Over the past ten years, more than 4,000 genome-wide association studies (GWAS) have helped to shed light on the genetic architecture of complex traits and diseases. In recent years, phenotyping of the samples has often gone beyond single traits and it has become common to record multi- to high-dimensional phenotypes for individu- als. Whilst these rich datasets offer the potential to analyse complex trait structures and pleiotropic effects at a genome-wide level, novel analytic challenges arise. This thesis summarises my research into genetic associations for high-dimensional phen- otype data. First, I developed a novel and computationally efficient approach for multivari- ate analysis of high-dimensional phenotypes based on linear mixed models, com- bined with bootstrapping (LiMMBo). Both in simulation studies and on real data, I demonstrate the statistical validity of LiMMBo and that it can scale to hundreds of phenotypes. I show the gain in power of multivariate analyses for high-dimensional phenotypes compared to univariate approaches, and illustrate that LiMMBo allows for detecting pleiotropy in a large number of phenotypic traits. Aside from their computational challenges in GWAS, the true dimensionality of very high-dimensional phenotypes is often unknown and lies hidden in high-dimen- sional space. Retaining maximum power for association studies of such phenotype data relies on using an appropriate phenotype representation. I systematically ana- lysed twelve unsupervised dimensionality reduction methods based on their per- formance in finding a robust phenotype representation in simulated data of different structure and size. I propose a stability criteria for choosing low-dimensional phen- otype representations and demonstrate that stable phenotypes can recover genetic associations. Finally, I analysed genetic variants for associations to high-dimensional cardiac phenotypes based on MRI data from 1,500 healthy individuals. I used an unsuper- vised approach to extract a low-dimensional representation of cardiac wall thickness and conducted a GWAS on this representation. In addition, I investigated genetic associations to a trabeculation phenotype generated from a supervised feature ex- traction approach on the cardiac MRI data. In summary, this thesis highlights and overcomes some of the challenges in per- forming genetic association studies on high-dimensional phenotypes. It describes new approaches for phenotype processing, and genotype to phenotype mapping for high-dimensional datasets, as well as providing new insights in the genetic structure of cardiac morphology in humans.

Made available in DSpace on 2016-04-28T14:58:36Z (GMT). No. of bitstreams: 1 2008 - Fabio Mathias Correa.pdf: 2421517 bytes, checksum: 7f7f9e77fc6d68db6e05dbd9994c1e38 (MD5) Previous issue date: 2008-02-28 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The late blight of the tomato, caused by Phytophthora infestans (Mont) of Bary it is one of the main diseases of the tomato. However, the quantification of the severity of the disease, doesn't possess a standard method of evaluation and that, it can interfere in the comparison of results among and inside of experiments, once the scale of evaluation of the disease should be standardized. A diagrammatic scale should represent all variation of the existent disease in the field and to make possible necessary evaluations and perfected, independent of the existent differences among appraisers. Another important factor in the epidemiological studys, is the correct application of the methodologies of evaluation of treatments or cultivars. Therefore, the present work has as objectives: 1) to develop and to validate a diagrammatic scale for quantification of the severity of the late blight in tomateiro leaves and 2) to compare the use of AUDPC (area under disease progress curve), certain according to Shanner & Finney (1977), with the use of mixed models and mixed lineal models widespread in the selection of gen?tipos of resistant tomateiro to the requeima. Three diagrammatics scales were proposed for evaluation of the late blight in tomato leaves. The first scale, denominated scale-detailed, it was composed by nine values of severity intensity (0, 3, 6, 12, 22, 40, 60, 77 and 90%), the second climb, call of having scale-simplified, it was composed by seven severity values (0, 3, 12, 22, 40, 60 and 77%) and the third scale, of having James-modified, composed by seven severity values (0, 1, 5, 10, 16, 32 and 50%). For the validation of the scales, 24 appraisers accomplished two evaluations in leaves 50 tomato leaves with different severity levels, where the precision, acuracy and repetibility were appraised through simple lineal regression, analysis of variance of the mistakes and correlation coefficient. Among the proposed scales, two came as tools that allow a good precision and acuracy in the evaluation of the severity of the late blight in tomato leaves, being the detailed scale and the simplified scale. With relationship to the analysis methods, the use of direct AACPD, calculated by the sum of Riemann, and of mixed and mixed models widespread, it was verified that