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Title:   Author  item
                                            Edwards, Jodeitem
                                            JANNINK, JEAN-LUC - IOWA STATE UNIV
  Submitted to: Crop Science
                                    Publication Type: Peer Reviewed Journal
                                    Publication Acceptance Date: 10/30/2005
                                    Publication  Date: 3/17/2006
                                    Citation: Edwards, J.W., Jannink, J. 2006. Bayesian modeling of heterogeneous error and genotype by environment interaction variances. Crop Science. 46:820-833.Interpretive Summary: Identifying plant varieties (commercial and experimental) that provide superior performance for growers across a wide range of growing conditions is a very expensive task.  Varieties must be evaluated in many environments and performance data summarized in order to identify not only the best varieties, but also those with the most stable performance.  A new method for more efficiently summarizing the data from plant variety evaluations has been tested.  The objectives were i.) to take advantage of technological advantages in statistics and computing in order to provide more precise rankings of experimental varieties, and ii.) to provide a more precise method for identifying varieties that do not provide stable performance across varying environmental conditions.  This new method will increase precision of plant variety evaluations because greater value will be realized from existing data, and will potentially reduce cost as the number of locations and replications in such evaluations may be reduced.  As such, use of this method will benefit all parties involved in plant variety evaluation including public and private plant breeders, seed companies, and public yield testing programs.  Growers will realize indirect benefits in the form of improved varieties, more stable varieties in particular.  Growers will benefit directly from better information available on existing commercial and public varieties.
                                Technical Abstract: An important assumption in the analysis of multi-environment cultivar trials is homogeneity of error and genotype by environment interaction variances.  When variances are heterogeneous, the best estimators of performance are obtained by weighting inversely to variance components.  However, because variances must be estimated, the additional error introduced into the model from estimating many variances may cause weighted estimators to perform poorly.  Our objective was to test a Bayesian approach to estimating heterogeneous error and genotype by environment interaction variances.  A Bayesian model for multienvironment yield trials that includes a linear model for error and genotype by environment interaction variances was applied to yield data from the Iowa State University Oat Variety Trial for the years 1997 to 2003.  The Bayesian approach revealed that error variances were highly heterogeneous among environments and that genotype by environment interaction variances were heterogeneous among environments and genotypes.  Incorporation of heterogeneity of variances significantly decreased estimates of marginal error, genotypic, and genotype by environment variance components, with the largest change being a reduction in the marginal genotype by environment interaction variance.  Repeatiblities were higher in the heterogeneous variance model, but not at a high level of statistical significance.  Genotype specific estimates of genotype by environment interaction variances were correlated with estimated genotypic yields and heading dates providing biological validity to our estimates of genotype-specific estimators of genotype by environment interaction variances as stability estimators.


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