O uso de simulação de Monte Carlo via cadeias de Markov no melhoramento genético
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2009-02-20
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Universidade Federal de Viçosa
Resumo
Este trabalho teve por objetivo fornecer um referencial teórico e aplicado sobre os principais métodos de simulação de Monte Carlo via cadeias de Markov (MCMC), buscando dar ênfase em aplicações no melhoramento genético. Assim, apresentaram-se os algoritmos de Metropolis-Hastings, simulated annealing e amostrador de Gibbs. Os aspectos teóricos dos métodos foram abordados através de uma discussão detalhada de seus fundamentos com base na teoria de cadeias de Markov. Além da discussão teórica, aplicações concretas foram desenvolvidas. O algoritmo de Metropolis- Hastings foi utilizado para obter estimativas das freqüências de recombinação entre pares de marcadores de uma população F2, de natureza codominante, constituída de 200 indivíduos. O simulated annealing foi aplicado no estabelecimento da melhor ordem de ligação na construção de mapas genéticos de três populações F2 simuladas, com marcadores de natureza codominantes, de tamanhos 50, 100 e 200 indivíduos respectivamente. Para cada população foi estabelecido um genoma com quatro grupos de ligação, com 100 cM de tamanho cada. Os grupos de ligação possuem 51, 21, 11 e 6 marcadores, com uma distância de 2, 5, 10 e 20 cM entre marcas adjacentes respectivamente, ocasionando diferentes graus de saturação. Já o amostrador de Gibbs foi utilizado na obtenção das estimativas dos parâmetros de adaptabilidade e estabilidade, do modelo proposto por Finlay e Wilkinson (1963), através da inferência bayesiana. Foram utilizados os dados de médias de rendimento de cinco genótipos avaliados em nove ambientes, provenientes de ensaios em blocos ao acaso com quatro repetições. Em todas as aplicações os algoritmos se mostraram computacionalmente viáveis e obtiveram resultados satisfatórios.
The objective of this work was to provide a theoretical and applied reference on the main Monte Carlo simulation methods via Markov chains (MCMC), seeking to focus on applications in genetic breeding. Thus, the algorithms of Metropolis-Hastings, simulated annealing and the Gibbs sampler were presented. The theoretical aspects of the methods were approached through a detailed discussion about their foundations based on the Markov chain theory. Besides the theoretical discussion, concrete applications were developed. The Metropolis-Hastings algorithm was used to achieve estimates from the frequencies of recombination between pairs of markers of a population F2, of co-dominant nature, with 200 individuals. The simulated annealing was applied to establish a better linking order in the construction of genetic maps of three simulated populations F2, with markers of co-dominant nature, containing 50, 100 and 200 individuals, respectively. For each population, it was established a genome with four linking groups, each with 100 cM of size. The linking groups present 51, 21, 11 and 6 markers, with a distance of 2, 5, 10 and 20 cM between the adjacent marks, respectively, providing different degrees of saturation. The Gibbs sampler, on the other hand, was used for the achievement of the estimates of the adaptability and stability parameters of the model proposed by Finlay and Wilkinson (1963), through the Bayesian inference. The data of the productivity averages of five genotypes evaluated in nine environments were used, come from essays in randomized blocks with four replications. In all the applications, the algorithms were computationally viable and achieved satisfactory results.
The objective of this work was to provide a theoretical and applied reference on the main Monte Carlo simulation methods via Markov chains (MCMC), seeking to focus on applications in genetic breeding. Thus, the algorithms of Metropolis-Hastings, simulated annealing and the Gibbs sampler were presented. The theoretical aspects of the methods were approached through a detailed discussion about their foundations based on the Markov chain theory. Besides the theoretical discussion, concrete applications were developed. The Metropolis-Hastings algorithm was used to achieve estimates from the frequencies of recombination between pairs of markers of a population F2, of co-dominant nature, with 200 individuals. The simulated annealing was applied to establish a better linking order in the construction of genetic maps of three simulated populations F2, with markers of co-dominant nature, containing 50, 100 and 200 individuals, respectively. For each population, it was established a genome with four linking groups, each with 100 cM of size. The linking groups present 51, 21, 11 and 6 markers, with a distance of 2, 5, 10 and 20 cM between the adjacent marks, respectively, providing different degrees of saturation. The Gibbs sampler, on the other hand, was used for the achievement of the estimates of the adaptability and stability parameters of the model proposed by Finlay and Wilkinson (1963), through the Bayesian inference. The data of the productivity averages of five genotypes evaluated in nine environments were used, come from essays in randomized blocks with four replications. In all the applications, the algorithms were computationally viable and achieved satisfactory results.
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Palavras-chave
Simulação estocástica, MCMC, Estatística genômica, Inferência bayesiana, Stochastic simulation, MCMC, Genomic statistics, Bayesian inference
Citação
NASCIMENTO, Moysés. The use of Monte Carlo simulation via Markov chains in genetic breeding. 2009. 111 f. Dissertação (Mestrado em Estatística Aplicada e Biometria) - Universidade Federal de Viçosa, Viçosa, 2009.