Yield response of winter wheat cultivars to environments modeled by different variance-covariance structures in linear mixed models
Abstract
The main objectives of multi-environmental trials (METs) are to assess cultivar adaptation patterns under different environmental conditions and to investigate genotype by environment (G×E) interactions. Linear mixed models (LMMs) with more complex variance-covariance structures have become recognized and widely used for analyzing METs data. Best practice in METs analysis is to carry out a comparison of competing models with different variance-covariance structures. Improperly chosen variance-covariance structures may lead to biased estimation of means resulting in incorrect conclusions. In this work we focused on adaptive response of cultivars on the environments modeled by the LMMs with different variance-covariance structures. We identified possible limitations of inference when using an inadequate variance-covariance structure. In the presented study we used the dataset on grain yield for 63 winter wheat cultivars, evaluated across 18 locations, during three growing seasons (2008/2009-2010/2011) from the Polish Post-registration Variety Testing System. For the evaluation of variance-covariance structures and the description of cultivars adaptation to environments, we calculated adjusted means for the combination of cultivar and location in models with different variance-covariance structures. We concluded that in order to fully describe cultivars adaptive patterns modelers should use the unrestricted variance-covariance structure. The restricted compound symmetry structure may interfere with proper interpretation of cultivars adaptive patterns. We found, that the factor-analytic structure is also a good tool to describe cultivars reaction on environments, and it can be successfully used in METs data after determining the optimal component number for each dataset.
Downloads
References
Burgueño J, Crossa J, Cotes JM, Vicente FS, Das B, 2011. Prediction assessment of linear mixed models for multienvironment trials. Crop Sci 51: 944-954. http://dx.doi.org/10.2135/cropsci2010.07.0403
Crossa J, Vargas M, Joshi AK, 2010. Linear, bilinear, and linear-bilinear fixed and mixed models for analyzing genotype x environment interaction in plant breeding and agronomy. Can J Plant Sci 90: 561574. http://dx.doi.org/10.4141/CJPS10003
Gilmour AR, Gogel BJ, Cullis BR, Thompson R, 2009. ASReml User Guide Release 3.0 VSN International Ltd, Hemel Hempstead, HP1 1ES, UK. 398 pp.
Hu X, 2015. A comprehensive comparison between ANOVA and BLUP to valuate location-specific genotype effects for rape cultivar trials with random locations. Field Crop Res 179: 144-149. http://dx.doi.org/10.1016/j.fcr.2015.04.023
Hu X, Spilke J, 2011. Variance-covariance structure and its influence on variety assessment in regional crop trials. Field Crop Res 120: 1-8. http://dx.doi.org/10.1016/j.fcr.2010.09.015
Hu X, Yan S, Shen K, 2013. Heterogeneity of error variances and its influence on genotype comparison in multi-location trials. Field Crop Res 149: 322-328. http://dx.doi.org/10.1016/j.fcr.2013.05.011
Kelly AM, Smith AB, Eccleston JA, Cullis BR, 2007. The accuracy of varietal selection using factor analytic models for multi-environment plant breeding trials. Crop Sci 47: 1063-1070. http://dx.doi.org/10.2135/cropsci2006.08.0540
Littell RC, Milliken GA, Stroup WW, Wolfinger RD, Schabenberger O, 2006. SAS for mixed models, 2nd ed. SAS Institute, Cary, NC, USA. 814 pp.
Mądry W, Gacek ES, Paderewski J, Gozdowski D, Drzazga T, 2011. Adaptive yield response of winter wheat cultivars across environments in Poland using combined AMMI and cluster analyses. Int J Plant Prod 5: 299-309.
Meyer K, 2009. Factor-analytic models for genotype × environment type problems and structured covariance matrices. Gene Sel Evol 41: 21. http://dx.doi.org/10.1186/1297-9686-41-21
Möhring J, Piepho HP, 2009. Comparison of weighting in two-stage analyses of series of experiments. Crop Sci 49: 1977-1988. http://dx.doi.org/10.2135/cropsci2009.02.0083
Piepho HP, 1997. Analyzing genotype-environment data by mixed models with multiplicative terms. Biometrics 53: 761-766. http://dx.doi.org/10.2307/2533976
Piepho HP, 1998. Empirical best linear unbiased prediction in cultivar trials using factor analytic variance-covariance structures. Theor Appl Genet 97: 195-201. http://dx.doi.org/10.1007/s001220050885
Piepho HP, Möhring J, Schulz-Streeck T, Ogutu JO, 2012. A stage-wise approach for analysis of multi-environment trials. Biometrical J 54: 844-860. http://dx.doi.org/10.1002/bimj.201100219
Roostaei M, Mohammadi R, Amri A, 2014. Rank correlation among different statistical models in ranking of winter wheat genotypes. Crop J 2: 154-163. http://dx.doi.org/10.1016/j.cj.2014.02.002
Smith AB, Cullis BR, Thompson R, 2001. Analyzing variety by environment data using multiplicative mixed models and adjustments for spatial field trend. Biometrics 57: 1138-1147. http://dx.doi.org/10.1111/j.0006-341X.2001.01138.x
Smith AB, Cullis BR, Thompson R, 2005. The analysis of crop cultivar breeding and evaluation trials: An overview of current mixed model approaches. J Agric Sci 143: 1-14. http://dx.doi.org/10.1017/S0021859605005587
So Y, Edwards J, 2009. A comparison of mixed-model analyses of the Iowa crop performance test for corn. Crop Sci 49: 1593-1601. http://dx.doi.org/10.2135/cropsci2008.09.0574
Spilke J, Piepho HP, Hu X, 2005. Analysis of unbalanced data by mixed linear models using the MIXED procedure of the SAS System. J Agron Crop Sci 191: 47-54. http://dx.doi.org/10.1111/j.1439-037X.2004.00120.x
Stefanova KT, Buirchell B, 2010. Multiplicative mixed models for genetic gain assessment in lupin breeding. Crop Sci 50: 880-891. http://dx.doi.org/10.2135/cropsci2009.07.0402
Welham SJ, Cullis BR, Gogel BJ, Gilmour AR, Thompson R, 2004. Prediction in linear mixed models. Aust Nz J Stat 46: 325-347. http://dx.doi.org/10.1111/j.1467-842X.2004.00334.x
Welham SJ, Gogel BJ, Smith AB, Thompson R, Cullis BR, 2010. A comparison of analysis methods for late-stage variety evaluation trials. Aust New Zeal J Stat 52: 125-149. http://dx.doi.org/10.1111/j.1467-842X.2010.00570.x
Yang RC, 2010. Towards understanding and use of mixed-model analysis of agricultural experiments. Can J Plant Sci 90: 605-627. http://dx.doi.org/10.4141/CJPS10049
© CSIC. Manuscripts published in both the printed and online versions of this Journal are the property of Consejo Superior de Investigaciones Científicas, and quoting this source is a requirement for any partial or full reproduction.
All contents of this electronic edition, except where otherwise noted, are distributed under a “Creative Commons Attribution 4.0 International” (CC BY 4.0) License. You may read here the basic information and the legal text of the license. The indication of the CC BY 4.0 License must be expressly stated in this way when necessary.
Self-archiving in repositories, personal webpages or similar, of any version other than the published by the Editor, is not allowed.