ancestral de Xenarthra e também em relação ao mais recente cariótipo proposto como ancestral de Eutheria. 11. A conservação da eucromatina do cromossomo X foi evidenciada nos experimentos de pintura cromossômica interespecífica, entre as preguiças B. torquatus e B. variegatus e entre os marsupiais M. incanus e M. nudicaudatus. Os segmentos heterocromáticos desses cromossomos se mostraram divergentes, não permitindo a hibridação in situ interespecífica. / In an attempt to shed additional light on mammalian karyotype evolution, we studied, by chromosome painting, the chromosomes of species from two mammalian basal groups, sloths and marsupials. We compared human chromosomes with the chromosomes of two species of three-toed sloths, Bradypus torquatus and Bradypus variegatus, establishing homologies. Analyzing together ours and published data on chromosome painting in Xenarthra species allowed us to identify or confirm chromosome synapomorphies and ancestral characteristics. We also used chromosome painting to compare the X chromosomes of Bradypus torquatus and Bradypus variegatus as well as the X chromosomes of two American marsupials, Marmosops incanus and Metachirus nudicaudatus. Our main results and conclusions are summarized below. 1. The karyotypes of both B. torquatus and B. variegatus include (a) the human chromosomes associations HSA 4/8, 7/10, 7/16, 12/22, 14/15 and 17/19, (b) the conservation of HSA 5, 6, 9, 11, 13, 14, 15, 17, 18, 20 and X, (c) the disruption into two blocks of HSA 2, 7, 10, 12, 19 and 22, (d) three pairs sharing homologous segments with HSA 8, and (e) the absence of the ancestral eutherian association HSA 16/19. 2. B. variegatus (2n=54) presents a more rearranged karyotype, in relation to the human karyotype, than B. torquatus (2n=50), in particular due to fissions of ancestral chromosomes, which account for its higher diploid number. 3. Our data on B. variegatus and B. torquatus together with the previously published comparisons between human and Xenarthra chromosomes confirm, as characteristics common to the species of this super-order (a) the conservation of HSA 9, 13, 17, 18, 20 and X, (b) the disruption of HSA 19 and 22 into two blocks, and (c) the presence of the human chromosome associations HSA 4/8, 7/16, 12/22 and 14/15. 4. The human chromosome association HSA 7/10 and the disruption of HAS 8 into three blocks were confirmed as chromosome signatures for the super-order Xenarthra, supporting the monophyly of the group. 76 5. The HSA 17/19 association, which we demonstrated to be shared by B. variegatus, B. torquatus and B. tridactylus karyotypes, appears as a chromosome signature for the genus Bradypus, supporting the monophyly of the group. 6. The HSA 12/22/16 association seems to be a chromosome synapomorphic trait linking the species B. variegatus e B. tridactylus. 7. Take into account the correspondence between human and Bradypus chromosomes we observed that B. variegatus and B. tridactylus karyotypes are the most similar in the genus. 8. Based on the comparison of the human chromosomes sequences to the chromosomes sequences of the chicken and a marsupial species (outgroups to placental mammals), available in Ensembl database, we showed that a HSA 7/10 association, which is present in the super-order Xenarthra, is also present in the karyotype of the two outgroup species. As the homology between this chromosome association in Xenarthra and the outgroups are demonstrated, strong support for the classifications of this association as ancestral to Eutheria and of Xenarthra as a basal group in the eutherian phylogenetic tree will be given. 9. Our comparative analysis allow us to propose an ancestral Xenarthra karyotype with 2n=48, including (a) the human chromosome associations HSA 3/21, 4/8, 7/10, 7/16, 12/22 (2x), 14/15 and 16/19, (b) the conservation of HSA 1, 3, 4, 5, 6, 9, 11, 13, 14, 15, 17, 18, 20, 21 and X, (c) the disruption into two blocks of HSA 2, 7, 10, 12, 16, 19 and 22, and (d) three pairs sharing homologous segments with HSA 8. 10. Among Xenarthra species, B. torquatus and C. hoffmanni, with the lowest diploid number of the super-order, show the most conserved karyotypes in relation to our proposed ancestral Xenarthra karyotype as well as to the most recently proposed ancestral eutherian karyotype. 11. The conservation of the X chromosome euchromatin was demonstrated by interspecific chromosome painting between the sloths, B. torquatus and B. variegatus, and between the marsupials, M. incanus and M. nudicaudatus. The X chromosome heterochromatic segments were shown to be divergent in the extent to prevent in situ hybridization between species.

