Magister Scientiae - MSc / Traditionally in human genetic linkage analysis, extended families were only used in the analysis of dichotomous traits, such as Disease/No Disease. For quantitative traits, analyses initially focused on data from family trios (for example, mother, father, and child) or sib-pairs. Recently however, there have been two very important developments in genetics: It became clear that if the disease status of several generations of a family is known and their genetic information is obtained, researchers can pinpoint which pieces of genetic material are linked to the disease or trait. It also became evident that if a trait is quantitative (numerical), as blood pressure or viral loads are, rather than dichotomous, one has much more power for the same sample size. This led to the development of statistical mixed models which could incorporate all the features of the data, including the degree of relationship between each pair of family members. This is necessary because a parent-child pair definitely shares half their genetic material, whereas a pair of cousins share, on average, only an eighth. The statistical methods involved here have however been developed by geneticists, for their specific studies, so there does not seem to be a unified and general description of the theory underlying the methods. The aim of this dissertation is to explain in a unified and statistically comprehensive manner, the theory involved in the analysis of quantitative trait genetic data from extended families. The focus is on linkage analysis: what it is and what it aims to do. There is a step-by-step build up to it, starting with an introduction to genetic epidemiology. This includes an explanation of the relevant genetic terminology. There is also an application section where an appropriate human genetic family dataset is analysed, illustrating the methods explained in the theory sections. / South Africa

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Recent technological advances and remarkable successes have led to genome-wide association studies (GWAS) becoming a tool of choice for investigating the genetic basis of common complex human diseases. These studies typically involve samples from thousands of individuals, scanning their DNA at up to a million loci along the genome to discover genetic variants that affect disease risk. Hundreds of such variants are now known for common diseases, nearly all discovered by GWAS over the last three years. As a result, many new studies are planned for the future or are already underway. In this thesis, I present analysis results from actual studies and some developments in theory and methodology. The Wellcome Trust Case Control Consortium (WTCCC) published one of the first large-scale GWAS in 2007. I describe my contribution to this study and present the results from some of my follow-up analyses. I also present results from a GWAS of a bipolar disorder sub-phenotype, and a recent and on-going fine mapping experiment. Building on methods developed as part of the WTCCC, I describe a Bayesian approach to GWAS analysis and compare it to widely used frequentist approaches. I do so both theoretically, by interpreting each approach from the perspective of the other, and empirically, by comparing their performance in the context of replicated GWAS findings. I discuss the implications of these comparisons on the interpretation and analysis of GWAS generally, highlighting the advantages of the Bayesian approach. Finally, I examine the effect of linkage disequilibrium on the detection and estimation of various types of genetic effects, particularly non-additive effects. I derive a theoretical result showing how the power to detect a departure from an additive model at a marker locus decays faster than the power to detect an association.

Genome-wide association studies (GWAS) exploit the correlation in ge- netic diversity along chromosomes in order to detect effects on disease risk without having to type causal loci directly. The inevitable downside of this approach is that, when the correlation between the marker and the causal variant is imperfect, the risk associated with carrying the predisposing allele is diluted and its effect is underestimated. This thesis explores four different facets of this risk dilution: (1) estimating true effect sizes from those observed in GWAS; (2) asking how the context of a GWAS, including the population studied, the genotyping chip employed, and the use of im- putation, affects risk estimates; (3) assessing how often the best-associated SNP in a GWAS coincides with the causal variant; and (4) quantifying how departures from the simplest disease risk model at a causal variant distort the observed disease risk model. Using simulations, where we have information about the true risk at the causal locus, we show that the correlation between the marker and the causal variant is the primary driver of effect size underestimation. The extent of the underestimation depends on a number of factors, including the population in which the study is conducted, the genotyping chip employed, whether imputation is used, and the strength, frequency, and disease model of the risk allele. Suppose that a GWAS study is conducted in a European population, with an Affymetrix 6.0 genotyping chip, without imputation, and that the causal loci have a modest effect on disease risk, are common in the population, and follow an additive disease risk model. In such a study, we show that the risk estimated from the most associated SNP is very close to the truth approximately two-thirds of the time (although we predict that fine mapping of GWAS loci will infrequently identify causal variants with considerably higher risk), and that the best-associated variant is very often perfectly or nearly-perfectly correlated with, and almost always within 0.1cM of, the causal variant. However, the strong correlations among nearby loci mean that the causal and best-associated variants coincide infrequently, less than one-fifth of the time, even if the causal variant is genotyped. We explore ways in which these results change quantitatively depending on the parameters of the GWAS study. Additionally, we demonstrate that we expect to identify substantial deviations from the additive disease risk model among loci where association is detected, even though power to detect departures from the model drops off very quickly as the correlation between the marker and causal loci decreases. Finally, we discuss the implications of our results for the design and interpretation of future GWAS studies.

