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Estimation in a multiplicative mixed model involving a genetic relationship matrix

By Alison M Kelly, Brian R Cullis, Arthur R Gilmour, John A Eccleston and Robin Thompson

Abstract

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments

Topics: Research
Publisher: BioMed Central
OAI identifier: oai:pubmedcentral.nih.gov:2686677
Provided by: PubMed Central

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Citations

  1. (1976). A simple method for computing the inverse of a numerator relationship matrix used in prediction of breeding values. Biometrics
  2. (2007). A: Modelling additive × environment and additive × additive × environment using genetic covariances of relatives of wheat genotypes. Crop Sci
  3. (2006). A: Modelling genotype × environment interaction using additive genetic covariances of relatives for predicting breeding values of wheat genotypes. Crop Sci
  4. (2001). Analysing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics
  5. (2003). AR: A sparse implementation of the average information algorithm for factor analytic and reduced rank variance models.
  6. (2004). Charmet G: Quantitative trait loci (QTL) detection in multi-cross inbred designs: Recovering QTL identical-by-descent status information from marker data. Genetics
  7. (1976). Computing the diagonal elements and inverse of a large numerator relationship matrix. Biometrics
  8. (1995). Cullis BR: Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models. Biometrics
  9. (2007). Cullis BR: The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials. Crop Sci
  10. (2007). Joint modelling of additive and non-additive (genetic line) effects in multi-environment trials. Theor Appl Genet
  11. (2006). Joint modelling of additive and non-additive genetic line effects in single field trials. Theor Appl Genet
  12. (1992). Luo Z: Computing inbreeding coefficients in large populations. Genet Sel Evol
  13. (2006). On the design of early generation variety trials with correlated data.
  14. R: ASReml, user guide. Release 2.0 Hemel Hempstead:
  15. (1971). Recovery of interblock information when block sizes are unequal. Biometrika
  16. (2005). Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices. Genet Sel Evol
  17. (1996). TFC: Introduction to Quantitative Genetics 4th edition. London: Longman Scientific and Technical;
  18. (2005). The analysis of crop cultivar breeding and evaluation trials: An overview of current mixed model approaches. J Agric Sci

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