Skip to main content

Statistical Analyses of Genotype by Environment Data

  • Chapter
  • First Online:
Cereals

Part of the book series: Handbook of Plant Breeding ((HBPB,volume 3))

Abstract

We introduce in this chapter a series of linear and bilinear models for the study of genotype by environment interaction (GE) and adaptation. These models increasingly incorporate available genetic, physiological, and environmental information for modelling genotype by environment interaction (GE). They are based on analyses of variance and regression and can be formulated in most standard statistical packages. We use the data of a series of trials for 65 barley genotypes (G) grown in 12 environments (E) for illustration and interpretation of the output of such analyses. We aim at identifying key environmental covariables to explain differential phenotypic responses as well as to estimate genotypic sensitivities to these covariables. Using genetic covariables in the form of molecular markers, we partition genotypic main effect terms and GE terms into main effects for quantitative trait loci (QTL) and QTL by environment interaction (QTL.E). The QTL.E estimates can be further regressed on environmental covariables to target differential QTL expression potentially related to environmental factors. We believe that the statistical models that describe GE in direct association to genetic, physiological, and environmental information provide insight in GE and facilitate the development and deployment of new breeding strategies

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Annicchiarico, P. (2002) Genotype x Environment Interactions – Challenges and Opportunities for Plant Breeding and Cultivar Recommendations. Food and Agriculture Organization of the United Nations, Rome.

    Google Scholar 

  • Boer, M., Wright, D. Feng, L., Podlich, D., Luo, L., Cooper, M. and van Eeuwijk, F.A. (2007) A mixed model QTL analysis for multiple environment trial data using environmental covariables for QTLxE, with an example in maize. Genetics (in press) .

    Google Scholar 

  • Comadran, J., Russell, J.R., van Eeuwijk, F., Ceccarelli, S., Grando, S., Stanca, A.M., Francia, E., Pecchioni., N., Akar, T., Al-Yassin, A., Benbelkacem, A., Choumane, W.,Ouabbou, H., Bort, J., Araus, J.L., Pswarayi, A., Romagosa, I., Hackett, C.A. and Thomas, W.T.B. (2007) Mapping adaptation of barley to droughted environments. Euphytica doi: 10.1007/s10681-007-9508-1.

    Google Scholar 

  • Cooper, M. and Hammer, G.L. (Eds.) (1996) ‘Plant Adaptation and Crop Improvement’. CAB International, Wallingford, UK.

    Google Scholar 

  • Corsten, L.C.A. and Denis, J.B. (1990) Structuring interaction in two-way tables by clustering. Biometrics 46, 207–215.

    Article  Google Scholar 

  • Crossa, J. and Cornelius, P. (2002) Linear–bilinear models for the analysis of genotype–environment interaction. In: Kang, M.S. (Ed.) Quantitative genetics, genomics and plant breeding. pp. 305–322. CAB International, Wallingford, UK.

    Google Scholar 

  • Denis , J.B. (1988) Two-way analysis using covariates. Statistics 19, 123–132.

    Article  Google Scholar 

  • Denis, J.B. and Gower, J.C. (1996) Asymptotic confidence regions for biadditive models: interpreting genotype-environment interactions. Applied Statistics 45, 479–492.

    Article  Google Scholar 

  • Falush, D., Stephens, M., and Pritchard, J.K. (2003) Inference of population structure: Extensions to linked loci and correlated allele frequencies. Genetics, 164, 1567–1587.

    CAS  Google Scholar 

  • Falush, D., Stephens, M., and Pritchard, J.K. (2007) Inference of population structure using multilocus genotype data: dominant markers and null alleles. Molecular Ecology Notes. doi: 10.1111/j.1471-8286.2007.01758.x.

    Google Scholar 

  • Finlay, K.W. and Wilkinson, G.N. (1963) The analysis of adaptation in a plant breeding programme. Australian Journal of Agricultural Research 14, 742–754.

