This thesis develops and evaluates statistical methods for different types of genetic analyses, including quantitative trait loci (QTL) analysis, genome-wide association study (GWAS), and genomic evaluation. The main contribution of the thesis is to provide novel insights in modeling genetic variance, especially via random effects models. In variance component QTL analysis, a full likelihood model accounting for uncertainty in the identity-by-descent (IBD) matrix was developed. It was found to be able to correctly adjust the bias in genetic variance component estimation and gain power in QTL mapping in terms of precision.  Double hierarchical generalized linear models, and a non-iterative simplified version, were implemented and applied to fit data of an entire genome. These whole genome models were shown to have good performance in both QTL mapping and genomic prediction. A re-analysis of a publicly available GWAS data set identified significant loci in Arabidopsis that control phenotypic variance instead of mean, which validated the idea of variance-controlling genes.  The works in the thesis are accompanied by R packages available online, including a general statistical tool for fitting random effects models (hglm), an efficient generalized ridge regression for high-dimensional data (bigRR), a double-layer mixed model for genomic data analysis (iQTL), a stochastic IBD matrix calculator (MCIBD), a computational interface for QTL mapping (qtl.outbred), and a GWAS analysis tool for mapping variance-controlling loci (vGWAS).

Meningitis is an infection of the meninges, a layer of tissue surrounding the brain. In cases of pneumococcal meningitis (where the bacterium Streptococcus pneumoniae is the causat- ive agent) this causes severe inflammation, requiring intensive care and rapid antibiotic treatment. The contribution of variation in host and pathogen genetics to pneumococcal meningitis is unknown. In this thesis I develop and apply statistical genetics techniques to identify genomic variation associated with the various stages of pneumococcal meningitis, including colonisation, invasion and severity. I start by describing the development of a method to perform genome-wide association studies (GWAS) in bacteria, which can find variation in bacterial genomes associated with bacterial traits such as antibiotic resistance and virulence. I then applied this method to longitudinal samples from asymptomatic carriage, and found lineages and specific variants associated with altered duration of carriage. To assess meningitis versus carriage samples I applied similar analysis techniques, and found that the bacterial genome is crucial in determining invasive potential. As well as bacterial serotype, which I found to be the main effect, I discovered many independent sequence variants associated with disease. Separately, I analysed within host-diversity during the invasive phase of disease and found it to be of less relevance to disease progression. Finally, I analysed host genotype data from four independent studies using GWAS and heritability estimates to determine the contribution of human sequence variation to pneumococcal meningitis. Host sequence accounted for some variation in susceptibility to and severity of meningitis. The work concludes with a combined analysis of pairs of bacterial and human sequences from meningitis cases, and finds variation correlated between the two.

