Os efeitos genéticos aditivos e de heterozigoses são importantes na avaliação genética de populações compostas. Quando existem fortes relações lineares entre as variáveis explanatórias, os coeficientes de regressão tem erros-padrão elevados, são sensíveis a mudanças nos dados e a adição ou eliminação de variáveis explicativas no modelo. A alternativa usada na tentativa de diminuir esse problema foi aplicar o método de regressão de cumeeira - RC, pois na presença de multicolinearidade, pode permitir a obtenção de estimativas mais estáveis dos efeitos aditivos de origem genética e de heterozigose, em relação às obtidas pelo método dos quadrados mínimos - QM. Foram analisados os dados de pesos ao nascimento - PESNAS, ao desmame - PESDES, perímetro escrotal aos 390 dias - CE e escore para musculosidade aos 390 dias - MUSC de bovinos compostos Montana Tropicalr, com diferentes composições raciais NABCs, obtidos em várias fazendas brasileiras, relativos aos animais nascidos no período de 1994 a 2008. O modelo incluiu os efeitos aditivos e não aditivos. O grau da multicolinearidade foi obtido através do valor do fator de inflação da variância - V IF, dos índices de condição e da decomposição proporcional da variância. Os parâmetros de cumeeira foram obtidos a partir da multiplicação de uma constante, pela razão entre o V IF da covariável correspondente e o maior V IF. O traço de cumeeira foi utilizado para verificar se as estimativas dos coeficientes se estabilizaram, para o parâmetro de cumeeira obtido para cada variável explicativa. Duas análises foram aplicadas: i) os efeitos foram estimados por quadrados mínimos; ii) os efeitos foram estimados por regressão de cumeeira. Para cada variável resposta foi identificado o número de colinearidades, seus respectivos graus e as variáveis explicativas envolvidas em cada uma. As covariáveis envolvidas no modelo, para peso ao nascimento participaram de uma colinearidade forte e quatro colinearidades fracas; para peso ao desmame e escore de musculosidade aos 390 dias, houve duas relações de quase dependência fortes e três fracas, enquanto que para perímetro escrotal aos 390 dias obteve-se três colinearidades fortes e três fracas. O método que estimou os coeficientes por regressao de cumeeira foi melhor que o método dos quadrados mínimos, para todas as caracter´sticas. A m´edia dos V IFs para PESNAS, PESDES, CE e MUSC reduziram de 15, 5; 16; 17, 5 e 23, 9 para 5, 8; 5, 3; 5, 7 e 5, 1 respectivamente, após o uso da RC. Os erros-padrão diminuíram fornecendo estimativas mais estáveis que as obtidas por quadrados mínimos. Apenas para a covariável A sobre a variável resposta peso ao nascimento as soluções obtidas por QM e RC diferiram em direção, no mais, houve diferenças em magnitude / The genetic additive and heterozygosity effects are important in the genetic evaluation of multibreed populations. When there is strong linear relation between the explanatory variables, the regression coefficients have large standard errors and are sensitive to changes in the data set and to the addition or removal of explanatory variables in the model. The alternative used to try to reduce this problem was to apply the method of ridge regression - RC, which could allow for the estimation of more stable coefficients of direct and maternal breed additive effects of genetic origin and heterozygosity in relation to those obtained by the method of least squares QM . The objective is to analyze the data of birth weight - PESNAS, weaning - PESDES, the scrotal perimeter 390 days - CE and scoring for the muscularity 390 days - MUSC of cattle compounds Montana Tropical r, with different racial compositions NABCs, obtained in several Brazilian farms on of animals born from 1994 to 2008. The model included additive and non-additive effects. The degrees of multicollinearity were obtained through the value of the variance inflation factor - V IF, the index conditions - IC and by proportional decomposition of Variance. The ridge parameters were obtained from the multiplication of a constant to the ratio of the VIF from each covariate and the highest VIF. For each explanatory variable, the ridge trace was used to verify that the estimated coefficients were stabilized using the ridge parameter. Two different methods were applied: i) the effects were estimated by least squares; ii) the effects were estimated by ridge regression. For each response variable the number of colinearities was identified, their degrees and the variables involved in each. The covariates used in the model for birth weight participated in a strong colinearity and four other weak colinearities; for weaning weight and muscle score for 390 days, there were two strong relations of dependency and three almost weak, while for the perimeter scrotal 390 days it was observed three strong and three weak colinearities. The ridge regression coefficients method was considered better than that of least squares for all factors. The V IFs average for PESNAS, PESDES, CE and MUSC reduced from 15.5, 16, 17.5 and 23.9 to 5.8, 5.3, 5.7 and 5.1 respectively, after using the RC. The standard errors of the estimators decreased providing estimates more stable than those obtained by least squares. Only for A covariate on the response variable weight at birth the solutions obtained by QM and RC differ in direction, where the other ones differed only in magnitude.