    Article  Google Scholar 

  • Fox, P.N., Crossa, J. and Romagosa, I. (1997) Multi-environment testing and genotype environment interaction. In: R.A. Kempton and P.N. Fox (Eds.) Statistical Methods for Plant Variety Evaluation. pp. 117–137. Chapman and Hall, London.

    Google Scholar 

  • Gabriel, K.R. (1978) Least squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society, Series B 40, 186–196.

    Google Scholar 

  • Gabriel , K.R. (1998) Generalised bilinear regression. Biometrika 85, 689–700.

    Article  Google Scholar 

  • Gabriel , K.R. and Zamir, S. (1979) Lower rank approximations of matrices by least squares with any choice of weights. Technometrics, 21, 489–498.

    Article  Google Scholar 

  • Gauch, H.G. (1988) Model selection and validation for yield trials with interaction. Biometrics, 44, 705–715.

    Article  Google Scholar 

  • Gauch, H.G. (1992) Statistical Analysis of Regional Yield Trials. Elsevier, Amsterdam.

    Google Scholar 

  • Gauch, H.G. (2006) Statistical Analysis of Yield Trials by AMMI and GGE. Crop Science, 46, 1488–1500.

    Article  Google Scholar 

  • Gollob, H.F. (1968) A statistical model which combines features of factor analysis and analysis of variance techniques. Psychometrika, 33, 73–115.

    Article  CAS  Google Scholar 

  • Kang, M.S. (Ed.). (1990) Genotype-By-Environment Interaction and Plant Breeding. Louisiana State University, Baton Rouge, Louisiana.

    Google Scholar 

  • Kang, M.S. (1998) Using genotype-by-environment interaction for crop cultivar development. Advances in Agronomy, 62, 199–252.

    Article  Google Scholar 

  • Kang, M.S. and Gauch, H.G. (1996) Genotype by Environment Interaction: New Perspectives. CRC Press, Boca Raton, FL.

    Google Scholar 

  • Kempton, R.A. (1984) The use of biplots in interpreting variety by environment interactions Journal of Agricultural, 103, 123–135.

    Article  Google Scholar 

  • Kempton, R.A. and Fox, P.N. (1997) Statistical Methods for Plant Variety Evaluation. Chapman and Hall, London.

    Google Scholar 

  • Kleinhofs, A. and Han, F. (2002) Molecular Mapping of the Barley Genome. In: Slafer G.A., Molina-Cano, J.L., Savin, R., Araus, J.L. and Romagosa, I. (Eds.) Barley Science: Recent Advances from Molecular Biology to Agronomy of Yield and Quality. pp. 31–63. Haworth Pres, Binghamton, NY.

    Google Scholar 

  • Kleinhofs, A., Kudrna, D.A. and Matthews, D. (1998) Co-ordinators report: Integrating barley molecular and morphological/physiological marker maps. Barley Genetics Newsletter, 28, 89–91.

    Google Scholar 

  • Li, J. and Ji, L. (2005) Adjusting multiple testing in multilocus analyses using the eigenvalues of a correlation matrix. Heredity, 95, 221–227.

    Article  CAS  Google Scholar 

  • Lynch, M. and Walsh, J.B. (1998) ‘Genetics and analysis of quantitative traits’. Sinauer Associates, Sunderland, Massachusetts.

    Google Scholar 

  • Malosetti, M., Voltas, J., Romagosa, I., Ullrich, S.E. and van Eeuwijk, F.A. (2004) Mixed models including environmental variables for studying QTL by environment interaction. Euphytica, 137, 139–145.

    Article  CAS  Google Scholar 

  • Mandel , J. (1969) The partitioning of interaction in analysis of variance. J Res NBS 73B, 309–328.

    Google Scholar 

  • Paterson, A.H. (Ed.) (1998) Molecular Dissection of Complex Traits. CRC Press., Boca Raton, FL.