A obtenção de híbridos de milho está relacionada com o aumento de produtividade dessa cultura. Para isso, normalmente são realizados cruzamentos entre linhagens de diferentes grupos heteróticos, que são determinados pelos melhoristas de forma que seja maximizada a divergência entre eles. A escolha dos genitores a serem cruzados pode ser facilitada pelo uso de cruzamentos dialélicos. Os modelos usados para a análise dos dialélicos permitem a estimação de parâmetros úteis para a seleção dos genitores e o estabelecimento de grupos heteróticos, sendo que os efeitos genéticos normalmente podem ser considerados como aleatórios. A forma tradicional de análise inclui tais efeitos na matriz de incidência dos efeitos fixos e emprega o método dos mínimos quadrados ordinários, o que impossibilita a análise usando a metodologia dos modelos mistos. Os objetivos deste trabalho foram comparar os resultados das análises dialélicas obtidas considerando o modelo fixo e o modelo misto e avaliar a eficiência do melhor preditor linear não viesado (BLUP) para predição de cruzamentos não realizados entre linhagens de milho, utilizando informações de marcadores moleculares RFLP para a estimação da matriz de parentesco. Foram considerados dados de 80 híbridos interpopulacionais e 20 testemunhas comerciais, avaliados em um látice 10 x 10 em três locais. Esses híbridos foram obtidos pelo cruzamento entre 8 linhagens do grupo heterótico BR-105 e 10 do grupo BR-106, as quais foram genotipadas com marcador RFLP. A análise dialélica foi realizada segundo a metodologia que considera o modelo genético como fixo e usa o método dos mínimos quadrados ordinários, e também usando a metodologia de modelos mistos, assumindo que a capacidade geral de combinação (CGC) dos dois grupos heteróticos e a capacidade específica de combinação (CEC) representam efeitos aleatórios. Além disso, foi avaliada a predição de híbridos simples não realizados, com base na matriz de covariâncias genéticas entre o híbrido não realizado e os híbridos preditores, usando as informações do marcador RFLP. Como todos os híbridos foram obtidos, foi simulada a retirada de cada um deles do conjunto, sendo sua performance predita a partir dos 79 restantes. Os resultados mostraram que, na comparação entre as análises dialélicas obtidas com as duas metodologias, embora os valores da CGC das linhagens da população BR-106 e da CEC tenham baixa correlação entre as duas metodologias (r=-0,11 e r=-0,06, respectivamente), a classificação dos híbridos mais produtivos sofre poucas alterações (r=0,99) e não causa dificuldades na seleção. A eficiência do BLUP para predição de cruzamentos não realizados entre linhagens de milho, utilizando informações de marcadores moleculares para a estimação da matriz de parentesco, mostrou a existência de moderada correlação entre os valores dos BLUP’s da produção de grãos e os valores preditos a partir dos híbridos observados restantes (r=0,35), o que indica que essa metodologia tem capacidade em predizer a estimativa de valores não observados, porém com alguma imprecisão. Os mesmos resultados foram observados entre as capacidades específicas de combinação observadas e as preditas (r=0,30). Conclui-se que a metodologia de modelos mistos pode ser usada, desde que com ressalvas, dada as correlações moderadas. / The obtainment of maize single crosses is related with increasing in productivity. To do so, inbred lines derived of different heterotic groups are crossed. These groups are established in such a way that the genetic divergences among them are maximized. Using diallel crosses can facilitate the choice of the inbred lines to be crossed. The models used to perform these analyses allow estimating genetic parameters that are useful in the selection of parental lines and in determining the heterotic groups. In these models, generally, the genetic effects are considered as random. However, these analyses are usually performed considering these effects in the matrix of fixed effects, and obtaining the parameter estimates according to the ordinary least squares method, making impossible using mixed linear models theory. The aims of this research were to compare the results of diallel analyses obtained by using fixed and mixed models, and evaluate the efficiency of the best linear unbiased predictor (BLUP) in predicting non-realized single crosses. Eighty interpopulation hybrids and twenty commercial checks were evaluated in a 10 x 10 lattice design with two replications located in three environments. These single crosses were obtained by crossing eight and ten inbred lines from BR-105 and BR-106 heterotic groups, respectively. These eighteen lines were genotyped by using RFLP molecular markers and then the coefficient of parentage among them was estimated. The genetic parameters general (GCA) and specific (SCA) combining abilities were estimated through diallel analyses, considering the linear model as fixed and using the ordinary least squares as the estimation method. Besides, GCA and SCA were predicted using BLUP and assuming the genetic effects as random. Besides, the prediction of non-realized single crosses was evaluated. To do so, each one of the 80 realized hybrids was predicted based on information of the others 79 single crosses and using the genetic variance-covariance matrix estimated using RFLP information. According to the results, it was found poor correlation between estimatives and predictions obtained considering the model as fixed or mixed, for GCA within BR-106 population (r=-0.11) and for SCA (r=-0.06). However, the ranking of the single crosses for productivity did not change (r=0.99) and did not make selection process more difficult. The efficiency of BLUP in predicting unrealized single crosses was moderated since the correlation between observed and predicted values was r=0.35, indicating some imprecision in these predictions. Similar results were obtained when comparing observed and predicted SCAs (r=0.30). It was possible to conclude that BLUP can be useful in diallel analyses and in prediction of single crosses, but some caution have to be account since the correlations presented moderate values.