Os efeitos genéticos aditivos e de heterozigoses são importantes na avaliação genética de populações compostas. Quando existem fortes relações lineares entre as variáveis explanatórias, os coeficientes de regressão tem erros-padrão elevados, são sensíveis a mudanças nos dados e a adição ou eliminação de variáveis explicativas no modelo. A alternativa usada na tentativa de diminuir esse problema foi aplicar o método de regressão de cumeeira - RC, pois na presença de multicolinearidade, pode permitir a obtenção de estimativas mais estáveis dos efeitos aditivos de origem genética e de heterozigose, em relação às obtidas pelo método dos quadrados mínimos - QM. Foram analisados os dados de pesos ao nascimento - PESNAS, ao desmame - PESDES, perímetro escrotal aos 390 dias - CE e escore para musculosidade aos 390 dias - MUSC de bovinos compostos Montana Tropicalr, com diferentes composições raciais NABCs, obtidos em várias fazendas brasileiras, relativos aos animais nascidos no período de 1994 a 2008. O modelo incluiu os efeitos aditivos e não aditivos. O grau da multicolinearidade foi obtido através do valor do fator de inflação da variância - V IF, dos índices de condição e da decomposição proporcional da variância. Os parâmetros de cumeeira foram obtidos a partir da multiplicação de uma constante, pela razão entre o V IF da covariável correspondente e o maior V IF. O traço de cumeeira foi utilizado para verificar se as estimativas dos coeficientes se estabilizaram, para o parâmetro de cumeeira obtido para cada variável explicativa. Duas análises foram aplicadas: i) os efeitos foram estimados por quadrados mínimos; ii) os efeitos foram estimados por regressão de cumeeira. Para cada variável resposta foi identificado o número de colinearidades, seus respectivos graus e as variáveis explicativas envolvidas em cada uma. As covariáveis envolvidas no modelo, para peso ao nascimento participaram de uma colinearidade forte e quatro colinearidades fracas; para peso ao desmame e escore de musculosidade aos 390 dias, houve duas relações de quase dependência fortes e três fracas, enquanto que para perímetro escrotal aos 390 dias obteve-se três colinearidades fortes e três fracas. O método que estimou os coeficientes por regressao de cumeeira foi melhor que o método dos quadrados mínimos, para todas as caracter´sticas. A m´edia dos V IFs para PESNAS, PESDES, CE e MUSC reduziram de 15, 5; 16; 17, 5 e 23, 9 para 5, 8; 5, 3; 5, 7 e 5, 1 respectivamente, após o uso da RC. Os erros-padrão diminuíram fornecendo estimativas mais estáveis que as obtidas por quadrados mínimos. Apenas para a covariável A sobre a variável resposta peso ao nascimento as soluções obtidas por QM e RC diferiram em direção, no mais, houve diferenças em magnitude / The genetic additive and heterozygosity effects are important in the genetic evaluation of multibreed populations. When there is strong linear relation between the explanatory variables, the regression coefficients have large standard errors and are sensitive to changes in the data set and to the addition or removal of explanatory variables in the model. The alternative used to try to reduce this problem was to apply the method of ridge regression - RC, which could allow for the estimation of more stable coefficients of direct and maternal breed additive effects of genetic origin and heterozygosity in relation to those obtained by the method of least squares QM . The objective is to analyze the data of birth weight - PESNAS, weaning - PESDES, the scrotal perimeter 390 days - CE and scoring for the muscularity 390 days - MUSC of cattle compounds Montana Tropical r, with different racial compositions NABCs, obtained in several Brazilian farms on of animals born from 1994 to 2008. The model included additive and non-additive effects. The degrees of multicollinearity were obtained through the value of the variance inflation factor - V IF, the index conditions - IC and by proportional decomposition of Variance. The ridge parameters were obtained from the multiplication of a constant to the ratio of the VIF from each covariate and the highest VIF. For each explanatory variable, the ridge trace was used to verify that the estimated coefficients were stabilized using the ridge parameter. Two different methods were applied: i) the effects were estimated by least squares; ii) the effects were estimated by ridge regression. For each response variable the number of colinearities was identified, their degrees and the variables involved in each. The covariates used in the model for birth weight participated in a strong colinearity and four other weak colinearities; for weaning weight and muscle score for 390 days, there were two strong relations of dependency and three almost weak, while for the perimeter scrotal 390 days it was observed three strong and three weak colinearities. The ridge regression coefficients method was considered better than that of least squares for all factors. The V IFs average for PESNAS, PESDES, CE and MUSC reduced from 15.5, 16, 17.5 and 23.9 to 5.8, 5.3, 5.7 and 5.1 respectively, after using the RC. The standard errors of the estimators decreased providing estimates more stable than those obtained by least squares. Only for A covariate on the response variable weight at birth the solutions obtained by QM and RC differ in direction, where the other ones differed only in magnitude.

