OVERVIEW OF WOMBAT* AND ITS APPLICATIONS IN ANIMAL BREEDING DATA ANALYSIS

 

A.S. Ghai & Avtar Singh

 

WOMBAT replaces DFREML which has been withdrawn from distribution at the end of 2005.
 

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 The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can bedownloaded free of charge from http://agbu.une.edu.au/~kmeyer/wombat.html.

There are no license requirements, but it is a condition that
a) use of WOMBAT is credited in any publications or reports,

b) that WOMBAT is not used commercially. Released in August 2006.

WOMBAT is aimed at the analysis of data from animal breeding programmes. It accommodates most models commonly fitted for such data, and employs up-to-date methods for ordering the mixed model equations and maximising the likelihood. It is particularly suitable for analyses of large data sets fitting simple models. WOMBAT performs uni- and multivariate analyses for both standard and random regression models.

 

Introduction

 

Purpose

 

WOMBAT is a program to facilitate analyses fitting a linear, mixed model via restricted maximum likelihood (REML). It is assumed that traits analyzed are continuous and have a multivariate normal distribution. WOMBAT is set up with quantitative genetic analyses in mind, but is readily applicable in other areas. Its main purpose is the estimation of (co)variance components and the resulting genetic parameters. It is particularly suited to analyses of moderately large to large data sets from livestock improvement programmes, fitting relatively simple models. It can, however, also be used as simple generalized least-squares program, to obtain estimates of fixed and predictions (BLUP) of random effects. In addition, it provides the facilities to simulate data for a given data and pedigree structure, invert a matrix or combine estimates from different analyses. WOMBAT replaces DfReml which has been withdrawn from distribution at the end of 2005.

 

Features

 

WOMBAT consists of a single program. All information on the model of analysis, input files and their layout, and (starting) values for (co)-variance components is specified in a parameter file. A large number of run options are available to choose between (partial) analyses steps, REML algorithms to locate the maximum of the likelihood function, strategies to re-order the mixed model equations, and parameterizations of the model.

 

Types of Analysis

 

WOMBAT accommodates standard uni- and multivariate analyses, analyses as well as random regression (RR) analyses, allowing a wide range of common models to be fitted and offering a choice between full and reduced rank estimation of covariance matrices.
 

REML Algorithms

 

WOMBAT incorporates the so-called ‘average information’ (AI) REML algorithm, and the standard (EM) as well as the ‘parameter exalgorithms panded’ (PX) variant of the expectation-maximization algorithm. In addition, derivative-free maximization via Powell’s method of conjugate directions or the Simplex procedure is available. By default, WOMBAT carries out a small number of PX-EM iterates 3 to begin with, then switches to an AI REML algorithm.

 

Ordering strategies

 

Computational efficiency and memory requirements during estimation depend strongly on the amount of ‘fill-in’ created during Ordering the factorization of the coefficient matrix. This can be reduced strategies by judicious ordering of the equations in the mixed model, so that rows and columns with few elements are processed first. Several ordering procedures aimed at minimizing fill-in are available in WOMBAT, a multilevel nested dissection procedure which has been found to perform well for large data sets from livestock improvement programmes.

 

Analysis Steps

 

WOMBAT allows for analyses to be broken up into individual steps steps. In particular, carrying out the ‘set-up’ steps separately facilitates thorough checking and allows memory requirements in the estimation step to be minimised.

 

Parameterisation

 

Generally, WOMBAT assumes covariance matrices to be estimated to be unstructured. Estimation can be carried out on the ’original’ scale, i.e. by estimating the covariance components Parame- directly, or by reparameterising to the matrices to be estimated terisation elements of the Cholesky factors of the covariance matrices. The latter guarantees estimates within the parameter space, in particular when combined with a transformation of the diagonal elements to logarithmic scale. Reduced rank estimation, equivalent to estimating the leading principal components only, is readily carried out by estimating the corresponding columns of the respective Cholesky factor(s) only. WOMBAT offers few features related to data editing, such as selection of subsets of records, transformation of variables or tabulation of data features. There are a number of general statistical packages to choose from which perform these tasks admirably, including free software.

 

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*Karin Meyer, Animal Genetics and Breeding Unit, University of New England, Armidale, NSW 2351 AUSTRAILIA  kmeyer@didgeridoo.une.edu.au 
*A program for Mixed Model Analyses by Restricted  Maximum Likelihood