Methods of analysing genotype-environment interaction were extensively reviewed by Freeman (1973) and Hill (1975). A large number of papers involving such analyses have been published since then, some of them providing new methods, particularly of the multivariate type.
While making no pretensions to be a comprehensive review, the present paper attempts an examination of some of these new techniques. It also offers a critique of some established methods, while pointing out others which have been neglected. The methods considered include the linear regression approach and related stability parameters, cluster analysis, principal components analysis, geometrical methods and stochastic dominance.
In all these methods, environments are measured by the mean value of the genotypes grown in them: a case is made for research into the use of environmental variables
Abou-El-Fittouh, H A, Rawling, J O, and Miller, P A. 1969. Classification of environments to control genotype by environment interactions with an application to cotton. Crop Science, 9, 135–140.
Anderson, E. 1960. A semigraphical method for the analysis of complex problems. Technometrics, 2, 87–391.
Anderson, J R. 1974. Risk-efficiency in the interpretation of agricultural production research. Review of Marketing and Agricultural Economics, 42, 131–184.
Anderson, J R, Dillon, J L, and Hardaker, J B. 1977. Agricultural Decision Analysis. Iowa State University Press, Ames.
Arnold, M H. 1972. Modal selection in BP52. Cotton Growing Review, 49, 107–125.
Baker, R J. 1969. Genotype-environment interactions in yields of wheat. Canadian Journal of Plant Science, 49, 743–751.
Basford, K E. 1982. The use of multidimensional scaling in analysing multi-attribute genotype response across environments. Australian Journal of Agricultural Research, 33, 473–480.
Beckett, J L. 1982. Variety x environment interactions in sugar beet variety trials. Journal of Agricultural Science, 98, 425–435.
Berk, K N. 1978. Comparing subset regression procedures. Technometrics, 20, 1–6.
Byth, D E, Eisemann, R L, and De Lacy, I H. 1976. Two-way pattern analysis of a large data set to evaluate genotype adaptation. Heredity, 37, 189–201.
Campbell, L G, and Lafever, H N. 1977. CultivarX environment interactions in soft red winter wheat yield tests. Crop Science, 17, 604–608.
Carroll, J D, and Chang, J-J. 1970. Analysis of individual differences in multidimensional scaling via an n-way generalisation of Eckart-Young decomposition. Psychometrika, 35, 283–319.
Cormack, R M. 1971. A review of classification (with discussion). Journal of the Royal Statistical Society, A 134, 321–367.
Daniel, C, and Wood, F S. 1980. Fitting Equations to Data. Second Edition. Wiley, New York.
Easton, H S, and Clements, R J. 1973. The interaction of wheat genotypes with a specific factor of the environment. Journal of Agricultural Science, 80, 43–52.
Eberhart, S A, and Russell, W A. 1966. Stability parameters for comparing varieties. Crop Science, 6, 36–40.
Eckart, C, and Young, G. 1936. The approximation of one matrix by another of lower rank. Psychometrika, 1, 211–218.
Feyerherm, A M, and Paulsen, G M. 1981. Development of a wheat yield prediction model. Agronomy Journal, 73, 277–282.
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.
Fox, P N, and Rosielle, A A. 1982. Reducing the influence of environmental main effects on pattern analysis of plant breeding environments. Euphytica, 31, 645–656.
Freeman, G H. 1973. Statistical methods for the analysis of genotype-environment interactions. Heredity, 31, 339–354.
Freeman, G H, and Dowker, B D. 1973. The analysis of variation between and within genotypes and environments. Heredity, 30, 97–109.
Freeman, G H, and Perkins, J M. 1971. Environmental and genotype-environmental components of variability. VIII. Relations between genotypes grown in different environments and measures of these environments. Heredity, 27, 15–23.
Gabriel, K R. 1971. Biplot display of multivariate matrices with application to principal component analysis. Biometrika, 58, 453–467.
Ghaderi, A, Adams, M W, and Saettler, A W. 1982. Environmental response patterns in commercial classes of common bean (Phaseolus vulgaris L.). Theoretical and Applied Genetics, 63, 17–22.
Ghaderi, A, Everson, E H, and Cress, C E. 1980. Classification of environments and genotypes in wheat. Crop Science, 20, 707–710.
Gnanadesikan, R. 1977. Methods for Statistical Data Analysis of Multivariate Observations. Wiley, New York.
Goodchild, N A, and Boyd, W J R. 1975. Regional and temporal variations in wheat yield in Western Australia and their implications in plant breeding. Australian Journal of Agricultural Research, 26, 209–217.
Gordon, A D. 1981. Classification. Chapman and Hall, London.
Gower, J C. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.
Gower, J C. 1975. Generalized procrustes analysis. Psychometrika, 40, 33–51.
Gower, J C, and Ross, G J S. 1969. Minimum spanning trees and single linkage cluster analysis. Applied Statistics, 18, 54–64.
Hamblin, J, Fisher, H M, and Ridings, H I. 1980. The choice of locality for plant breeding when selecting for high yield and general adaptation. Euphytica, 29, 161–168.