Ce mémoire analyse l’espérance du temps de fixation conditionnellement à ce qu’elle se produise et la probabilité de fixation d’un nouvel allèle mutant dans des populations soumises à différents phénomènes biologiques en uti- lisant l’approche des processus ancestraux. Tout d’abord, l’article de Tajima (1990) est analysé et les différentes preuves y étant manquantes ou incomplètes sont détaillées, dans le but de se familiariser avec les calculs du temps de fixa- tion. L’étude de cet article permet aussi de démontrer l’importance du temps de fixation sur certains phénomènes biologiques. Par la suite, l’effet de la sé- lection naturelle est introduit au modèle. L’article de Mano (2009) cite un ré- sultat intéressant quant à l’espérance du temps de fixation conditionnellement à ce que celle-ci survienne qui utilise une approximation par un processus de diffusion. Une nouvelle méthode utilisant le processus ancestral est présentée afin d’arriver à une bonne approximation de ce résultat. Des simulations sont faites afin de vérifier l’exactitude de la nouvelle approche. Finalement, un mo- dèle soumis à la conversion génique est analysé, puisque ce phénomène, en présence de biais, a un effet similaire à celui de la sélection. Nous obtenons finalement un résultat analytique pour la probabilité de fixation d’un nouveau mutant dans la population. Enfin, des simulations sont faites afin de détermi- nerlaprobabilitédefixationainsiqueletempsdefixationconditionnellorsque les taux sont trop grands pour pouvoir les calculer analytiquement. / The expected time for fixation given its occurrence, and the probability of fixa- tion of a new mutant allele in populations subject to various biological phe- nomena are analyzed using the approach of the ancestral process. First, the paper of Tajima (1990) is analyzed, and the missing or incomplete proofs are fully worked out in this Master thesis in order to familiarize ourselves with calculations of fixation times. Our study of Tajima’s paper helps to show the importance of the fixation time in some biological phenomena. Thereafter, we extend the work of Tajima (1990) by introducing the effect of natural selec- tion in the model. Using a diffusion approximation, the work of Mano (2009) provides an interesting result about the expected time of fixation given its oc- currence. We derived an alternative method that uses an ancestral process that approximates well Mani’s result. Simulations are made to verify the accuracy ofthenewapproach.Finally,onemodelsubjecttogeneconversionisanalyzed, since this phenomenon, in the presence of bias, has a similar effect as selection. We deduce an analytical result for the probability of fixation of a new mutant in the population. Finally, simulations are made to determine the probability of fixation and the time of fixation given its occurrence when rates are too large to be calculated analytically.

Ce mémoire analyse l’espérance du temps de fixation conditionnellement à ce qu’elle se produise et la probabilité de fixation d’un nouvel allèle mutant dans des populations soumises à différents phénomènes biologiques en uti- lisant l’approche des processus ancestraux. Tout d’abord, l’article de Tajima (1990) est analysé et les différentes preuves y étant manquantes ou incomplètes sont détaillées, dans le but de se familiariser avec les calculs du temps de fixa- tion. L’étude de cet article permet aussi de démontrer l’importance du temps de fixation sur certains phénomènes biologiques. Par la suite, l’effet de la sé- lection naturelle est introduit au modèle. L’article de Mano (2009) cite un ré- sultat intéressant quant à l’espérance du temps de fixation conditionnellement à ce que celle-ci survienne qui utilise une approximation par un processus de diffusion. Une nouvelle méthode utilisant le processus ancestral est présentée afin d’arriver à une bonne approximation de ce résultat. Des simulations sont faites afin de vérifier l’exactitude de la nouvelle approche. Finalement, un mo- dèle soumis à la conversion génique est analysé, puisque ce phénomène, en présence de biais, a un effet similaire à celui de la sélection. Nous obtenons finalement un résultat analytique pour la probabilité de fixation d’un nouveau mutant dans la population. Enfin, des simulations sont faites afin de détermi- nerlaprobabilitédefixationainsiqueletempsdefixationconditionnellorsque les taux sont trop grands pour pouvoir les calculer analytiquement. / The expected time for fixation given its occurrence, and the probability of fixa- tion of a new mutant allele in populations subject to various biological phe- nomena are analyzed using the approach of the ancestral process. First, the paper of Tajima (1990) is analyzed, and the missing or incomplete proofs are fully worked out in this Master thesis in order to familiarize ourselves with calculations of fixation times. Our study of Tajima’s paper helps to show the importance of the fixation time in some biological phenomena. Thereafter, we extend the work of Tajima (1990) by introducing the effect of natural selec- tion in the model. Using a diffusion approximation, the work of Mano (2009) provides an interesting result about the expected time of fixation given its oc- currence. We derived an alternative method that uses an ancestral process that approximates well Mani’s result. Simulations are made to verify the accuracy ofthenewapproach.Finally,onemodelsubjecttogeneconversionisanalyzed, since this phenomenon, in the presence of bias, has a similar effect as selection. We deduce an analytical result for the probability of fixation of a new mutant in the population. Finally, simulations are made to determine the probability of fixation and the time of fixation given its occurrence when rates are too large to be calculated analytically.

