Abstract
Following the recognition of the importance of dealing with the effects of genotype-by-environment (G ×E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substantial development in the area of analytical methodology to quantify and describe these interactions. Three major areas where there have been developments are the analysis of variance, indirect selection, and pattern analysis methodologies. This has resulted in a wide range of analytical methods each with their own advocates. There is little doubt that the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form ofG ×E interactions and our ability to quantify their presence in a multi-environment experiment. However, our understanding of the environmental and physiological bases of the nature ofG ×E interactions in plant breeding has not improved commensurably with the availability of these methodologies. This may in part be due to concentration on the statistical aspects of the analytical methodologies rather than on the complementary resolution of the biological basis of the differences in genotypic adaptation observed in plant breeding experiments. There are clear relationships between many of the analytical methodologies used for studying genotypic variation andG ×E interaction in plant breeding experiments. However, from the numerous discussions on the relative merits of alternative ways of analysingG ×E interactions which can be found in the literature, these relationships do not appear to be widely appreciated. This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis methodologies, and their practical implications for the plant breeder interested in assessing the effects ofG ×E interaction on the response to selection. The variance components estimated from the combined analysis of variance can be used to judge the relative magnitude of genotypic andG ×E interaction variance. Where concern is on the effect of lack of correlation among environments, theG ×E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlation among environments. In addition, the pooled genetic correlation among all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance. WhereG ×E interaction accounts for a large proportion of the variation among genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation. Indirect selection theory can be applied to the case where the same character is measured on the same genotypes in different environments. Where there are no correlations of error effects among environments, the phenotypic correlation between environments may be used to investigate indirect response to selection. Pattern analysis (classification and ordination) methods based on standardised data can be used to summarise the relationships among environments in terms of the scope to exploit indirect selection. With the availability of this range of analytical methodology, it is now possible to investigate the results of more comprehensive experiments which attempt to understand the nature of differences in genotypic adaptation. Hence a greater focus of interest on understanding the causes of the interaction can be achieved.
Similar content being viewed by others
References
Abou-El-Fittouh HA, Rawlings JO and Miller PA (1969) Classification of environments to control genotype-by-environment interactions with an application to cotton. Crop Sci 9:135–140
Allard RW and Bradshaw AD (1964) Implications of genotypeenvironmental interactions in applied plant breeding. Crop Sci 4:503–508
Atlin GN and Frey KJ (1989) Breeding crop varieties for low-input agriculture. Am J. Alternative Agri 4:53–58
Atlin GN and Frey KJ (1990) Selecting oat lines for yield in low-productivity environments. Crop Sci 30:556–561
Baker RJ (1969) Genotype-environmerit interactions in yield of wheat. Can J Plant Sci 49:743–751
Baker RJ (1988a) Analysis of genotype-environmental interactions in crops. ISI atlas of science: animal and plant Science 1:1–4
Baker RJ (1988b) Differential response to environmental stress. In: Weir BS, Eisen EJ, Goodman MM, Namkoong G (eds) Proc 2nd Int Conf Quant Genet. Sinauer Associates, Inc, Sunderland, Massachusetts, pp 492–504
Baker RJ (1988c) Tests for crossover genotype-environmental interactions. Can J Plant Sci 68:405–410
Baker RJ (1990) Crossover genotype-environmental interaction in spring wheat. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 42–51
Basford KE, Kroonenberg PM and DeLacy IH (1991) Three-way methods for multiattribute genotype × environment data: an illustrated partial survey. Field Crops Res 27:131–157
Brennan PS and Byth DE (1979) Genotype × environmental interactions for wheat yields and selection for widely-adapted wheat genotypes. Aust J Agric Res 30:221–232
Brennan PS, Byth DE, Drake DW, DeLacy IH and Butler DG (1981) Determination of the location and number of test environments for a wheat cultivar evaluation program. Aust J Agric Res 32:189–201
Bull JK, Cooper M, DeLacy IH, Basford KE and Woodruff DR (1992) Utility of repeated checks for hierarchical classification of data from plant breeding trials. Field Crops Res 30:70–95
Burdon RD (1977) Genetic correlation as a concept for studying genotype-environment interaction in forest tree breeding. Silvae Genet 26:168–175
Burr EJ (1968) Cluster sorting with mixed character types. I. Standardization of character values. Aust Computer J 1:97–99
Burr EJ (1970) Cluster sorting with mixed character types. II. Fusion strategies. Aust Computer J 2:98–103
Byth DE, Eisemann RL and DeLacy IH (1976) Two-way pattern analysis of a large data set to evaluate genotypic adaptation. Heredity 37:215–230
Cockerham CC (1963) Estimation of genetic variances. In: Hanson WD, Robinson HF (eds) Statistical genetics and plant breeding. National Academy of Sciences — National Research Council, Publication 982, Washington, D.C., pp 53–93
Comstock RE and Moll RH (1963) Genotype-environment interactions. In: Hanson WD, Robinson HF (eds) Statistical genetics and plant breeding. National Academy of Sciences — National Research Council, Publication 982, Washington, D.C., pp 164–196
Cooper M, Byth DE, DeLacy IH and Woodruff DR (1993a) Predicting grain yield in Australian environments using data from CIMMYT international wheat performance trials. 1. Potential for exploiting correlated response to selection. Field Crops Res 32:305–322
Cooper M, DeLacy IH, Byth DE and Woodruff DR (1993b) Predicting grain yield in Australian environments using data from CIMMYT international wheat performance trials. 2. The application for classification to identify environmental relationships which exploit correlated response to selection. Field Crops Res 32:323–342
Cooper M, DeLacy IH and Eisemann RL (1993c) Recent advances in the study of genotype × environment interactions and their application to plant breeding. In: Imrie BC, Hacker JB (eds) Focused plant improvement: towards responsible and sustainable agriculture. Proc 10th Aust Plant Breeding Conf, Vol. 1. Organising Committee, Australian Convention and Travel Service, Canberra, pp 116–131
Cooper M, Byth DE and DeLacy IH (1993d) A procedure to assess the relative merit of classification strategies for grouping environments to assist selection in plant breeding regional evaluation trials. Field Crops Res 35:63–74
Crossa J (1990) Statistical analyses of multilocation trials. Adv Agron 44:55–85
Crossa J, Gauch HG and Zobel RW (1990) Additive main effects and multiplicative interaction analysis of two international maize cultivar trials. Crop Sci 30:493–500
Crossa J, Fox PN, Pfeiffer WH, Rajaram S and Gauch HG Jr (1991) AMMI adjustment for statistical analysis of an international wheat yield trial. Theor Appl Genet 81:27–37
DeLacy IH (1981) Cluster analysis for the interpretation of genotype by environment interaction. In: Byth DE, Mungomery VE (eds) Interpretation of plant response and adaptation to agricultural environments. Queensland Branch, Australian Institute of Agricultural Science, Brisbane, pp 277–292
DeLacy IH (1989) Experimental techique and control of micro-environmental variation in agricultural adaptation experiments. In: DeLacy IH (ed) Analysis of Data from Agricultural Adaptation Experiments. Australian Cooperation with the Thai/World Bank National Agricultural Project (ACNARP) Training Course, Bangkok, Thailand, pp 24–35
DeLacy IH and Cooper M (1990) Pattern analysis for the analysis of regional variety trials. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 301–334
DeLacy IH, Cooper M and Lawrence P (1990a) Pattern analysis over years of regional variety trials: relationship among sites. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 189–213
DeLacy IH, Eisemann RL and Cooper M (1990b) The importance of genotype-by-environment interaction in regional variety trials. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 287–300
Dickerson GE (1962) Implications of genetic-environmental interaction in animal breeding. Anim Prod 4:47–63
Eisemann RL, Cooper M and Woodruff DR (1990) Beyond the analytical the analytical methodology — better interpretation of genotype-by-environment interaction. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 108–117
Falconer DS (1952) The problem of environment and selection. Am Nat 86:293–298
Falconer DS (1989) Introduction to quantitative genetics, 3rd edn. Longman, London
Finlay KW and Wilkinson GN (1963) The analysis of adaptation in a plant breeding programme. Aust J Agric Res 14:742–754
Fox PN and Rosielle AA (1982) Reducing the influence of environmental main-effects on pattern analysis of plant breeding environments. Euphytica 31:645–656
Freeman GH (1973) Statistical methods for the analysis of genotype-environment interactions. Heredity 31:339–354
Freeman GH (1990) Modern statistical methods for analyzing geno-type-by-environment interactions. In: Kang MS (ed) Genotype by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 118–125