The Major Histocompatibility Complex (MHC) is a genomic region in chromosome 6 which has been consistently found to be associated with the risk of developing virtually all common autoimmune diseases. Although its importance in disease pathogenesis has been known for decades, efforts to disentangle the roles of the classical human leukocyte antigens (HLA) and other variants responsible for the susceptibility to disease have often met with limited success, owing to the complex structure and extreme heterogeneity of the region. In this thesis, I interrogate the MHC for association with three common autoimmune diseases, ankylosing spondylitis, psoriasis and multiple sclerosis, with the aim of confirming the previously-reported associations and of identifying novel ones. To do so, I employ a systematic, joint analysis of single nucleotide polymorphism (SNP) and HLA allele data, in a logistic regression framework, using a recently developed algorithm to predict the HLA alleles for samples where such information is unavailable. To ensure the reliability of the analysis, I apply stringent quality control procedures and integrate over the uncertainty of the HLA allele predictions. Moreover, I resolve the haplotype phase of individuals from the HapMap project to create reliable reference panels, used in both HLA prediction and in quality control procedures. By directly testing HLA subtypes for association with the disease, the power to detect such associations is increased. I present the results of the analysis on the three disease phenotypes and discuss the evidence for important novel findings amongst both SNPs and HLA alleles in two of the diseases. In the final part of this thesis, I introduce a novel, model-based approach to detect inconsistencies in the data and show how it can be used to flag problematic SNPs which conventional quality control procedures may fail to identify.

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

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.

[Truncated abstract] This thesis investigates novel methods for the genetic association analysis of haplotype data in samples of unrelated individuals, and applies these methods to the analysis of coronary heart disease and related phenotypes. Determining the inheritance pattern of genetic variants in studies of unrelated individuals can be problematic because family members of the studied individuals are often not available. For the analysis of individual genetic loci, no problem arises because the unit of interest is the observed genotype. When the unit of interest is the linear combination of alleles along one chromosome, inherited together in a haplotype, it is not always possible to determine with certainty the inheritance pattern, and therefore statistical methods to infer these patterns must be adopted. Due to genotypic heterozygosity, mutliple possible haplotype configurations can often resolve an individual's genotype measures at multiple loci. When haplotypes are not known, but are inferred statistically, an element of uncertainty is thus inherent which, if not dealt with appropriately, can result in unreliable estimates of effect sizes in an association setting. The core aim of the research described in this thesis was to develop and implement a general method for haplotype-based association analysis using multiple imputation to appropriately deal with uncertainty haplotype assignment. Regression-based approaches to association analysis provide flexible methods to investigate the influence of a covariate on a response variable, adjusting for the effects of other variables including interaction terms. ... These methods are then applied to models accommodating binary, quantitative, longitudinal and survival data. The performance of the multiple imputation method implemented was assessed using simulated data under a range of haplotypic effect sizes and genetic inheritance patterns. The multiple imputation approach performed better, on average, than ignoring haplotypic uncertainty, and provided estimates that in most cases were similar to those observed when haplotypes were known. The haplotype association methods developed in this thesis were used to investigate the genetic epidemiology of cardiovascular disease, utilising data for the cholesteryl ester transfer protein gene (CETP), the hepatic lipase (LIPC) gene and the 15- lipoxygenase (ALOX15) gene on a total of 6,487 individuals from three Western Australian studies. Results of these analyses suggested single nucleotide polymorphisms (SNPs) and haplotypes in the CETP gene were associated with increased plasma high-density lipoprotein cholesterol (HDL-C). SNPs in the LIPC gene were also associated with increased HDL-C and haplotypes in the ALOX15 gene were associated with risk of carotid plaque among individuals with premature CHD. The research presented in this thesis is both novel and important as it provides methods for the analysis of haplotypic associations with a range of response types, while incorporating information about haplotype uncertainty inherent in populationbased studies. These methods are shown to perform well for a range of simulated and real data situations, and have been written into a statistical analysis package that has been freely released to the research community.

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).