WOMBAT—A tool for mixed model analyses in quantitative genetics by restricted maximum likelihood (REML)

WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by restricted maximum likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http：//agbu. une.edu.au/-kmeyer/wombat.html

Genetic Parameters for Milk,Fat Yield and Age at First Calving of Chinese Holsteins in Heilongjiang

Genetic parameters for milk,fat yield and age at first calving of Chinese Holsteins in Heilongjiang were evaluated using multiple trait restricted maximum likelihood procedures with an animal model.Data consisted of records of 2496 Chinese Holsteins first lactation cows collected from 1989 to 2000.The model included 21 herd effects,four calving season effects,nine age at first calving effects,6697 animal effects.(Co)variance components of milk yield,fat yield and age at first calving were estimated with the software package for variance component estimation(VCE) by an animal model. The heritabilities were 0.14,0.21,0.38 for milk yield,fat yield and age at first calving,respectively.The estimates of genetic correlation between milk yield and fat yield,age at first calving were 0.96,-0.29,respectively.The estimate of genetic correlation between fat yield and age at first calving was -0.28.

Influence of parental sample sizes on the estimating genetic parameters in cultured clam Meretrix meretrix based on factorial mating designs

The precise and accurate knowledge of genetic parameters is a prerequisite for making efficient selection strategies in breeding programs.A number of estimators of heritability about important economic traits in many marine mollusks are available in the literature,however very few research have evaluated about the accuracy of genetic parameters estimated with different family structures.Thus,in the present study,the effect of parent sample size for estimating the precision of genetic parameters of four growth traits in clam M.meretrix by factorial designs were analyzed through restricted maximum likelihood（REML） and Bayesian.The results showed that the average estimated heritabilities of growth traits obtained from REML were 0.23-0.32 for 9 and 16 full-sib families and 0.19-0.22 for 25 full-sib families.When using Bayesian inference,the average estimated heritabilities were0.11-0.12 for 9 and 16 full-sib families and 0.13-0.16 for 25 full-sib families.Compared with REML,Bayesian got lower heritabilities,but still remained at a medium level.When the number of parents increased from 6 to 10,the estimated heritabilities were more closed to 0.20 in REML and 0.12 in Bayesian inference.Genetic correlations among traits were positive and high and had no significant difference between different sizes of designs.The accuracies of estimated breeding values from the 9 and 16 families were less precise than those from 25 families.Our results provide a basic genetic evaluation for growth traits and should be useful for the design and operation of a practical selective breeding program in the clam M.meretrix.

Quadratic Loss of Isotonic Normal Means under Simultaneous Order Restrictions

For two normal populations with unknown means μ and unknown variances σ2, assume that there are simple order restrictions among the means and variances: μ1 < μ2 and σ12 >σ22 > 0. This case is said to be simultaneous order restriction by Shi (Maximum likelihood estimation of means and variances from normal populations under simultaneous order restrictions, J. Multivariate Anal., 50(1994), 282-293.) and an iterative algorithm of computing the order restricted maximum likelihood estimates of μi and σi2 was given in that paper. This paper shows that the restricted maximum likelihood estimate of μi has smaller mean square loss than the usual estimate xi under some conditions.

Estimation of Ordered Means of Two Normal Distributions with Ordered Variances

The authors consider the problem of estimating the ordered means of two normal distributions with unknown ordered variances. The authors discuss the estimation of two ordered means, individually, in terms of stochastic domination and MSE （mean squared error）. The authors show that in estimating the mean with larger variance, the usual estimator under order restriction on means can be improved upon. However, in estimating the mean with smaller variance, the usual estimator can＇t be improved upon even under MSE. The authors also discuss simultaneous estimation problem of two ordered means when unknown variances are ordered.

A new exact p-value approach for testing variance homogeneity

To test variance homogeneity,various likelihood-ratio based tests such as the Bartlett's test have been proposed.The null distributions of these tests were generally derived asymptotically or approximately.We re-examine the restrictive maximum likelihood ratio(RELR)statistic,and sug-gest a Monte Carlo algorithm to compute its exact null distribution,and so its p-value.It is much easier to implement than most existing methods.Simulation studies indicate that the proposed procedure is also superior to its competitors in terms of type I error and powers.We analyse an environmental dataset for an illustration.