A cultura da cana-de-açúcar (Saccharum spp.) possui uma importância histórica e econômica para o Brasil. O agronegócio sucroalcooleiro vem experimentando forte expansão na última década não só no Brasil como também em todo o mundo em função, principalmente, da demanda por fontes de energia menos agressivas ao ambiente. Para atender a uma maior demanda por seus subprodutos, principalmente de etanol, a área cultivada com cana-de-açúcar vem aumentando a cada ano no Brasil, ocupando áreas novas de cultivo nas regiões centrais do país. Nesse contexto, o melhoramento genético tem um papel fundamental no desenvolvimento de novas cultivares adaptadas a essas condições de cultivo. A maioria dos caracteres de importância econômica possui uma natureza genética complexa fazendo com que o desenvolvimento de uma nova cultivar de cana-de-açúcar leve mais de 10 anos. Desta forma, o uso de abordagens que permitam a identificação de genes ou de QTLs associados a caracteres quantitativos de forma precisa e rápida tem grande utilidade no melhoramento dessa espécie. O mapeamento por associação baseado no fenômeno do desequilíbrio de ligação é uma metodologia que visa detectar associações entre genes e caracteres agronômicos, podendo contribuir desta forma para o melhoramento da cana-de-açúcar. Assim, este trabalho teve como principal objetivo avaliar o uso da abordagem de mapeamento por associação na detecção de associações importantes entre marcadores moleculares do tipo SSR e AFLP e os caracteres Altura, Diâmetro e Número de Colmos; Percentual de Fibra na Cana (Fibra % Cana); Porcentagem em massa de sacarose (Pol % cana) e Tonelada de Cana por Hectare (TCH) em cana-de-açúcar. Os dados fenotípicos dos genótipos avaliados são oriundos de experimentos conduzidos em quatro regiões: Ribeirão Preto, Jaú e Piracicaba em São Paulo e Goianésia em Goiás no período entre 1990 e 2009. Associações entre os marcadores e os caracteres fenotípicos foram avaliadas em cada região e em todas simultaneamente. A análise de associação realizada através de modelos mistos sugeriu a existência de doze associações envolvendo os caracteres Número de Colmos, Porcentagem em massa de sacarose (Pol % cana) e Tonelada de Cana por Hectare (TCH). Quatro associações envolveram a característica Número de Colmos sendo três (CIR56, ACG_CGT e AGG_CAG) de caráter geral, ou seja, relacionada à média das quatro regiões e uma associação na região de Goiás (ACG_CAT). Sete associações entre a característica Pol % Cana e as marcas CV60, CV106, AAG_CAC, AAG_CAG e ACG_CTT foram específicas para a região de cultivo de Ribeirão Preto. Uma associação entre Tonelada de Cana por Hectare (TCH) e a marca ACG_CGC foi detectada na região de Piracicaba. / Sugarcane (Saccharum spp.) has an historical and economic relevance in Brazil. We are the largest producer and exporter of sugar and ethanol in the world. Sugar agribusiness has experienced a xx in the last decade not only in Brazil but also around the world as a consequence of increasing demand on renewable and clean sources of energy. As a consequence, the growing area with sugarcane in Brazil is expanding, reaching the central regions of the country. Sugarcane breeding has an important role in developing new cultivars adapted to these new conditions. However, most traits of economic importance in sugarcane have complex genetic architecture making the improvement of new sugarcane cultivars a challenging process. Thus, adoption of strategies that allow for rapid and precise detection of genes associated with quantitative traits is of great interest, representing a valuable tool for sugarcane breeding. Association mapping based on linkage disequilibrium represents a strategy useful for detection of marker-trait associations and may contribute for identifying genes useful for sugarcane breeding. In the present study, association mapping approach was applied to sugarcane in order to evaluate its potential contribution in detecting important associations between SSR and AFLP molecular markers and the characters Height, Diameter and Number of Stalks; % Fiber; % Pol and TCH. Phenotypic data for genotypes were collected from field trials in four locations: Ribeirão Preto, Jaú and Piracicaba in São Paulo and Goianésia in Goiás between 1993 and 2009. Marker-trait associations were tested for each location individually and for all locations simultaneously. A mixed model approach was adopted to test for marker-trait associations. The results suggested the existence of twelve associations involving the characters Stalk Number, % Pol and TCH. Four associations involved stalk number from which three (markers CIR56, ACG_CGT e AGG_CAG) were for all locations and one specific to Goiás (ACG_CAT). Seven associations between % Pol and markers CV60, CV106, AAG_CAC, AAG_CAG e ACG_CTT were detected in Ribeirão Preto. One association between TCH and ACG_CGC was detected in Piracicaba