the direct use of AUDPC, doesn't get to describe all existent variation in the sample, probably for the great number of treatments. The use of mixed models widespread, that it considers the distribution of Poisson, it was shown more appropriate for to describe the epidemic caused by late blight in tomato, being more suitable in the selection of tomato cultivars seeking to the resistance the this disease. / A requeima, causada por Phytophthora infestans ? uma das principais doen?as do tomateiro. Para quantificar a severidade da doen?a, n?o h? um m?todo padr?o, o que pode interferir na compara??o de resultados entre e dentro de experimentos, uma vez que a escala de avalia??o da doen?a deve ser padronizada. Uma escala diagram?tica deve representar toda a varia??o da severidade no campo e possibilitar avalia??es precisas e acuradas, independente das diferen?as entre avaliadores. Outro fator importante no estudo epidemiol?gico ? a correta aplica??o das metodologias de avalia??o de tratamentos ou gen?tipos. Portanto, o presente trabalho objetivou: 1) desenvolver e validar uma escala diagram?tica para quantifica??o da severidade da requeima em folhas de tomateiro e 2) comparar o uso da ?rea abaixo da curva de progresso da doen?a (AACPD), com o uso de modelos mistos e modelos lineares mistos generalizados na sele??o de gen?tipos de tomateiro resistentes ? requeima. Tr?s escalas diagram?ticas foram propostas para avalia?ar a requeima em folhas de tomateiro. A primeira, denominada escala-detalhada, foi composta por nove valores de intensidade de severidade (0, 3, 6, 12, 22, 40, 60, 77 e 90%). A segunda escala, chamada de escala-simplificada, foi composta por sete valores de severidade (0, 3, 12, 22, 40, 60 e 77%) e a terceira, de Jamesmodificada, composta por sete valores de severidade (0, 1, 5, 10, 16, 32 e 50%). Para a valida??o das escalas, 24 avaliadores realizaram duas avalia??es em 50 folhas de tomateiro com diferentes n?veis de severidade, e a precis?o, acur?cia e a repetibilidade dos avaliadores foram avaliados atrav?s de regress?o linear simples, an?lise de vari?ncia dos erros e coeficiente de correla??o de Pearson. Dentre as escalas propostas, duas (escala detalhada e escala simplificada) apresentaram uma boa precis?o e acur?cia para a avalia??o da severidade da requeima em folhas de tomateiro. Quanto aos m?todos de an?lise, constatou-se que o uso direto da AACPD, obtido pela soma de Riemann, n?o conseguiu descrever toda varia??o existente na amostra, provavelmente pelo grande n?mero de tratamentos. O uso de modelos mistos generalizados, que considera a distribui??o de Poisson, foi mais adequado para descrever a epidemia, sendo mais indicado na sele??o de gen?tipos de tomate resistentes a doen?a.

Nas últimas décadas, a produção e exportação de carne bovina no Brasil consolidaram o país como um importante fornecedor no mercado internacional. No ano de 2012 o Brasil produziu aproximadamente 17% da demanda mundial de carne, exportando 1.325 milhão de toneladas (USDA, 2012). No entanto, apesar desta posição privilegiada, a produção brasileira é caracterizada pela criação extensiva dos animais e pela baixa qualidade do produto final. O rebanho é composto basicamente por animais Bos indicus e seus cruzamentos, com predominância da raça Nelore. Estes animais, por sua vez, apresentam ótima adaptabilidade e resistência ao ambiente tropical, porém com qualidade de carne e carcaça inferior quando comparados a bovinos Bos taurus. Assim, buscando indivíduos com maior rusticidade e com melhores índices de crescimento e acabamento de carcaça, os produtores vem utilizando cruzamentos entre bovinos Bos taurus X Bos indicus, aproveitando os efeitos de heterose e complementariedade entre raças. Os resultados já obtidos reforçam a contribuição dos mestiços na produção de carne, sendo utilizados com maior frequência em ambientes onde animais puros não apresentariam bons desempenhos. Diante disso, a identificação e seleção de animais superiores para ambientes tropicais possibilitariam o atendimento das demandas do mercado, principalmente no que diz respeito à qualidade da carne produzida. Portanto, efeitos genéticos aditivos e não aditivos que influenciam as características de importância econômica devem ser considerados nas avaliações genéticas de animais cruzados. Desta forma, os objetivos deste trabalho foram: I) Estudar a influência dos efeitos genéticos não aditivos na estimação de componentes de variância, parâmetros genéticos e ranking dos animais através de diferentes modelos; II) Estudar a influência da regressão de cumeeira ponderada na redução de colinearidade e na estimação de componentes de variância e parâmetros genéticos. A partir dos resultados foi possível observar que modelos que consideraram efeitos genéticos aditivos e não aditivos da epistasia e de heterozigose foram em geral os mais adequados para descrever o peso a desmama e o ganho de peso da desmama ao sobreano. Para a análise de peso ao nascer, peso aos 12 meses, área do olho do lombo e a espessura de gordura da picanha o efeito da epistasia foi desprezível. Da mesma maneira, foi possível observar que a aplicação da regressão ridge ponderada