Incluir como ag?ncias financiadoras: Funda??o de Amparo ? Pesquisa do Estado de Minas Gerais (FAPEMIG), Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES), Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico (CNPq). / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2018-01-05T18:15:19Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thaiza_silva_campideli.pdf: 3972827 bytes, checksum: d46dcbd4e39c922c90034d3992c8ad54 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-01-19T16:55:01Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thaiza_silva_campideli.pdf: 3972827 bytes, checksum: d46dcbd4e39c922c90034d3992c8ad54 (MD5) / Made available in DSpace on 2018-01-19T16:55:01Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) thaiza_silva_campideli.pdf: 3972827 bytes, checksum: d46dcbd4e39c922c90034d3992c8ad54 (MD5) Previous issue date: 2017 / Esta pesquisa foi realizada com o objetivo de avaliar a sensibilidade dos valores gen?ticos aos n?veis diet?ticos de lisina digest?vel para caracter?sticas de desempenho e medidas morfom?tricas de til?pias do Nilo da linhagem tailandesa. Vinte e nove fam?lias de irm?os completos foram produzidas pelo acasalamento de 21 machos e 29 f?meas. A distribui??o entre os tanques foi feita aleatoriamente, por fam?lia, ap?s marca??o dos peixes, entre 94 a 109 dias de idade, at? formar um lote inicial de vinte alevinos por tanque, totalizando 700 peixes. ? idade aproximada de 150 dias os peixes foram aleatoriamente redistribu?dos no sistema, at? formar lotes com aproximadamente 138 peixes por n?vel de lisina digest?vel na dieta. Os peixes foram alimentados quatro vezes ao dia com dietas contendo diferentes n?veis de lisina digest?vel: 1,43; 1,53; 1,63; 1,73; e 1,83% nas idades entre 94 a 150 dias; e 1,28; 1,38; 1,48; 1,58 e 1,68% a partir da idade de 150 at? 255 dias. As informa??es individuais das til?pias (peso, comprimento total, comprimento padr?o, comprimento de cabe?a, altura e largura) foram padronizadas para 150, 185, 220 e 255 dias de idade. A partir de ent?o foram calculados o ganho de peso total, o ganho de peso di?rio, rela??o entre cabe?a e comprimento padr?o, rela??o entre largura e altura e a rela??o entre comprimento padr?o e comprimento total. Para as an?lises foi utilizado modelo de regress?o aleat?ria, sob modelo animal uni-caracter?stica. Foram testados modelos de ordens 2 e 3 do polin?mio de Legendre para o efeito fixo e ordem 2 para os efeitos gen?tico aditivo e de fam?lia e testados modelos com vari?ncia residual homog?nea (1classe) a heterog?nea (2, 3, e 4 classes). Os modelos que proporcionaram melhor ajuste na maioria das caracter?sticas foram os que consideraram vari?ncia residual homog?nea. De forma geral, os valores da correla??o de posto foram altas. As normas de rea??o de 25 til?pias tailandesas amostradas aleatoriamente indicaram altera??o na sensibilidade dos valores gen?ticos de algumas caracter?sticas ?s mudan?as no n?vel nutricional de lisina digest?vel. Observou-se, portanto, que as til?pias apresentam altera??o nos valores gen?ticos, sugerindo de maneira geral, a exist?ncia da intera??o gen?tipo x n?veis de lisina digest?vel para caracter?sticas, o que pode acarretar em sele??o de diferentes animais nos diferentes ambientes. / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Zootecnia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / This research was carried out with the aim of evaluating the sensitivity of breeding values to dietary digestible lysine level for performance traits and morphometric measurements of Nile tilapia of Thai lineage. Twenty-nine full sib families were produced by mating 21 males and 29 females. The distribution among the tanks was randomized by family, after marking the fish, between 94 and 109 days of age, until forming an initial batch of twenty fingerlings per tank, totaling 700 fish. At the approximate age of 150 days the fish were randomly redistributed into the system until they formed lots with approximately 138 fish per level of digestible lysine in the diet. Four times a day the fishes were fed diets containing different levels of lysine: 1.43; 1.53; 1.63; 1.73 and 1.83% in the growing phase; and 1.28; 1.38; 1.48; 1.58 and 1.68% in the finishing phase. The individual tilapia information (weight, total length, standard length, head length, height and width) were standardized for 150, 185, 220 and 255 days of age. From then on the weight gain, daily weight gain, head to standard length ratio, width to height ratio and the relationship between standard length and total length were calculated. . For the analyses, a random regression model was used