    Google Scholar 

  • Payne, R.W., Harding, S.A., Murray, D.A., Soutar, D.M., Baird, D.B., Welham, S.J., Kane, A.F., Gilmour, A.R., Thompson, R., Webster, R., Tunnicliffe, E., Wilson, G. (2006) GenStat release 9 reference manual, part 2 directives. VSN International, Hemel Hempstead, UK.

    Google Scholar 

  • Piepho, H.P. (1997) Analyzing genotype-environment data by mixed models with multiplicative effects. Biometrics 53, 761–766.

    Article  Google Scholar 

  • Piepho, H.P. (2000) A mixed model approach to mapping quantitative trait loci in barley on the basis of multiple environment data. Genetics 156, 2043–2050.

    PubMed  CAS  Google Scholar 

  • Piepho, H.P. and Pillen, K. (2004) Mixed modeling for QTL x environment interaction analysis. Euphytica 137, 147–153.

    Article  CAS  Google Scholar 

  • Pritchard, J. K., Stephens, M. and Donnelly, P. (2000) Inference of population structure using multilocus genotype data. Genetics 155, 945–959.

    PubMed  CAS  Google Scholar 

  • Pswarayi , A., van Eeuwijk, F., Ceccarelli, S., Grando, S., Comadran, J., Russell, J.R., Stanca, A.M., Francia, E., Pecchioni, N., Akar, T., Al-Yassin, A., Benbelkacem, A., Choumane, W., Karrou, M., Ouabbou, H., Bort, J., Araus, J.L., Molina-Cano, J.L., Thomas, W.T.B., and Romagosa, I. Barley adaptation and improvement in the Mediterranean basin. Submitted for publication.

    Google Scholar 

  • Romagosa, I. and Fox, P.N. (1993) Genotype-environment interaction and adaptation. In: Hayward, M.D., Bosemark, N.O., and Romagosa, I. (Eds.) Plant Breeding, Principles and Prospects. Pp. 373–390. Chapman and Hall, London

    Google Scholar 

  • Russell, J., Booth. A., Fuller, J., Harrower, B., Hedley, P., Machray, G., andPowell, W. (2004) A comparison of sequence-based polymorphism and haplotype content in transcribed and anonymous regions of the barley genome. Genome 47, 389–398.

    Article  PubMed  CAS  Google Scholar 

  • Slafer, G.A., Molina-Cano, J.L., Savin, R., Araus, J.L. and Romagosa, I. (Eds.) (2002) Barley Science: Recent Advances from Molecular Biology to Agronomy of Yield and Quality. Haworth Press, Binghamton, NY.

    Google Scholar 

  • Smith, A.B. (1999) Multiplicative mixed models for the analysis of multi-environment trial data. PhD thesis, Dpt of Statistics, University of Adelaide, South Australia.

    Google Scholar 

  • Smith, A.B., Cullis, B.R. and Thompson, R. (2005) The analysis of crop cultivar breeding and evaluation trials: an overview of current mixed model approaches; Journal of Agricultural Science Cambridge 143, 1–14.

    Article  Google Scholar 

  • Spiertz, J.H.J., Struik, P.C. and van Laar, H.H. (Eds.) (2007) Scale and Complexity in Plant Systems Research. Gene-Plant-Crop relations. Wageningen UR Frontier Series. Vol 21. Springer .

    Google Scholar 

  • van Eeuwijk, F.A. (1995a) Linear and bilinear models for the analysis of multi-environment trials: I An inventory of models. Euphytica 84, 1–7.

    Article  Google Scholar 

  • van Eeuwijk, F.A. (1995b) Multiplicative interaction in generalized linear models. Biometrics 51, 1017–1032.

    Article  Google Scholar 

  • van Eeuwijk, F.A. (1996) Between and Beyond Additivity and Non-Additivity: the Statistical Modelling of Genotype by Environment Interaction in Plant Breeding. PhD Thesis. Wageningen, The Netherlands.

    Google Scholar 

  • van Eeuwijk, F.A. (2006) Genotype by environment interaction: basics and beyond. In: Lamkey, K. and Lee, M. (Ed.) Plant Breeding: The Arnell Hallauer International Symposium, pp. 155–170. Blackwell Publishing, Oxford.

    Google Scholar 

  • van Eeuwijk, F.A. Crossa, J., Vargas, M. and Ribaut, J.M. (2001) Variants of factorial regression for analysing QTL by environment interaction. In: Gallais, A., Dillmann, C. and Goldringer, I. (Eds.) ‘Eucarpia, Quantitative Genetics and Breeding Methods: the way Ahead’. pp. 107–116. INRA Editions Versailles Les Colloques series 96.

    Google Scholar 

  • van Eeuwijk, F.A., Crossa, J., Vargas, M. and Ribaut, J.M. (2002) Analysing QTL by environment interaction by factorial regression, with an application to the CIMMYT drought and low nitrogen stress programme in maize. In: Kang, M.S. (Ed.) ‘Quantitative Genetics, Genomics and Plant Breeding’. pp. 245–256. CAB International, Wallingford, UK.

    Google Scholar 

  • van Eeuwijk, F.A., Denis, J.B. and Kang, M.S. (1996) Incorporating additional information on genotypes and environments in models for two-way genotype by environment tables. In Kang, M.S. and Gauch H.G. (Eds.) ‘Genotype-by-Environment Interaction’. pp. 15–50. CRC Press, Boca Raton, FL.

    Google Scholar 

  • van Eeuwijk, F.A., Keizer, L.C.P. and Bakker, J.J. (1995) Linear and bilinear models for the analysis of multi-environment trials. II. An application to data from the Dutch Maize Variety Trials. Euphytica 84, 9–22.

    Article  Google Scholar 

  • van Eeuwijk, F.A., Malosetti, M., Yin, X., Struik, P.C. and Stam, P. (2005) Statistical models for genotype by environment data; From conventional ANOVA models to eco-physiological QTL models. Australian Journal of Agricultural Research 56, 883–894.

    Article  Google Scholar 

  • van Eeuwijk, F.A., Malosetti, M. and Boer, M.P. (2007) Modelling The Genetic Basis Of Response Curves Underlying Genotype By Environment Interaction. In: Spiertz, J.H.J., Struik, P.C. and van Laar, H.H. (Eds.) Scale and Complexity in Plant Systems Research. Gene-Plant-Crop relations. Wageningen UR Frontier Series. Vol 21. Springer .

    Google Scholar 

  • Vargas, M., Crossa, J., van Eeuwijk, F.A., Ramírez, M.E. and Sayre, K. (1999) Using AMMI, factorial regression, and partial least squares regression models for interpreting genotype x environment interaction. Crop Science 39, 955–967.

    Article  Google Scholar 

  • Verbyla, A., Eckermann, P.J., Thompson, R. and Cullis, B. (2003) The analysis of quantitative trait loci in multienvironment trials using a multiplicative mixed model. Australian Journal of Agricultural Research 54, 1395–1408.

    Article  CAS  Google Scholar 

  • Voltas, J., van Eeuwijk, F., Igartua, E., Garcia del Moral, L.F., Molina-Cano, J.L. and Romagosa, I. (2002) Genotype by Environment Interaction and Adaptation in Barley Breeding: Basic Concepts and Methods of Analysis. In: Slafer G.A., Molina-Cano, J.L., Savin, R., Araus, J.L. and Romagosa, I. (Eds.) Barley Science: Recent Advances from Molecular Biology to Agronomy of Yield and Quality. pp. 205–241. Haworth Pres. Binghamton, NY.

    Google Scholar 

  • Voltas J., van Eeuwijk, F.A., Sombrero, A., Lafarga, A., Igartua, E. and Romagosa, I (1999a) Integrating statistical and ecophysiological analysis of genotype by environment interaction for grain filling of barley in Mediterranean areas I. Individual grain weight. Field Crops Research 62, 63–74.

    Article  Google Scholar 

  • Voltas, J., van Eeuwijk, F.A., Araus, J.L. and Romagosa, I. (1999b) Integrating statistical and ecophysiological analysis of genotype by environment interaction for grain filling of barley in Mediterranean areas II. Grain growth. Field Crops Research 62, 75–84.

    Article  Google Scholar 

  • Wenzl, P., Li, H., Carling, J., Zhou, M., Raman, H., Paul, E., Hearnden, P., Maier, C., Xia, L., Caig, V., Ovesná, J., Cakir, M., Poulsen, D., Wang, J., Raman, R., Smith, K.P, Muehlbauer, G.P, Chalmers, K.J., Kleinhofs, A., Huttner, E. andKilian, A. (2006)A high-density consensus map of barley linking DArT markers to SSR, RFLP and STS loci and agricultural traits. BMC Genomics 7, 206.

    Article  PubMed  Google Scholar 

  • Yan, W. and Kang, M.S. (2003) GGE Biplot Analysis: A Graphical Tool for Breeders, Geneticists, and Agronomists. CRC Press. Boca Raton, FL.

    Google Scholar 

  • Yan, W., Cornelius, P.L., Crossa, J. and Hunt, L.A. (2001) Two Types of GGE Biplots for Analyzing Multi-Environment Trial Data. Crop Science 41:656–663.

    Article  Google Scholar 

  • Yan, W., Hunt. L.A., Sheng, Q. and Szlavnics, Z. (2000) Cultivar evaluation and mega-environment investigation based on the GGE biplot. Crop Science 40, 597–605.

    Article  Google Scholar 

  • Yan, W., Kang, M.S., Baoluo Ma B, Woods, S. and Cornelius, P.L. (2007) GGE Biplot vs. AMMI Analysis of Genotype-by-Environment Data. Crop Science 47, 643–653.

    Article  Google Scholar 

Download references

Acknowledgements

Contribution of the other partners of the EU FP5 INCO-MED project ‘Mapping Adaptation of Barley to Droughted Environments’ in assembling this data set is highly appreciated, namely, Salvatore Ceccarelli and Stefania Grando from ICARDA, Syria; Michele Stanca from the Istituto Sperimentale per la Cerealicoltura, Italy; José Luis Molina-Cano and Alexander Pswarayi from the Centre UdL-IRTA, Spain; Tanner Akar from the Central Research for Field Crops, Turkey; Adnan Al-Yassin from NCARTT, Jordan; Abdelkader Benbelkacem from ITGC, Algeria; Mohammed Karrou and Hassan Ouabbou from INRA, Morocco; Nicola Pecchioni and Enrico Francia from the Università di Modena e Reggio Emilia, Italy; Wafaa Choumane from Tishreen University, Latakia, Syria; and Jordi Bort and José Luis Araus from the University of Barcelona. We also want to express our gratitude to Jordi Comadran, Joanne Russell from SCRI for providing the marker data used for association mapping and to Christine Hackett from BioSS for fruitful statistical discussions. The above work was funded by the European Union-INCO-MED program (ICA3-CT2002-10026). The Centre UdL-IRTA acknowledges partial funding from grant AGL2005-07195-C02-02 from the Spanish Ministry of Science and Education.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ignacio Romagosa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science + Business Media, LLC

About this chapter

Cite this chapter

Romagosa, I., Eeuwijk, F., Thomas, W. (2009). Statistical Analyses of Genotype by Environment Data. In: Carena, M. (eds) Cereals. Handbook of Plant Breeding, vol 3. Springer, New York, NY. https://doi.org/10.1007/978-0-387-72297-9_10

Download citation

Publish with us

Policies and ethics