diminuiu a inflação da variância associada aos efeitos fixos genéticos diretos e maternos e, proporcionou estimativas mais estáveis e plausíveis para as características de crescimento. Em relação aos componentes de variância não foram verificadas diferenças em função da aplicação de regressão ridge ponderada em características de crescimento. / In last year Brazilian beef production and exportation consolidated the country as an important provider in the international market. Thus, in 2012, Brazil provided approximately 17% of global meat demand, exporting 1,325 million tons (USDA, 2012). However, Brazilian production is characterized by extensive grazing system and low meat quality. The Brazilian herd is composed mainly of Bos indicus (mostly Nelore) and their crosses. These animals have great adaptability and resistance to tropical environment, but they show lower carcass and meat quality than Bos taurus cattle. Thus, looking for individuals with more rusticity and better growth rates and carcass traits, the farmers have been using crossbreed between Bos taurus X Bos indicus, exploring the heterosis and complementarity effects. Results obtained affirmed the crossbred contribution in meat production, especially in environments where purebred animals would not show good performances. Therefore, the identification and selection of genetically superior animals would meet specific market needs. Thus, is necessary to consider additive and non-additive genetic effects in genetic evaluation. The aims of this study were: I) to study the influence of non-additive genetic effects in the estimation of genetic parameters and ranking of animals across different models. II) To study the influence of weighted ridge regression in collinearity reduction and their effects in genetic parameters estimation. The results showed that models that considered non-additive genetic effects of epistasis and heterozygosity were generally the most suitable to describe the weaning weight and weight gain from weaning to yearling. The epistasis effect was unimportant for birth weight, weight at 12 months, loin rib eye area and fat thickness of. Similarly, it was observed that ridge regression application allowed decreased the inflation variance and provided stable and plausible estimates. No differences due to the application of ridge regression were observed in growth traits.

<p>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&nbsp / 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.&nbsp / 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.</p>

<p>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&nbsp / 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.&nbsp / 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.</p>

Made available in DSpace on 2015-03-26T13:32:19Z (GMT). No. of bitstreams: 1 texto completo.pdf: 1498414 bytes, checksum: a554a4debb559e9eaa2ce04ffbc8d4c9 (MD5) Previous issue date: 2013-02-26 / Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The genomic wide selection (GWS) emerged in 2001 with the goal of increasing efficiency and accelerating the selection gain in genetic improvement based exclusively on markers after their genetic effects estimated from phenotypic data. In the context of survival analysis, Cox s proportional risk model with random effects was compared to the mixed linear model, both using parenthood matrices based on markers in substitution to basing on pedigree, this method being named GBLUP. The application was made on real data from an F2 population of pigs in which the dependent variable was the time in days, from birth to slaughter of the animal and the covariables: SNP markers (238), sex and handled lot. The data was previously corrected for fixed effects and the accuracy of the method was calculated based on the correlation of the ranks of genomic genetic values predicted in both models with the phenotypic values corrected. The analysis was repeated considering the least number of SNP markers that presented the greatest effect in module. The results showed agreement in the prediction of genomic genetic values and estimation of the effects of markers for both models in the situation of uncensored data and normality. However, when considering censored data, the Cox model with normal random effect was more appropriate, since there was no agreement in the prediction of genomic genetic values and estimation of the effects of markers with the mixed linear model with imputed data. The selection of markers allowed an increase in correlations between the positions of genomic genetic values predicted by the linear model and the Cox frailty model with phenotypic values corrected, being that for the characteristic being analyzed, 120 markers were sufficient to increase the predictive power. / A seleção genômica ampla (GWS) surgiu em 2001 com o objetivo de aumentar a eficiência e acelerar o ganho de seleção no melhoramento genético baseando-se exclusivamente em marcadores após terem seus efeitos genéticos estimados a partir de dados fenotípicos. No contexto de análise de sobrevivência, o modelo de riscos proporcionais de Cox com efeito aleatório foi comparado ao modelo linear