Files in this item
Files  Description  Format 

application/pdf 8114383.pdf (3MB)  (no description provided) 
Description
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 UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
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 fullsib 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 autoregression 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 ShapiroWilk W statistic. These results failed to find nonnormality 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 leastsquares. It was concluded, therefore, that ordinary leastsquares 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 sireplusdam components of variance. As expected from the design of the experiment, the most precise heritability estimates were those based on the sireplusdam components of variance. Heritability estimates from the sireplusdam 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 sireplusdam 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 
Type:  Text 
Language:  English 
Description:  104 p. Thesis (Ph.D.)University of Illinois at UrbanaChampaign, 1981. 
URI:  http://hdl.handle.net/2142/68560 
Other Identifier(s):  (UMI)AAI8114383 
Date Available in IDEALS:  20141214 
Date Deposited:  1981 
This item appears in the following Collection(s)

Dissertations and Theses  Dairy Science

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois