Statistical models for genotype by environment data: from conventional ANOVA models to eco-physiological QTL models
Fred A. van Eeuwijk A C , Marcos Malosetti A , Xinyou Yin B , Paul C. Struik B and Piet Stam AA Laboratory of Plant Breeding, Wageningen University, PO Box 386, 6700 AJ Wageningen, The Netherlands.
B Crop and Weed Ecology Group, Wageningen University, PO Box 430, 6700 AK Wageningen, The Netherlands.
C Corresponding author. Email: fred.vaneeuwijk@wur.nl
Australian Journal of Agricultural Research 56(9) 883-894 https://doi.org/10.1071/AR05153
Submitted: 9 May 2005 Accepted: 27 June 2005 Published: 28 September 2005
Abstract
To study the performance of genotypes under different growing conditions, plant breeders evaluate their germplasm in multi-environment trials. These trials produce genotype × environment data. We present statistical models for the analysis of such data that differ in the extent to which additional genetic, physiological, and environmental information is incorporated into the model formulation. The simplest model in our exposition is the additive 2-way analysis of variance model, without genotype × environment interaction, and with parameters whose interpretation depends strongly on the set of included genotypes and environments. The most complicated model is a synthesis of a multiple quantitative trait locus (QTL) model and an eco-physiological model to describe a collection of genotypic response curves. Between those extremes, we discuss linear-bilinear models, whose parameters can only indirectly be related to genetic and physiological information, and factorial regression models that allow direct incorporation of explicit genetic, physiological, and environmental covariables on the levels of the genotypic and environmental factors. Factorial regression models are also very suitable for the modelling of QTL main effects and QTL × environment interaction. Our conclusion is that statistical and physiological models can be fruitfully combined for the study of genotype × environment interaction.
Additional keywords: AMMI-model, crop growth model, factorial regression, genotype by environment interaction, multi-environment trial, QTL by environment interaction.
Acknowledgments
An earlier version of this paper was published in the Proceedings of the 4th International Crop Science Congress, held in Brisbane, 26 September to 1 October 2004. We thank the Congress organisers for permission to publish this updated manuscript.
Boer MP,
ter Braak CJF, Jansen RC
(2002) A penalized likelihood method for mapping epistatic quantitative trait loci with one-dimensional genome searches. Genetics 162, 951–960.
| PubMed |
Chapman SC,
Cooper M,
Butler DG, Henzell RG
(2000a) Genotype by environment interactions affecting grain sorghum. I. Characteristics that confound interpretation of hybrid yield. Australian Journal of Agricultural Research 51, 197–207.
| Crossref | GoogleScholarGoogle Scholar |
Chapman SC,
Cooper M, Hammer GL
(2002) Using crop simulation to generate genotype by environment interaction effects for sorghum in water-limited environments. Australian Journal of Agricultural Research 53, 379–389.
| Crossref | GoogleScholarGoogle Scholar |
Chapman SC,
Cooper M,
Hammer GL, Butler DG
(2000b) Genotype by environment interactions affecting grain sorghum. II. Frequencies of different seasonal patterns of drought stress are related to location effects on hybrid yields. Australian Journal of Agricultural Research 51, 209–221.
| Crossref | GoogleScholarGoogle Scholar |
Chapman SC,
Cooper M,
Podlich D, Hammer GL
(2003) Evaluating plant breeding strategies by simulating gene action and dryland environment effects. Agronomy Journal 95, 99–113.
Chapman SC,
Hammer GL,
Butler DG, Cooper M
(2000c) Genotype by environment interactions affecting grain sorghum. III. Temporal sequences and spatial patterns in the target population of environments. Australian Journal of Agricultural Research 51, 223–233.
| Crossref | GoogleScholarGoogle Scholar |
Comstock RE
(1977) Quantitative genetics and the design of breeding programs. ‘Proceedings of the International Conference on Quantitative Genetics’. 16–21 August 1976. (Iowa State University Press: Ames, IA)
Cooper M,
Chapman SC,
Podlich DW, Hammer GL
(2002a) The GP problem: Quantifying gene-to-phenotype relationships. In Silico Biology 2, 151–164.
| PubMed |
Cooper, M ,
and
Hammer, GL (Eds) (1996).
Cooper M, Podlich DW, Micallef KP, Smith OS, Jensen NM, Chapman SC, Kruger NL
(2002) Complexity, quantitative traits and plant breeding: a role for simulation modelling in the genetic improvement of crops. ‘Quantitative genetics, genomics and plant breeding’. (Ed. MS Kang)
pp. 143–166. (CAB International: Wallingford, UK)
Cooper M,
Podlich DW, Smith OS
(2005) Gene-to-phenotype models and complex trait genetics. Australian Journal of Agricultural Research 56, 895–918.
Crossa J, Cornelius P
(2002) Linear–bilinear models for the analysis of genotype–environment interaction. In ‘Quantitative genetics, genomics and plant breeding’. (Ed. MS Kang)
pp. 305–322. (CAB International: Wallingford, UK)
Denis J-B
(1988) Two-way analysis using covariates. Statistics 19, 123–132.
Denis J-B, Gower JC
(1996) Asymptotic confidence regions for biadditive models: interpreting genotype-environment interactions. Applied Statistics 45, 479–492.
Edwards, D (2000).
van Eeuwijk FA
(1995a) Linear and bilinear models for the analysis of multi-environment trials: I An inventory of models. Euphytica 84, 1–7.
| Crossref | GoogleScholarGoogle Scholar |
van Eeuwijk FA
(1995b) Multiplicative interaction in generalized linear models. Biometrics 51, 1017–1032.
van Eeuwijk FA,
Cooper M,
DeLacy IH,
Ceccarelli S, Grando S
(2001a) Some vocabulary and grammar for the analysis of multi-environment trials, as applied to the analysis of FPB and PPB trials. Euphytica 122, 477–490.
| Crossref | GoogleScholarGoogle Scholar |
van Eeuwijk FA, Crossa J, Vargas M, Ribaut JM
(2001) Variants of factorial regression for analysing QTL by environment interaction. ‘Eucarpia, quantitative genetics and breeding methods: the way ahead’. Les colloques series 96. (Eds A Gallais, C Dillmann, I Goldringer)
pp. 107–116. (INRA Editions: Versailles, France)
van Eeuwijk FA, Crossa J, Vargas M, 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. ‘Quantitative genetics, genomics and plant breeding’. (Ed. MS Kang)
pp. 245–256. (CAB International: Wallingford, UK)
van Eeuwijk FA, Denis J-B, Kang MS
(1996) Incorporating additional information on genotypes and environments in models for two-way genotype by environment tables. ‘Genotype-by-environment interaction’. (Eds MS Kang, HG Gauch)
pp. 15–50. (CRC Press: Boca Raton, FL)
Finlay KW, Wilkinson GN
(1963) The analysis of adaptation in a plant breeding programme. Australian Journal of Agricultural Research 14, 742–754.
| Crossref | GoogleScholarGoogle Scholar |
Gabriel KR
(1978) Least squares approximation of matrices by additive and multiplicative models. Journal of the Royal Statistical Society: Series B 40, 186–196.
Gabriel KR
(1998) Generalised bilinear regression. Biometrika 85, 689–700.
| Crossref | GoogleScholarGoogle Scholar |
Gabriel KR, Zamir S
(1979) Lower rank approximations of matrices by least squares with any choice of weights. Technometrics 21, 489–498.
Gauch HG
(1988) Model selection and validation for yield trials with interaction. Biometrics 44, 705–715.
Gollob HF
(1968) A statistical model which combines features of factor analysis and analysis of variance techniques. Psychometrika 33, 73–115.
| PubMed |
Haley CS, Knott SA
(1992) A simple regression method for mapping quantitative trait loci in line crosses using flanking markers. Heredity 69, 315–324.
Hammer GL,
Chapman SC,
van Oosterom E, Podlich DW
(2005) Trait physiology and crop modelling as a framework to link phenotypic complexity to underlying genetic systems. Australian Journal of Agricultural Research 56, 947–960.