misto, ambos usando a matriz de parentesco baseada em marcadores em substituição à baseada em pedigree, método esse denominado GBLUP. A aplicação foi feita aos dados reais de uma população F2 de suínos em que a variável resposta foi o tempo em dias, do nascimento até o abate do animal e as covariáveis: marcadores SNPs (238), sexo e lote de manejo. Os dados foram previamente corrigidos para seus efeitos fixos e a acurácia do método foi calculada com base na correlação dos postos dos valores genéticos genômicos preditos em ambos os modelos com os valores fenotípicos corrigidos. A análise foi repetida considerando menor número de marcadores SNPs que apresentassem maiores efeitos em módulo. Os resultados demonstraram concordância na predição dos valores genéticos genômicos e na estimação dos efeitos de marcadores para ambos os modelos na situação de dados não censurados e normalidade. No entanto, ao considerar a censura, o modelo de Cox com efeito aleatório normal foi o mais apropriado, uma vez que não houve concordância na predição dos valores genéticos genômicos e na estimação dos efeitos de marcadores com o modelo linear misto com dados imputados. A seleção de marcas permitiu um aumento nas correlações entre os postos dos valores genéticos genômicos preditos pelo modelo linear e pelo modelo de fragilidade de Cox com os valores fenotípicos corrigidos, sendo que para a característica analisada, 120 marcadores foram suficientes para maximizar a capacidade preditiva.

abstract: Yield is a key process performance characteristic in the capital-intensive semiconductor fabrication process. In an industry where machines cost millions of dollars and cycle times are a number of months, predicting and optimizing yield are critical to process improvement, customer satisfaction, and financial success. Semiconductor yield modeling is essential to identifying processing issues, improving quality, and meeting customer demand in the industry. However, the complicated fabrication process, the massive amount of data collected, and the number of models available make yield modeling a complex and challenging task. This work presents modeling strategies to forecast yield using generalized linear models (GLMs) based on defect metrology data. The research is divided into three main parts. First, the data integration and aggregation necessary for model building are described, and GLMs are constructed for yield forecasting. This technique yields results at both the die and the wafer levels, outperforms existing models found in the literature based on prediction errors, and identifies significant factors that can drive process improvement. This method also allows the nested structure of the process to be considered in the model, improving predictive capabilities and violating fewer assumptions. To account for the random sampling typically used in fabrication, the work is extended by using generalized linear mixed models (GLMMs) and a larger dataset to show the differences between batch-specific and population-averaged models in this application and how they compare to GLMs. These results show some additional improvements in forecasting abilities under certain conditions and show the differences between the significant effects identified in the GLM and GLMM models. The effects of link functions and sample size are also examined at the die and wafer levels. The third part of this research describes a methodology for integrating classification and regression trees (CART) with GLMs. This technique uses the terminal nodes identified in the classification tree to add predictors to a GLM. This method enables the model to consider important interaction terms in a simpler way than with the GLM alone, and provides valuable insight into the fabrication process through the combination of the tree structure and the statistical analysis of the GLM. / Dissertation/Thesis / Ph.D. Industrial Engineering 2011

Submitted by Flávia Alves Marques da Silva null (flavia_alvesms@hotmail.com) on 2016-04-12T00:49:43Z No. of bitstreams: 1 Dissertação FAMS.pdf: 1151230 bytes, checksum: ca0a6199d3ff01fbcb0f85441e03066b (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-04-13T14:04:07Z (GMT) No. of bitstreams: 1 silva_fam_me_jabo.pdf: 1151230 bytes, checksum: ca0a6199d3ff01fbcb0f85441e03066b (MD5) / Made available in DSpace on 2016-04-13T14:04:07Z (GMT). No. of bitstreams: 1 silva_fam_me_jabo.pdf: 1151230 bytes, checksum: ca0a6199d3ff01fbcb0f85441e03066b (MD5) Previous issue date: 2016-02-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nos programas de melhoramento de milho, a avaliação das linhagens em cruzamentos é uma etapa de alto custo, sendo que o uso e a escolha dos testadores mais adequados podem reduzir a demanda de recursos. Assim, o objetivo desse trabalho foi utilizar a abordagem REML/BLUP de modelos mistos para predição de valores genotípicos de topcrosses, combinando testadores com estruturas genéticas diversificadas. Foram avaliados 234 topcrosses (39 linhagens x 6 testadores), no ano agrícola 2012/13, no delineamento experimental de blocos ao acaso para o caráter produtividade de grãos de milho (t ha-1), altura de plantas (cm) e