No description available.

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.

O objetivo do mapeamento de QTL (Quantitative Trait Loci ) e identificar sua posição no genoma, isto e, identificar em qual cromossomo esta e qual sua localização nesse cromossomo, bem como estimar seus efeitos genéticos. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são usados frequentemente para auxiliar no seu mapeamento. Alguns marcadores podem estar altamente ligados a um ou mais QTL e, dessa forma eles podem mostrar uma alta associação com a característica fenotípica. O efeito genético do QTL e os valores fenotípicos de uma característica quantitativa são normalmente descritos por um modelo linear. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são utilizados para representá-los. Em geral, e utilizado um numero grande de marcadores. Esses marcadores são utilizados no modelo linear para proceder ao processo de associação; dessa forma o modelo especificado contem um numero elevado de parâmetros a serem estimados. No entanto, e esperado que muitos destes parâmetros sejam não significativos, necessitando de um tratamento especial. Na estimação bayesiana esse problema e tratado por meio da estrutura de distribuições a priori utilizada. Um parâmetro que e esperado assumir o valor zero (não significativo) e naturalmente especificado por meio de uma distribuição que coloque um peso maior no zero, encolhimento bayesiano. Neste trabalho e proposta a utilização de dois modelos que utilizam distribuições a priori de encolhimento. Um dos modelos esta relacionado com o uso da distribuição a priori Laplace (Lasso bayesiano) e o outro com a Horseshoe (Estimador Horseshoe). Para avaliar o desempenho dos modelos na determinação da associação entre marcadores e QTL, realizou-se um estudo de simulação. Foi analisada a associação entre marcadores e QTL utilizando três características fenotípicas: produção de grãos, altura da espiga e altura da planta. Comparou-se os resultados obtidos neste trabalho com analises feitas na literatura na detecção dos marcadores associados a essas características. A implementação computacional dos algoritmos foi feita utilizando a linguagem C e executada no pacote estatístico R. O programa implementado na linguagem C e apresentado e disponibilizado. Devido a interação entre as linguagens de programação C e R, foi possível executar o programa no ambiente R. / The objective of the mapping of quantitative trait loci (QTL) is to identify its position in the genome, ie, identify which chromosome is and what is its location in the chromosome, as well as to estimate their genetic eects. Since the location of QTL are not known a priori, markers are often used to assist in it mapping. Some markers may be closely linked to one or more QTL, and thus they may show a strong association with the phenotypic trait. The genetic eect of QTL and the phenotypic values of a quantitative trait are usually described by a linear model. Since the QTL locations are not known a priori, markers are used to represent them. Generally is used a large number of markers. These markers are used in the linear model to make the process of association and thus the model specied contains a large number of parameters to be estimated. However, it is expected that many of these parameters are not signicant, requiring a special treatment. In Bayesian estimation this problem is treated through structure priori distribution used. A parameter that is expected to assume the value zero (not signicant) is naturally specied by means of a distribution that put more weight at zero, bayesian shrinkage. This paper proposes the use of two models using priori distributions to shrinkage. One of the models is related to the use of priori distribution Laplace (bayesian Lasso) and the other with Horseshoe (Horseshoe Estimator). To evaluate the performance of the models to determine the association between markers and QTL, we performed a simulation study. We analyzed the association between markers and QTL using three phenotypic traits: grain yield, ear height and plant height. We compared the results obtained in this study with analyzes in the literature on the detection of markers associated with these characteristics. The computational implementation of the algorithms was done using the C language and executed the statistical package R. The program is implemented in C languages presented and made available. Due to the interaction between the programming languages C and R, it was possible execute the program in the environment R.