本文以「嘗會」為研究的主題，並於前面加上「客家」一詞，是希望突顯以客家為主題的論述與特性，藉此來瞭解客家人的文化特徵，故從歷史脈絡看來，研究地區若非屬早期客家人開墾的地方，則未列入研究場域，冀望透過這樣的研究思維，並運用比較研究觀點，呈現出西湖溪流域內客家嘗會之一般與核心的文化特徵。 研究動機除了對客家嘗會的核心文化特徵加以探討外，亦綜合前人對中國傳統社會宗族理論成果之探討，運用於本文之研究；期望透過宗族相關理論的應用，並藉由西湖溪流域嘗會的族產統計分析，以達成研究目的，包含探討的早期宗族分布的情況、有哪些宗族對流域拓墾較具代表性、嘗會與宗族發展甚或對聚落發展的關聯性等；再以西湖溪流域客家嘗會為核心的觀察，探析國家政策與社會變遷對嘗會的挑戰。研究方法上，則採用文獻分析、參與觀察以及深度訪談。在資料處理方面，則運用2009年政府地政機關有關嘗會族產的公務登記資料為基礎，進而以統計方法加以整理、歸納、分析，並與相關文獻分析結果做比較與對話，以進一步提升研究資料分析結果之信度與效度。 研究結果發現客家嘗會可探析客家人早期來台拓墾的宗族發展的脈絡與聚落發展的關聯性，亦可分析出流域內前五大姓氏宗族分別依序為賴、李、彭、劉、邱，並可探討嘗會於客家地方社會發展的意義與特質；而「嘗」所展現的形式上與實質上的意涵，代表著客家人獨特的文化特徵，惟這些客家文化的特殊性，不僅正面臨社會轉型與時代變遷的衝擊，亦面臨著從日治時期政府以來，國家政策前所未有的挑戰。 / This paper takes Hakka Ancestral Estate Associations（嘗會cang hui）as the subject of the study. As the term “cang hui” is used only by the Hakka ethnic group in both mainland China and Taiwan, this study is to explore the characteristics and Hakka people and its culture features. Therefore, in terms of historical context, the region for the research is limited only to Xihu River basin area where early Hakka immigrants settled. Through this kind of study and by comparing various research points of view about cang hui, this paper hopes to present the general and core cultural characteristics of Hakka Ancestral Estate Associations in Xihu River Basin. In addition to exploring the core cultural characteristics of Hakka Ancestral Estate Associations, the study also deals with and applies discussions and findings of previous theories on traditional Chinese society lineage, hoping that through the application of lineage related theory and the statistical analysis of the Hakka Ancestral Estate Associations in Xihu River Basin to attain the research purposes. The purposes are the situation of the early lineage distribution, lineages which are more representative of the development of Xihu River Basin, the relationship between the development of Hakka Ancestral Estate Associations and the development of the lineage, and the relevance of the development of settlement, etc. The Hakka Ancestral Estate Associations in Xihu River Basin is the core observation. In addition, this study discusses further the impact of government policy and social change on the Hakka Ancestral Estate Associations. In terms of research method, we use document analysis, participation in observation and in-depth interviews. About data processing, we use the official registration information of the property of Ancestral Estate Associations owned by the government's land office in 2009 and then adopt suitable statistical methods to sort, summarize, analyze and compare the result of related historical documents to enhance the reliability and validity of the research data analysis results. The study finds that Hakka Ancestral Estate Associations can explore the relationship between the historical context of lineage development and the development of settlements in the early history. We can also use it to find that family names of the top five lineages in the river basin are Lai, Li, Peng, Liu and Chiu. Besides, we can analyze the meaning and characteristics of Hakka Ancestral Estate Associations in Hakka society. While formal and realistic meaning of “Chang”(嘗) represents Hakka people’s unique cultural characteristics, this uniqueness is not only facing the impact of social transformation and the change of the times, but also facing unprecedented challenges by government policy since Japanese Reign.

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.

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.

The Ayaawx is the ancient law of Ts’msyen people situated on the northwest coast of British Columbia. With principles for spiritual, social, political and economic relations, the Ayaawx has been taught both directly and indirectly in daily and ceremonial living for centuries. The Ayaawx holds transformational change as a natural event in human relationships with each other, the land, and the supernatural world. Yet the Ayaawx is not studied in depth in post secondary institutions in British Columbia or defined as a resource for program development by governments or a reliable resource by us as Ts’msyen people. Statistical data on Indigenous Canadians is prolific indicating the severity of suffering caused by social and legalized oppression. Indigenous peoples of Canada have received health, social, psychological, psychiatric and educational services from the federal and provincial governments for over one hundred years and yet the suffering remains inordinately high. For example, less than sixty years ago Sm’algyax was spoken by children, adolescents, adults and elders in Ts’msyen communities and individuals and House Groups knew the protocol for resolving conflicts in families and the community. The organization and interpretation of this dissertation has been structured here in the format of a contemporary Adaawx, (sacred story), with Sm’algyax, (Ts’msyen language) as the main reference for meaning when discussing the impact of cultural oppression and in identifying the main principles of the Ayaawx that will assist individuals, families and communities in transforming suffering. Transformation is a common act in Adaawx, art objects, dramatizations and song. Woven throughout Adaawx, the principles of the Ayaawx are a vital resource not only to transform suffering, but it is also a guide to direct all human beings into a progressive future.