acamamento e quebramento de plantas (%). Foram realizadas análises de variância e, com as médias fenotípicas dos topcrosses, obteve-se os valores dos BLUPs considerando diferentes níveis de eliminação de testadores. Para verificar a eficiência dos BLUPs foram estimadas as correlações entre as médias fenotípicas e os valores genotípicos preditos com diferentes números e combinação de testadores, bem como os coeficientes de determinação, a coincidência no ordenamento dos topcrosses para seleção e descarte, com 10 e 20% de intensidade, e classificações dos topcrosses quanto à média fenotípica. O método de REML/BLUP se mostra adequado na predição dos valores genotípicos dos topcrosses nas situações com todos os testadores e com diferentes níveis de eliminação de testadores, com resultados variados em função das diversas combinações obtidas, para todos os caracteres avaliados. É possível estipular um padrão quanto à origem e estrutura genética dos testadores mais recomendados para cada caráter e, considerando todos, é observada uma boa precisão experimental a partir do nível com conjuntos formados por 3 testadores, independente da origem dos constituintes. A predição genotípica, através do REML/BLUP, auxilia na seleção de testadores, sendo que o número de testadores utilizados tem maior influência do que a origem e estrutura dos mesmos. / In maize breeding programs the evaluation of lines at crosses is a costly step, and the use and the choice of the most appropriate testers can reduce the demand for resources. The objective of this work was to use the REML/BLUP approach of mixed models to predict genotypic values of topcrosses using testers with diverse genetic structures. Were evaluated 234 topcrosses (39 lines x 6 testers) in the agricultural year of 2012/13, under the experimental design of randomized blocks for the traits as grain yield (t ha-1 ), plant height (cm) and lodging and breakage of plants (%). Analyses of variance were conducted, and with the phenotypic means of topcrosses were obtained BLUPs values considering different levels of elimination of the testers. In order to check the efficiency of BLUPs, the correlations were estimated between the average phenotypic and the genotypic predicted values with different numbers and combination of the testers, as well as the coefficients of determination, the coincidence in the ranking of topcrosses for selection and discard, with 10 and 20% of intensity, and the classification of the topcrosses as to the phenotypic average. The method of REML/BLUP shown adequate to predict the genotypic values of topcrosses in situations with all testers and with different levels of testers elimination, with varying results depending on the various combinations obtained for all traits. Is possible to set a standard as to the origin and genetic structure of the most recommended testers for each trait, and considering all, a good experimental precision is observed from level with joint formed by three testers, regardless of the origin of the constituents. The genotype prediction, by REML/BLUP, assists in the selection of testers, and the number of testers used has greater influence than the origin and structure of the same.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work was done with the database of layers of brown-shelled eggs of Barred Plymouth Rock (BPR), White Plymouth Rock (WPR) and Rhode Island Red (RIR) breeds, for the years 1998 and 2010, created the Laboratory of Poultry Science (LAVIC) of Department of Animal Science, in the Federal University of Santa Maria (UFSM). In chapter 1 aimed to identify the mathematical model (linear or nonlinear) that best describes the curve of egg production of laying hens BPR, WPR and RIR; verify that a single equation can be used to describe the production of eggs different breeds through the test model identity and equal parameters, to study the biological interpretation of the parameters estimated by the models by correlations between parameters and egg production in different weeks old. The study indicated that the quartic polynomial regression and nonlinear models Quadratic Logarithm and Logistics II can be used to estimate the curve of egg production of birds BPR, WPR and RIR. The curves of egg production estimates by race are different, and egg production of breed WPR higher. A single curve of egg production estimated to be 1998 to 2010 birds WPR. The persistence of posture is similar among poultry breeds BPR and WPR. The potential maximum weekly posture of birds breed BPR is intermediate, and can be of the same birds WPR breed or RIR breed. Data productive of the 27th, 38th and 40th at 50 weeks of age can be used as partial data to estimate the curve of egg production, because they are correlated with the maximum potential posture weekly, and the rate of decline, which are highly correlated with the 1st principal component. In chapter 2 was to verify the existence of phenotypic divergence between layers of WPR and BPR through multivariate analysis (multivariate analysis of variance, principal components and clustering) of egg production weekly and accumulated periods. It is concluded that the egg production