On testing genetic covariance via the mean cross-products ratio

• Autor(a) principal: Silva, Anderson Rodrigo da
• Data de Publicação: 2015
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: http://www.teses.usp.br/teses/disponiveis/11/11134/tde-22092015-141749/
• topic: bootstrap; Bootstrap; Correlação genética; genetic correlation; Lambda de Wilks; MANOVA; MANOVA; Monte Carlo simulation; Simulação de Monte Carlo; Wilks\' Lambda

When a genetic factor is being studied for more than one response variable, estimates of the genetic covariances are essential, specially in breeding programs. In a genetic covariance analysis, genetic and residual mean cross-products are obtained. Stochastically, to quantify the magnitude of the joint variation of two response variables due to genetic effect with respect to the variation due to residual effect may allow one to make inferences about the significance of the associated genetic covariance. In this study it is presented tests of significance for genetic covariance upon a twofold way: tests that take into account the genetic and environmental effects and tests that only consider the genetic information. The first way refers to tests based on the mean cross-products ratio via nonparametric bootstrap resampling and Monte Carlo simulation of Wishart matrices. The second way of testing genetic covariance refers to tests based on adaptation of Wilks\' and Pillai\'s statistics for evaluating independence of two sets of variables. For the first type of tests, empirical distributions under the null hypothesis, i.e., null genetic covariance, were built and graphically analyzed. In addition, the exact distribution of mean cross-products ratio obtained from variables normally distributed with zero mean and finite variance was examined. Writing computational algorithms in R language to perform the proposed tests was also an objective of this study. Only under certain conditions does the probability density function of the product of two random Gaussian variables approximate a normal curve. Therefore, studying the distribution of a mean cross-products ratio as a quotient of two Gaussian variables is not suitable. Tests based on mean cross-products ratio are related to both the value of the genetic covariance and the magnitude of the latter relative to the residual covariance. And both approaches (bootstrap and simulation) are more sensitive than the tests based only on genetic information. The performance of the tests based on mean cross-products ratio is related to the quality of the original data set in terms of the MANOVA assumptions, and the test statistic does not depend on the estimation of the matrix of genetic covariances ΣG. The adaptation of Wilks\' and Pillai\'s statistics can be used to test the genetic covariance. Their approximations to a χ21 distribution were checked and the accuracy of their inferences is related to the quality of G.