Thesis Abstract

Abstract
Variance component estimation is a critical aspect of animal breeding and genetics research, particularly in farm animals where genetic improvement plays a crucial role in enhancing productivity. This research project focused on designing and analyzing experiments to investigate the methods of estimating variance components in farm animals. The primary objective was to compare the performance of different statistical approaches commonly used in animal breeding research for estimating variance components. The experimental design involved the collection of phenotypic data from a population of farm animals, including traits such as growth rate, milk yield, and reproductive performance. Several statistical methods were applied to estimate the variance components associated with these traits, including the Restricted Maximum Likelihood (REML) and Bayesian approaches. The data were analyzed using appropriate software packages capable of fitting mixed models and estimating variance components. The results of the experiments provided valuable insights into the performance of different methods for estimating variance components in farm animals. The comparison of REML and Bayesian approaches revealed differences in the precision and accuracy of estimates, highlighting the importance of selecting the most appropriate method based on the specific characteristics of the data and research objectives. Additionally, the study investigated the impact of sample size and genetic relationships on the estimation of variance components, demonstrating the importance of considering these factors in experimental design. Overall, the findings of this research project contribute to the existing knowledge on variance component estimation in farm animals and provide guidance for researchers and breeders in selecting suitable methods for their specific breeding programs. By understanding the strengths and limitations of different statistical approaches, stakeholders in the animal breeding industry can make informed decisions to improve genetic selection and breeding strategies. Future research could focus on expanding the scope of experiments to include more complex genetic models and exploring novel methods for variance component estimation in farm animals.

Thesis Overview

 1.1 BACKGROUND OF THE STUDYVariance measures the variability or difference from a mean or response. A variance value of 0 indicates that all values within a set of numbers are identical. Statisticians use variance to see how individual numbers or values relate to each other. Estimating variance components in statistics refers to the processes involved in efficiently calculating the variability within responses or values. Variance component are estimated whenA new improved trait is discoveredVariances or variability changes or alternate overtime due to environmental or genetic changes.A new trait is about to be defined or explainedA cardinal objective of many genetic surveys is the estimation of variance components associated with individual traits. Heritability, the proportion of variation in a trait that is contributed by average effects of genes, may be calculated from variance components. The heritability of a trait gives an indication of the ability of a population to respond to selection, and thus, the potential of that population to evolve (Lande & Shannon, 1996). Estimates of variance components are common in the discipline of animal breeding and production, where this information on the variance components is used in the development of selection regimes to improve economically important traits (Lynch & Walsh, 1998). A requirement for estimating variance components is knowledge of the relationship structure of the population. In a natural population, variance components are also of considerable interest for evolutionary studies (Boag, 1983) and also for conservation purposes. In natural populations, however, information on relationships may be unreliable or unavailable. These estimates of relationships may be combined with phenotypic information gathered from the same individuals, allowing inferences to be made about variance components (Ritland, 1996; Mousseau et al., 1998).Molecular data are used to infer relationships between animals on a pair-wise basis, because this provides the least complex level at which relationships may be estimated, while still allowing a population to be divided into several relationship classes. Estimates of pair-wise relationships are then combined with a pair-wise measure of phenotypic information. Several methods of estimating variance components have been studied, but for the purpose of clarity four different methods of estimating these variance components will be evaluated in this research work. They are;The ANOVA methodThe Maximum likelihood methodThe Restricted maximum likelihood methodThe Quasi maximum likelihood method.1.2 STATEMENT OF THE GENERAL PROBLEMThey have been general contradictions on the appropriate method to use in the estimating the variance components of animals. So this problem has led us into this research to ascertain the relatively best or appropriate method to be used in estimating these variance components in farm animals.1.3 OBJECTIVE OF THE STUDYThe major objective of this study is to determine the best method to be used between the methods enumerated above in estimating variance components of farm animals.1.4 SIGNIFICANCE OF THE STUDYA major significance of this study is to unravel the relatively best methods among the methods highlighted above with a view to advising animal breeders, producers and animal researchers on the best method to be used in estimating variance components as which relatively better method has generated a lot of controversies over time .1.5 SCOPE OF THE STUDYThe scope of the study is centered on the methods of estimating variance components in farm animals, to know which of the methods is relatively better in estimation.1.6 DEFINITION OF TERMSVariance: the amount by which something changes or is different from something else.Estimation: a judgment or opinion about the value or quality of somebody or something.Traits: a particular quality in someone’s personality.Genetic: the units in the cells of livings that controls its physical characteristics.Components: one of several parts of which something is made. 1.7 HYPOTHESIS TO BE TESTEDH0: there is no significant difference between the methods of estimating variance components.H1: there is a significant difference between the methods of estimating variance components.Level of significance: 0.05Decision rule: reject H0 if p-value is less than the level of significance. Accept H0 if otherwise. REFERENCESAnderson R.L., Bancroft T.A. (1952): Statistical Theory in Research. McGraw-Hill, New York.Federer W.T. (1968): Non-negative estimators for components of variance. Appl. Stat., 17, 171-174.Fisher R.A. (1925): Statistical Methods for Research Workers, Oliver and Boyd.Gamerman D. (1997): Markov Chain Monte Carlo. Chapman and Hall, New York.Gelman A., Carlin J.B., Stern H.S., Rubin D.B. (1995): Bayesian Data Analysis. Chapman and Hall, New York. Herbach L.H. (1959): Properties of model II type analysis of variance tests A: Optimum nature of the F-test for model II in balanced case. Ann. Math. Statist., 30, 939-959. Klotz J.H., Milton R.C., Zacks S. (1969): Mean square efficiency of estimators of variance components. J. Am. Stat. Assoc., 64, 1383-1402.LaMotte L.R. (1973): Quadratic estimation of variance components. Biometrics, 29, 311-330. Rao C.R. (1971a): Estimation of variance and covariance components: MINQUE theory. J. Multivar. Anal., 1, 257-275.Rao C.R. (1971b): Minimum variance quadratic unbiased estimation of variance components. J. Multivar. Anal., 1, 445-456. Rao C.R. (1972): Estimation of variance and covariance components in linear models. J. Am. Stat. Assoc., 67, 112-115.Rasch D. (1995): Mathematische Statistik. Joh. Ambrosius Barth and Wiley, Berlin, Heidelberg. 851 p. Rasch D., Tiku M.L.,Sumpf D. (1994): Elsevier’s Dictionary of Biometry. Elsevier, Amsterdam, London, New York. Rasch D., Verdooren L.R.,Gowers J.I. (1999): Fundamentals in the Design and Analysis of Experiments and Surveys - Grundlagen der Planung und Auswertung von Versuchen und Erhebungen. Oldenbourg Verlag, München,Wien. Reinsch N. (1996): Two Fortran programs for the Gibbs Sampler in univariate linear mixed models. Dummerstorf. Arch. Tierz., 39, 203-209. SarhaiH., Ojeda M.M. (2004): Analysis of Variance for Random Models, Balanced Data. Birkhäuser, Boston, Basel, Berlin. Sarhai H.,Ojeda M.M. (2005): Analysis of Variance for Random Models, Unbalanced Data. Birkhäuser, Boston, Basel, Berlin. Sorensen A., Gianola D. (2002): Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics. Springer, New York. Stein C (1969): Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean. Ann. Inst. Statist. Math. (Japan), 16, 155-160. Tiao G.C.,Tan W.Y. (1965): Bayesian analysis of random effects models in the analysis of variance I: Posterior distribution of variance components. Biometrika, 52, 37-53. Verdooren L.R. (1982): How large is the probability for the estimate of a variance component to be negative? Biom. J., 24, 339-360.