of poultry breeds BPR and WPR is different. The first two principal components meet the total variation of egg production accumulated the 21st to 25th, 21st to 30th, 21st to 40th, 21st to 45th, and 21st to 50th. Most of the phenotypic variation of the layers can be explained by the cumulative egg production of the 21st until the 40th week of age (10 months), and this variable is highly correlated with total egg production. Families from the race WPR and BPR form seven distinct groups, but homogeneous by the similarity between them. This allows direct crossings between different groups in search of heterosis. In chapter 3 aimed to define the mixed model that best fits the observed data of egg production of laying hens from 5th to 12th month of age, test different structures of the matrices G and R and to estimate broad-sense heritability and correlations environmental and genotype. This study indicated that the random regression model using regression of first grade and structures of (co)variance matrix for UN random effects (G) and UNR for waste matrix (R) models adequately curve of egg production from BPR and WPR laying hens. From the eighth month value heritability is moderate (0.34) with high genotypic correlation estimates (0.78 to 0.97) with nine months, 10, 11 and 12. It is also a high correlation of genotypic values of hens for egg production of the 8th month in the final months of posture. Thus, it is suggested phenotypic selection from the 8th month of production for birds BPR and WPR. / Este trabalho foi realizado com o banco de dados das poedeiras de ovos de casca marrom das raças Plymouth Rock Barrada (PRB), Plymouth Rock Branca (PRW) e Rhode Island Red (RIR), dos anos de 1998 e 2010, criadas no Laboratório de Avicultura (LAVIC) do Departamento de Zootecnia da Universidade Federal de Santa Maria (UFSM). No capítulo 1 objetivou-se identificar o modelo matemático (linear ou não linear) que melhor descreve a curva de produção de ovos das aves das raças PRB, PRW e RIR; verificar se uma única equação pode ser utilizada para descrever a produção de ovos das diferentes raças através do teste de identidade de modelos e igualdade de parâmetros; estudar as interpretações biológicas dos parâmetros estimados pelos modelos através das correlações existentes entre os parâmetros e a produção de ovos nas diferentes semanas de idade. O estudo indicou que o modelo de regressão polinomial quártica e os modelos não lineares Quadrático Logaritmo e Logístico II podem ser utilizados para estimar a curva de produção de ovos das aves PRB, PRW e RIR. As curvas de produções de ovos estimadas por raça são diferentes, sendo a produção de ovos da raça PRW superior. Uma única curva de produção de ovos pode ser estimada para os anos de 1998 e 2010 das aves PRW. A persistência de postura é semelhante entre as aves das raças PRB e PRW. O potencial máximo de postura semanal das aves da raça PRB é intermediário, e pode ser o mesmo das aves da raça PRW ou da raça RIR. Os dados produtivos da 27ª, 38ª e da 40ª a 50ª semana de idade podem ser utilizados como dados parciais para estimar a curva de produção de ovos, pois são correlacionados com o potencial máximo de postura semanal, e com a taxa de decréscimo, que são altamente correlacionados com o 1ª componente principal. No capítulo 2 teve como objetivo verificar a existência de divergência fenotípica entre poedeiras das raças PRB e PRW através de análises multivariadas (análise de variância multivariada, componentes principais e agrupamento) da produção de ovos semanal e acumulada por períodos. Concluiu-se que a produção de ovos das aves das raças PRB e PRW é diferente. Os dois primeiros componentes principais reúnem a variação total das produções de ovos acumuladas da 21ª a 25ª, 21ª a 30ª, 21ª a 40ª, 21ª a 45ª e 21ª a 50ª. A maior parte da variação fenotípica das poedeiras pode ser explicada pela produção de ovos acumulada da 21ª até a 40ª semana de idade (10 meses), sendo que essa variável tem alta correlação com a produção de ovos total. As famílias da raça PRW e da raça PRB, formam sete grupos distintos, mas homogêneos pela similaridade existente entre elas, o que permite direcionar cruzamentos entre os diferentes grupos, em busca da heterose. No capítulo 3 objetivou-se definir o modelo misto que melhor se ajusta aos dados observados da produção de ovos de poedeiras do 5º ao 12º mês de idade; testar diferentes estruturas das matrizes G e R; e estimar herdabilidade no sentido amplo e correlações ambientais e genotípicas. Este estudo indicou que o modelo de regressão aleatória que utiliza a regressão de primeiro grau e estruturas de (co)variância UN para matriz de efeitos aleatórios (G) e UNR para matriz de resíduos (R) modela adequadamente a curva de produção de ovos das aves das raças PRB e PRW. A partir do oitavo mês o valor da herdabilidade é moderada (0,34) com altas estimativas de correlação genotípica (0,78 a 0,97) com os meses 9, 10, 11 e 12. É alta também a correlação dos valores genotípicos das poedeiras para a produção de ovos do 8º mês com os meses finais de postura. Assim, sugere-se seleção fenotípica a partir do 8º mês de produção para as aves PRB e PRW.