Jiang C, Zeng Z-B
(1997) Mapping quantitative trait loci with dominant and missing markers in various crosses from two inbred lines. Genetica 101, 47–58.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Kraakman ATW,
Niks RE,
van den Berg PMMM,
Stam P, van Eeuwijk FA
(2004) Linkage disequilibrium mapping of yield and yield stability in modern spring barley cultivars. Genetics 168, 435–446.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Lynch, M ,
and
Walsh, JB (1998).
Ma CX,
Casella G, Wu R
(2002) Functional mapping of quantitative trait loci underlying the character process: a theoretical framework. Genetics 161, 1751–1762.
| PubMed |
Malosetti M,
Voltas J,
Romagosa I,
Ullrich SE, van Eeuwijk FA
(2004) Mixed models including environmental variables for studying QTL by environment interaction. Euphytica 137, 139–145.
| Crossref | GoogleScholarGoogle Scholar |
Mandel J
(1969) The partitioning of interaction in analysis of variance. Journal of Research – National Bureau of Standards, Mathematical Sciences 73B, 309–328.
Piepho HP
(2000) A mixed model approach to mapping quantitative trait loci in barley on the basis of multiple environment data. Genetics 156, 2043–2050.
| PubMed |
Piepho HP, Pillen K
(2004) Mixed modelling for QTL × environment interaction analysis. Euphytica 137, 147–153.
| Crossref | GoogleScholarGoogle Scholar |
Reymond M,
Muller B,
Leonardi A,
Charcosset A, Tardieu F
(2003) Combining QTL analysis and an ecophysiological model to analyse the genetic variability of the responses of maize leaf growth to temperature and water deficit. Plant Physiology 131, 664–675.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Schabensberger, O ,
and
Pierce, FJ (2002).
Smith AB
(1999) Multiplicative mixed models for the analysis of multi-environment trial data. PhD thesis, Dept of Statistics, University of Adelaide, South Australia.
Tardieu F,
Reymond M,
Muller B,
Granier C,
Simonneau T,
Sadok W, Welcker C
(2005) Linking physiological and genetic analyses of the control of leaf growth under changing environmental conditions. Australian Journal of Agricultural Research 56, 937–946.
Vargas M,
Crossa J,
van Eeuwijk FA,
Ramírez ME, Sayre K
(1999) Using AMMI, factorial regression, and partial least squares regression models for interpreting genotype × environment interaction. Crop Science 39, 955–967.
Verbyla AP,
Eckermann PJ,
Thompson R, Cullis B
(2003) The analysis of quantitative trait loci in multi-environment trials using a multiplicative mixed model. Australian Journal of Agricultural Research 54, 1395–1408.
| Crossref | GoogleScholarGoogle Scholar |
Voltas J,
van Eeuwijk FA,
Araus JL, 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.
| Crossref | GoogleScholarGoogle Scholar |
Voltas J,
van Eeuwijk FA,
Sombrero A,
Lafarga A,
Igartua E, 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.
| Crossref | GoogleScholarGoogle Scholar |
Walsh B
(2005) The struggle to exploit non-additive variation. Australian Journal of Agricultural Research 56, 873–881.
Welch SM,
Dong Z,
Roe JL, Das S
(2005) Flowering time control: gene network modelling and the link to quantitative genetics. Australian Journal of Agricultural Research 56, 919–936.
Wu W,
Zhou Y,
Li W,
Mao D, Chen Q
(2002) Mapping of quantitative trait loci based on growth models. Theoretical and Applied Genetics 105, 1043–1049.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Yin X,
Chasalow S,
Dourleijn CJ,
Stam P, Kropff MJ
(2000) Coupling estimated effects of QTLs for physiological traits to a crop growth model: predicting yield variation among recombinant inbred lines in barley. Heredity 85, 539–549.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Yin, X ,
and
van Laar, HH (2005).
Yin X,
Struik PC,
van Eeuwijk FA,
Stam P, Tang J
(2005) QTL analysis and QTL-based prediction of flowering phenology in recombinant inbred lines of barley. Journal of Experimental Botany 56, 967–976.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
Yin X,
Struik PC, Kropff MJ
(2004) Role of crop physiology in predicting gene-to-phenotype relationships. Trends in Plant Science 9, 426–432.
| Crossref | GoogleScholarGoogle Scholar | PubMed |
