Updated notes

Shayle Searle has just published some excellent notes (around 250 pages) that are a mathematical supplement to Henderson's classic book Applications of linear models in animal breeding. These are rather detailed and are quite informative.

• Ordering information

Dr. L. R. Schaeffer (Department of Animal & Poultry Science, University of Guelph, Ontario) has an outstanding set on notes on advanced topics in Animal Models , which has much on variance component estimation.

Dr. Schaeffer also has an excellent set of notes on historical approaches to variance component estimation. We did not discuss many of these (Henderson's Methods 1-4, MIVQUE, Method R ) as they are not longer widely used, but are still occasionally seen in the literature.

Notes from Jim Fry on using SAS software to perform Restricted Maximum Likelihood (REML) Analysis of Quantitative-Genetic Data.

1. Programs for REML Analysis of Nested Half-Sib Designs

Programs

• List of Pedigree Drawing Programs

• DFREML is a suite of programs by Karin Meyer (University of New England, Armidale, NSW, Australia) to estimate (co)variance components and genetic parameters for normally distributed traits by Restricted Maximum Likelihood, using a derivative-free algorithm. Analysis is carried out fitting a mixed linear model with a random effect for the additive genetic merit of each animal (the so-called "animal model"), allowing for some additional random effects.

• VCE 4 a suite program distributed by Eildert Groeneveld ( Institut fuer Tierzucht und Tierverhalten Forschungsanstalt fuer Landwirtschaft --- Institute of Animal Husbandry and Animal Ethology Federal Agricultural Research Centre) for Multivariate Variance Component Estimation in general pedigrees, using REML, Monte-Carlo EM and Gibbs sampling.

• Quercus is a suite of programs by Ruth G. Shaw and Frank H. Shaw (University of Minnesota) for the analysis of quantitative genetic data by maximum likelihood. The programs perform ML or REML on a two generation pedigree with multivariate phenotypic observations and fixed effects. Up to six variance components including additive genetic, dominance, maternal, paternal, and residual (and their covariances in the multivariate case) can be calculated. The MLE can be constrained to satisfy feasibility requirements or for hypothesis testing. A program is also included which will maximize the likelihood while constraining the additive covariance component matrices of two unrelated populations to be the same.
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• MTGSAM, Multiple Trait Gibbs Sampler for Animal Models, is a set of Fortran programs for Gibbs sampling in animal models. The programs support a flexible set of multiple trait models; the programs support the same model options as the MTDFREML programs. The programs generate the Gibbs sampling information and the posterior mean estimates for a variety of parameters including (co)variance components, heritabilities, and correlations. The programs were developed by Curt Van Tassell at the USDA Meat Animal Research Center and the University of Nebraska.

• MTDFREML, Multiple Trait Derivative Free REstricted Maximum Likelihood, is a flexible set of FORTRAN programs which can be used to estimate variance components using a derivative free restricted maximum likelihood algorithm. The programs were developed by Keith Boldman, Lisa Kriese, Dale Van Vleck, Curt Van Tassell, and Steve Kachman at the USDA Meat Animal Research Center and the University of Nebraska. The programs are designed to be used with animal breeding data where an animal genetic effect is used for each trait, however it is often straightforward to apply the programs to non-animal breeding data. The programs can handle an arbitrary number of fixed effects, uncorrelated random effects and covariates for a number of traits. The program also generates BLUP solutions to the mixed model equations, contrasts of solutions, prediction error variances of solutions and contrasts, and calculates expected values of solutions.

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Bruce Walsh. jbwalsh@u.arizona.edu . Comments welcome.