In research where experiments on humans and animals is performed, it is in advance important to determine how many observations that is needed in a study to detect any effects in groups and to save time and costs. This could be examined by power analysis, in order to determine a sample size which is enough to detect any effects in a study, a so called “power”. Power is the probability to reject the null hypothesis when the null hypothesis is false. Mälardalen University and the Caroline Institute have in cooperation, formed a study (The Climate Friendly and Ecological Food on Microbiota) based on individual’s dietary intake. Every single individual have been assigned to a specific diet during 8 weeks, with the purpose to examine whether emissions of carbon dioxide, CO2, differs reliant to the specific diet each individuals follows. There are two groups, one treatment and one control group. Individuals assigned to the treatment group are supposed to follow a climatarian diet while the individuals in the control group follows a conventional diet. Each individual have been followed up during 8 weeks in total, with three different measurements occasions, 4 weeks apart. The different measurements are Baseline assessment, Midline assessment and End assessment. In the CLEAR-study there are a total of 18 individuals, with 9 individuals in each group. The amount of individuals are not enough to reach any statistical significance in a test and therefore the sample size shall be examined through power analysis. In terms of, data, every individual have three different measurements occasions that needs to be modeled through mixed-design ANOVA and linear mixed models. These two methods takes into account, each individual’s different measurements. The models which describes data are applied in the computations of sample sizes and power. All the analysis are done in the programming language R with means and standard deviations from the study and the models as a base. Sample sizes and power have been computed for two different linear mixed models and one ANOVA model. The linear mixed models required less individuals than ANOVA in terms of a desired power of 80 percent. 24 individuals in total were required by the linear mixed model that had the factors group, time, id and the covariate sex. 42 individuals were required by ANOVA that includes the variables id, group and time. / Inom forskning där försök, dels utförs på människor och djur, vill man försäkra sig om en lämplig urvalsstorlek för att spara tid och kostnad samtidigt som en önskad statistisk styrka uppnås. Mälardalens högskola och Karolinska institutet har gjort en pilotstudie (CLEAR) som undersöker människors koldioxidutsläpp i förhållande till kosthållning. Varje individ i studien har fått riktlinjer om att antingen följa en klimatvänlig- eller en konventionell kosthållning i totalt 8 veckor. Individerna följs upp med 4 veckors mellanrum, vilket har resulterat i tre mättillfällen, inklusive en baslinjemätning. I CLEAR-studien finns variabler om individernas kön, ålder, kosthållning samt intag av makro- och mikronäringsämnen. Nio individer i respektive grupp finns, där grupperna är klimat- och kontrollgruppen. Totala antalet individer i pilotstudien är för få för att erhålla statistisk signifikans vid statistiska tester och därför bör urvalsstorleken undersökas genom att göra styrkeberäkningar. Styrkan som beräknas är sannolikheten att förkasta nollhypotesen när den är falsk. För att kunna beräkna urvalsstorlekar måste modeller skapas utifrån strukturen på data, vilket kommer att göras med metoderna mixed-design ANOVA och linjära mixade modeller. Metoderna tar hänsyn till att varje individ har fler än en mätning. Modellerna som beskriver data tillämpas i beräkningarna av styrka. Urvalsstorlekarna och styrkan som beräknats är simuleringsbaserad och har analyserats i programspråket R med modellerna och värden från pilotstudien som grund. Styrka och urvalsstorlekar har beräknats för två linjära mixade modeller och en ANOVA. De linjära mixade modellerna kräver färre individer än ANOVA för en önskad styrka på 80 procent. Av de linjära mixade modellerna som krävde minst individer behövdes totalt 24 individer medan mixed design-ANOVA krävde 42 individer totalt.