Gabriel KR (1971) The biplot-graphical display of matrices with applications to principal component analysis. Biometrica 58:453–67
Gardner CO (1963) Estimates of genetic parameters in cross-fertilizing plants and their implications in plant breeding. In: Hanson WD, Robinson HF (eds) Statistical genetics and plants breeding. National Academy of Sciences — National Research Council, Publication 982, Washington, D.C., pp 164–196
Gauch HG and Zobel RW (1988) Predictive and postdictive success of statistical analyses of yield trials. Theor Appl Genet 76:1–10
Gower JC (1966) Some distyance properties of latent root and vector methods used in multivariate analysis. Biometrika 53:325–338
Gower JC (1967) Multivariate analysis and multi-dimensional geometry. The Statistician 17:13–28
Haldane JBS (1947) The interaction of nature and nurture. Ann Eugen 13:197–205
Hill J (1975) Genotype-environment interactions — a challenge for plant breeding. J Agric Sci 85:477–493
Horner TW and Frey KJ (1957) Methods for determining natural areas for oat varietal recommendations. Agron J 49:313–315
Itoh Y and Yamada Y (1990) Relationships between genotype × environment interaction and genetic correlation of the same trait measured in different environments. Theor Appl Genet 80:11–16
Ivory DA, Kaewmeechai S, DeLacy IH and Basford KE (1991) Analysis of the environment component of genotype × environment interaction in crop adaptation evaluation. Field Crops Res 28:71–84
Kempton RA (1984) The use of bi-plots in interpreting variety by environment interactions. J Agric Sci 103:123–135
Lawn RJ and Imrie BC (1991) Crop improvement for tropical and subtropical Australia: designing plants for difficult climates. Field Crops Res 26:113–139
Lawn RJ and Imrie BC (1993) Exploiting physiological understanding in crop improvement. In: Imrie BC, Hacker JB (eds) Focused plant improvement: towards responsible and sustainable agriculture. Proc 10th Aust Plant Breeding Conf, vol. 1. Organising Committee, Australian Convention and Travel Service, Canberra, pp 136–146
Lefkovitch LP (1990) Genotype-by-environment interaction, heterogeneous variance, and significance. In: Kang MS (ed) Genotype by-environment interaction and plant Breeding. Louisiana State University, Baton Rouge, Louisiana, pp 20–27
Mirzawan PDN, Cooper M, and Hogarth DM (1993) The impact of genotype-by-environment interaction for sugar yield on the use of indirect selection in southern Queensland. Aust J Exp Agric 33:629–638
Moll RH and Stuber CW (1974) Quantitative genetics — empirical results relevant to plant breeding. Adv Agron 26:277–313
Nyquist WE (1991) Estimation of heritability and prediction of selection response in plant populations. Crit Rev Plant Sci 10:235–322
Pederson DG, Rathjen AJ (1983) The impact of site selection on breeding progress. In: Driscoll CJ (ed) Proc VIIIth Aust Plant Breeding Conf. The University of Adelaide, pp 32–37
Shaw DV (1989) Genetic parameters and selection efficiency using part-records for production traits in strawberries. Theor Appl Genet 78:560–566
Shorter R, Mungomery RE (1981) Analysis of variance of data from multi-environment trials. In: Byth DE, Mungomery VE (eds) Interpretation of plant response and adaptation to agricultural environments. Queensland Branch, Australian Institute of Agricultural Science, Brisbane, pp 12–26
Shorter R, Lawn RJ and Hammer GL (1991) Improving genetic adaptation in crops-A role for breeders, physiologists and modellers. Exp Agric 27:155–175
Ward JH (1963) Hierarchical grouping to optimise an objective function. J Am Stat Assoc 58:236–244
Westcott B (1986) Some methods of analysing genotype-environment interaction. Heredity 56:243–253
Williams WT (1976) Pattern analysis in agricultural science. Elsevier Scientific Publishing Company, Amsterdam
Wishart D (1969) An algorithm for hierarchical classification. Biometrics 22:165–170
Yamada Y (1962) Genotype-by-environment interaction and genetic correlation of the same trait under different environments. Jpn J Genet 37:498–509
Zobel RW (1990) A powerful statistical model for understanding genotype-by-environment interaction. In: Kang MS (ed) Genotype-by-environment interaction and plant breeding. Louisiana State University, Baton Rouge, Louisiana, pp 126–140
Zobel RW, Wright MJ and Gauch HG (1988) Statistical analysis of a yield trial. Agron J 80:388–393
Author information
Authors and Affiliations
Additional information
Communicated by G. Wenzel
Rights and permissions
About this article
Cite this article
Cooper, M., DeLacy, I.H. Relationships among analytical methods used to study genotypic variation and genotype-by-environment interaction in plant breeding multi-environment experiments. Theoret. Appl. Genetics 88, 561–572 (1994). https://doi.org/10.1007/BF01240919
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01240919