Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học quốc tế đề tài: Factor-analytic models for genotype × environment type problems and structured covariance matrices | Genetics Selection Evolution BioMed Central Open Access Review Factor-analytic models for genotype X environment type problems and structured covariance matrices Karin Meyer Address Animal Genetics and Breeding Unit University of New England Armidale NSW 2351 Australia Email Karin Meyer-kmeyer@ Published 30 January 2009 Received 22 January 2009 Genetics Selection Evolution 2009 41 21 doi 1297-9686-41 -21 Accepted 30 January 2009 This article is available from http content 41 1 21 2009 Meyer licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Abstract Background Analysis of data on genotypes with different expression in different environments is a classic problem in quantitative genetics. A review of models for data with genotype X environment interactions and related problems is given linking early analysis of variance based formulations to their modern mixed model counterparts. Results It is shown that models developed for the analysis of multi-environment trials in plant breeding are directly applicable in animal breeding. In particular the additive main effect multiplicative interaction models accommodate heterogeneity of variance and are characterised by a factor-analytic covariance structure. While this can be implemented in mixed models by imposing such structure on the genetic covariance matrix in a standard multi-trait model an equivalent model is obtained by fitting the common and specific factors genetic separately. Properties of the mixed model equations for alternative implementations of factor-analytic models are discussed and extensions to structured modelling of covariance matrices for multi-trait multi-environment scenarios are described. Conclusion Factor analytic models .