La plupart des maladies humaines ont une étiologie complexe avec des facteurs génétiques et environnementaux qui interagissent. Utiliser des phénotypes corrélés peut augmenter la puissance de détection de locus de trait quantitatif. Ce travail propose d’évaluer différentes approches d’analyse bivariée pour des traits corrélés en utilisantl’information apportée par les marqueurs au niveau de la liaison et de l’association. Legain relatif de ces approches est comparé aux analyses univariées. Ce travail a étéappliqué à la variation de la densité osseuse à deux sites squelettiques dans une cohorted’hommes sélectionnés pour des valeurs phénotypiques extrêmes. Nos résultats montrentl’intérêt d’utiliser des approches bivariées en particulier pour l’analyse d’association. Parailleurs, dans le cadre du groupe de travail GAW16, nous avons comparé lesperformances relatives de trois méthodes d’association dans des données familiales. / The majority of complex diseases in humans are likely determined by both genetic andenvironmental factors. Using correlated phenotypes may increase the power to map theunderlying Quantitative Trait Loci (QTLs). This work aims to evaluate and compare theperformance of bivariate methods for detecting QTLs in correlated phenotypes by linkageand association analyses. We applied these methods to data on Bone Mineral Density(BMD) variation, measured at the two skeletal sites, in a sample of males selected forextreme trait values. Our results demonstrate the relative gain, in particular for associationanalysis, of bivariate approaches when compared to univariate analyses. Finally, we studythe performances of association methods to detect QTLs in the GAW16 simulated familydata.

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.

Statistical heterogeneity refers to differences among results of studies combined in a meta-analysis beyond that expected by chance. On the one hand, excessive heterogeneity can diminish power to discover genetic signals; on the other, moderate heterogeneity can reveal important biological differences among studies. Given its double-edged nature, this thesis dissects heterogeneity in genetic association meta-analyses from three vantage points. First, a novel multi-variant statistic, M is proposed to detect genome-wide (systematic) heterogeneity patterns in genetic association meta-analyses. This was motivated by the limited availability of appropriate methodology to measure the impact of heterogeneity across genetic signals, since traditional metrics (Q, I² and T²) measure heterogeneity at individual variants. Second, given that meta-analyses comprising small numbers of studies typically report imprecise summary effect estimates; GWAS-derived empirical heterogeneity priors are used to improve precision in estimation of average genetic effects and heterogeneity in smaller meta-analyses (e.g. ≤ 10 studies). Third, a critical evaluation of the Han-Eskin random-effects model shows how it can identify small effect heterogeneous loci overlooked by traditional fixed and random-effects methods. This work draws attention to the existence of genome-wide heterogeneity patterns, to reveal systematic differences among the ascertainment criteria of participating studies in a meta-analysis of coronary disease (CAD) risk. Furthermore, simulation studies with the Han-Eskin random-effects model revealed inflated genetic signals at small effect loci when heterogeneity levels were high. However, it did reveal an additional CAD risk variant overlooked by traditional meta-analysis methods. We therefore recommend a holistic approach to exploring heterogeneity in meta-analyses which assesses heterogeneity of genetic effects both at individual variants with traditional statistics and across multiple genetic signals with the M statistic. Furthermore, it is critically important to review forest plots for small effect loci identified using the Han-Eskin random-effects model amidst moderate-to-high heterogeneity (I² ≥ 40%).