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A MULTIVARIATE EXTENSION OF A UNIVARIATE GENETIC MODEL ILLUSTRATED BY AN EXAMPLE OF INHERITANCE OF SOME FATTY ACID CONTENTS IN SOYBEAN OIL
Abstract
In the past, many statistical models have been proposed for estimating genetic effects such as additive, dominance and various digenic epistatic effects. However, these models are mostly for univariate analysis, i.e., for analyzing single, independent traits. In cases when several traits considered are intercorrelated, a multivariate model may be needed in order to obtain proper estimates of the genetic effects. A multivariate extension of a univariate model, proposed by Mather and Jinks (1971), is demonstrated and evaluated in this study. Regression techniques were used to estimate the genetic parameters. The inheritance of four correlated traits, contents of four fatty acids in soybean (Glycine max (L.) Merr.) oil, involved in a cross between two pure breeding lines and succeeding generations was analyzed numerically as a practical example. The multivariate model was described and compared to the equivalent univariate model. The distributions of the error terms and the structure of the variance-covariance matrix associated with the error terms were viewed and the genetic parameters were estimated using the Aitken estimator. The results of the numeric analyses showed that estimates of the genetic parameters differed when obtained from a multivariate model as compared to the univariate model. There was some gain in efficiency of estimation as seen from the reduced variances of the estimates of the genetic parameters. However, because most of the correlations between the variables were not very high, the reduction of the variances was not large. The adequacy of the model was tested using the Chi-square test of goodness of fit and a test of lack of fit. Different results were obtained, however, as the Chi-square tests showed that the additive-dominance model was not adequate for some variables while the test of lack of fit indicated that there was no significant deviation from the additive-dominance model for all variables studied. Judging from the R('2) values of the regressions, it was concluded that the Chi-square test was too sensitive for testing the adequacy of the model for this set of data and the test of lack of fit was more appropriate.
Subject Area
Biostatistics
Recommended Citation
SHAO, KUNG-PING PAM, "A MULTIVARIATE EXTENSION OF A UNIVARIATE GENETIC MODEL ILLUSTRATED BY AN EXAMPLE OF INHERITANCE OF SOME FATTY ACID CONTENTS IN SOYBEAN OIL" (1981). ETD collection for University of Nebraska-Lincoln. AAI8208380.
https://digitalcommons.unl.edu/dissertations/AAI8208380