under a single animal model. Legendre polynomial models of 2 and 3 orders were tested for the fixed effect, and of order 2 for the additive and family genetic effects. In addition, models were also tested using homogeneous residual variance (1 class) and heterogeneous variance (2, 3, and 4 classes). The models that provide better fit in most of the characteristics were those that considered homogeneous residual variance. In general, the rank correlations of breeding values of pairs of dietary digestible lysine levels were high. The reaction norms of 25 randomly sampled Thai tilapia showed change in the sensitivity of breeding values of some traits to changes in dietary digestible lysine level. Therefore, it was observed that breeding values of tilapia traits generally changed along the environment gradient, suggesting the existence of genotype x dietary digestible lysine level interaction which can lead to the selection of different fishes in different environments.

In most breeding programmes breeders use phenotypic data obtained in breeding trials to rank the performance of the parents or progeny on pre-selected performance criteria. Through this ranking the best candidates are identified and selected for breeding or production purposes. Best Linear Unbiased Prediction (BLUP), is an efficient selection method to use, combining information into a single index. Unbalanced or messy data is frequently found in tree breeding trial data. Trial individuals are related and a degree of correlation is expected between individuals over sites, which can lead to collinearity in the data which may lead to instability in certain selection models. A high degree of collinearity may cause problems and adversely affect the prediction of the breeding values in a BLUP selection index. Simulation studies have highlighted that instability is a concern and needs to be investigated in experimental data. The occurrence of instability, relating to collinearity, in BLUP of tree breeding data and possible methods to deal with it were investigated in this study. Case study data from 39 forestry breeding trials (three generations) of Eucalyptus grandis and 20 trials of Pinus patula (two generations) were used. A series of BLUP predictions (rankings) using three selection traits and 10 economic weighting sets were made. Backward and forward prediction models with three different matrix inversion techniques (singular value decomposition, Gaussian elimination - partial and full pivoting) and an adapted ridge regression technique were used in calculating BLUP indices. A Delphi and Clipper version of the same BLUP programme which run with different computational numerical precision were used and compared. Predicted breeding values (forward prediction) were determined in the F1 and F2 E. grandis trials and F1 P. patula trials and realised breeding performance (backward prediction) was determined in the F2 and F3 E. grandis trials and F2 P. patula trials. The accuracy (correlation between the predicted breeding values and realised breeding performance) was estimated in order to assess the efficiency of the predictions and evaluate the different matrix inversion methods. The magnitude of the accuracy (correlations) was found to mostly be of acceptable magnitude when compared to the heritability of the compound weighted trait in the F1F2 E. grandis scenarios. Realised genetic gains were also calculated for each method used. Instability was observed in both E. grandis and P. patula breeding data in the study, and this may cause a significant loss in realised genetic gains. Instability can be identified by examining the matrix calculated from the product of the phenotypic covariance matrix with its inverse, for deviations from the expected identity pattern. Results of this study indicate that it may not always be optimal to use a higher numerical precision programme when there is collinearity in the data and instability in the matrix calculations. In some cases, where there is a large amount of collinearity, the use of a higher precision programme for BLUP calculations can significantly increase or decrease the accuracy of the rankings. The different matrix inversion techniques particularly SVD and adapted ridge regression did not perform much better than the full pivoting technique. The study found that it is beneficial to use the full pivoting Gaussian elimination matrix inversion technique in preference to the partial pivoting Gaussian elimination matrix inversion technique for both high and lower numerical precision programmes. / Thesis (PhD)--University of Pretoria, 2013. / gm2014 / Genetics / unrestricted