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Title:   Author  item
                                            Edwards, Jodeitem
                                            MASSIEL, ORELLANA - Monsanto Corporation
  Submitted to: Crop Science
                                    Publication Type: Peer Reviewed Journal
                                    Publication Acceptance Date: 11/9/2012
                                    Publication  Date: 3/20/2015
                                    Citation: Edwards, J.W., Orellana, M. 2015. Increasing selection response by Bayesian modeling of heterogeneous environmental variances. Crop Science. 55:556-563. DOI: 10.2135/cropsci2014.08.0582.Interpretive Summary: Identifying high yielding cultivars and breeding lines is both time consuming and expensive for testing organizations and breeders.  A common problem with interpreting data from multi-location testing of breeding lines is that some lines perform consistently across locations and other lines are highly variable.  Breeders and producers need cultivars that perform consistently in diverse environmental conditions.  A basic statistical outcome of ranking means, as is done in breeding line evaluation, that lines with variable performance are more likely to be highly ranked typical cultivar trials than lines that are less variable in performance.  When breeders select for high performance they are inadvertently selecting for lines that are more variable in performance which is undesirable.  A statistical approach is described to solve this problem by providing optimal differential weights to the data on different breeding lines which are proportional to consistency of performance.  The method penalizes inconsistently performing lines so that they are not more likely to be highly ranked.  The method could increase selection response by up to 15 percent based on data available in cultivar evaluation trials in Iowa.  This method will benefit breeders, seed companies, and producers by more efficiently eliminating unstable lines and cultivars from breeding programs and from the seed market.
                                Technical Abstract: Heterogeneity of environmental variance among genotypes reduces selection response because genotypes with higher variance are more likely to be selected than low-variance genotypes.  Modeling heterogeneous variances to obtain weighted means corrected for heterogeneous variances is difficult in likelihood estimation.  We have selection response with a Bayesian approach to modeling heterogeneity of environmental variance among genotypes.  Data were simulated using broad range of parameters and analyzed with a heterogeneous-variance model and homogeneous-variance model using Bayesian estimation.  Selection among estimators computed from simulated data was performed at intensities of 3.125 percent and 12.5 percent.  Based on estimators of variances and the heterogeneity of variances from cultivar trials in Maize and Oat in Iowa and a presumed early generation testing program with one replicate per environment grown in four to eight environments, we estimated that modeling of heterogeneous variances with Bayesian estimation could increase selection response by 5-15 percent.


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