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Title:A Biometrical and Genetic Study of Tribolium Egg Production Curves as A Model for Lactation Curves
Author(s):Anderson, Clyde Ray
Department / Program:Dairy Science
Discipline:Dairy Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Biology, Genetics
Abstract:A considerable amount of research has been conducted to find a mathematical equation that describes the nonlinear lactation curve of dairy cattle. The most common method to obtain parameter estimates for these mathematical equations has been to transform the nonlinear function to its linear counterpart and then find parameter estimates for the transformed equation. These estimates are then transformed back to estimates for the original nonlinear equation.
One purpose of this research was to determine which of four nonlinear mathematical equations, two incomplete gamma (y = at('b) exp(-ct) of Wood, y = at('b) exp(-ct + d SQRT(t)) of McNally) and two inverse polynomial (the quadratic y = t/(a + bt + ct('2)), the cubic y = t/(a + bt + ct('2) + dt('3))) equations, best describe the egg production curve of 162 Purdue black Tribolium beetles as a model for the lactation curve of dairy cattle.
Selection of a model was based on its satisfying the underlying assumptions of regression analysis (constancy of error variance, independence of errors, and normality of errors) and having smallest error variance. Constancy of error variance was tested using Bartlett's likelihood ratio statistic on numbers of eggs of 24 full-sib groups from 162 beetles. These results indicated that the square root transformation of the data was useful to remove the heterogeneity of error variance. Independence of errors for the square root transformed number of eggs was tested using an auto-regression analysis. These results indicated significant autocorrelations among the errors of observations two, four, and six days prior to the present observation. Normality of errors for the square root transformed number of eggs was tested using the Shapiro-Wilk W statistic. These results failed to find non-normality of the residuals for any of the four models.
Similar models, i.e., Wood's and McNally's incomplete gamma, and inverse quadratic and cubic polynomial equations, were tested for smallest error variance using an F test. McNally's incomplete gamma and the inverse cubic polynomial were better than their counterparts. The inverse cubic polynomial was selected because it had a smaller error mean square than McNally's incomplete gamma model.
Parameter estimates of the inverse cubic polynomial model using autoregression analysis were similar to those using ordinary least-squares. It was concluded, therefore, that ordinary least-squares methods would provide estimates of the model parameters for sequent analyses.
The other purpose of this research was to study genetic parameters of six traits: four model parameters, and estimated and observed total yield, of the inverse cubic polynomial model. Estimates of heritability and genetic and phenotypic correlations were calculated from a nested analysis of variance for these traits for 344 Tribolium.
Heritability estimates were based on sire, dam, and sire-plus-dam components of variance. As expected from the design of the experiment, the most precise heritability estimates were those based on the sire-plus-dam components of variance. Heritability estimates from the sire-plus-dam components were not different from zero; the exception was the heritability estimate for observed total egg production which was 0.208 (+OR-) 0.095.
The genetic correlations were based on sire, dam, and sire-plus-dam components of variance and covariance. Standard errors of these correlations were large. Phenotypic correlations were high in absolute value for all pairs of model parameter estimates. The phenotypic correlations between observed total production and other traits, however, were small in absolute value.
Because of the low estimates of heritability and the imprecision of the estimates of the genetic correlations, no additional improvement would be expected from indirect selection for observed total yield using the model parameter estimates or estimated total yield.
Issue Date:1981
Description:104 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1981.
Other Identifier(s):(UMI)AAI8114383
Date Available in IDEALS:2014-12-14
Date Deposited:1981

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