Hanson, W D. 1970. Genotypic stability. Theoretical and Applied Genetics, 40, 226–231.
Hardwick, R C, and Wood, J T. 1972. Regression methods for studying genotype-environment interactions. Heredity, 28, 290–222.
Haun, J R. 1982. Early prediction of corn yields from daily weather data and single predetermined seasonal constants. Agricultural Meteorology, 27, 191–207.
Hill, J. 1975. genotype-environment interactions—a challenge for plant breeding. Journal of Agricultural Science, 85, 477–493.
Hill, J, and Goodchild, N A. 1981. Analysing environments for plant breeding purposes as exemplified by multivariate analysis of long term wheat yields. Theoretical and Applied Genetics, 59, 317–325.
Hill, M O. 1974. Correspondence analysis: a neglected multi-variate method. Applied Statistics, 23, 340–354.
Johnson, G R. 1977. Analysis of genotypic similarity in terms of mean yield and stability of environmental response in a set of maize hybrids. Crop Science, 17, 837–842.
Jones, H G. 1979. Effects of weather on spring barley yields in Britain. Journal of the National Institute of Agricultural Botany, 15, 24–33.
Kempton, R A. 1984. The use of biplots in interpreting variety by environment interactions. Journal of Agricultural Science, 103, 123–135.
Knight, R. 1970. The measurement and interpretation of genotype-environment interactions. Euphytica, 19, 225–235.
Lance, G N, and Williams, W T. 1967. A general theory of classificatory sorting strategies. I. Hierarchical systems. Computer Journal, 9, 373–380.
Lin, C S. 1982. Grouping genotypes by a cluster method directly related to genotype-environment interaction mean square. Theoretical and Applied Genetics, 62, 277–280.
Lin, C S, and Thompson, B. 1975. An empirical method of grouping genotypes based on a linear function of the genotype-environment interaction. Heredity, 34, 255–263.
Mandel, J. 1959. The measuring process. Technometrics, 1, 251–267.
Mandel, J. 1961. Non-additivity in two-way analysis of vari-ance. Journal of the American Statistical Association, 56, 878–888.
Mandel, J. 1971. A new analysis of variance model for non-additive data. Technometrics, 13, 1–18.
Mandel, J, and Lashof, T W. 1959. The interlaboratory evaluation of testing methods. Bulletin of the American Society for Testing Materials, 239, 53–61.
Menz, K M. 1980. A comparative analysis of wheat adaptation across international environments using stochastic dominance and pattern analysis. Field Crops Research, 3, 33–41.
Miller, A J. 1984. Selection of subsets of regression variables (with discussion). Journal of the Royal Statistical Society, A 147, 389–425.
Mooers, C A. 1921. The agronomic placement of varieties. Journal of the American Society of Agronomy, 13, 337–352.
Mungomery, V E, Shorter, R, and Byth, D E. 1974. Genotype x environment interactions and environmental adaptation. I. Pattern analysis-application to soya bean populations. Australian Journal of Agricultural Research, 25, 59–72.
Patterson, H D, and Silvey, V. 1980. Statutory and recommended list trials of crop varieties in the United Kingdon (with discussion). Journal of the Royal Statistical Society, A 143, 219–252.
Pederson, D G, and Rathjen, A J. 1981. Choosing trial sites to maximize selection response for grain yield in spring wheat. Australian Journal of Agricultural Research, 32, 411–424.
Perkins, J M, and Jinks, J L. 1968. Environmental and genotype-environmental components of variability. IV. Non-linear interactions for multiple inbred lines. Heredity, 23, 525–535.
Plaisted, R L, and Peterson, L C. 1959. A technique for evaluating the ability of selections to yield consistently in different locations or seasons. American Potato Journal, 36, 381–385.
Ramey, T B, and Rosielle, A A. 1983. H ASS cluster analysis: a new method of grouping genotypes or environments in plant breeding. Theoretical and Applied Genetics, 66, 131–133.
Scheffe, H. 1959. The analysis of variance. Wiley, New York.
Schoenberg, I J. 1935. Remarks to Maurice Frechet's article 'Sur la définition axiomatique d'une classe d'espace distancies vectoriellement applicable sur l'espace d'Hilbert'. Annals of Mathematics (2nd Series), 36, 724–732.
Shorter, R, Byth, D E, and Mungomery, V E. 1977. Genotype x environment interactions and environmental adaptation. II. Assessment of environment contributions. Australian Journal of Agricultural Research, 28, 223–235.
Silvey, V. 1982. Analysis of crop variety adaptation from performance trials in England and Wales. In Proceedings of the XIth International Biometric Conference, pp. 157–163, Toulouse.
Sokal, R R, and Michener, C D. 1958. A statistical model for evaluating systematic relationships. University of Kansas Science Bulletin, 38, 1409–1438.
St-Pierre, C A, Klinck, H R, and Gauthier, F M. 1967. Early generation selection under different environments as it influences adaptation of barley. Canadian Journal of Plant Science, 47, 507–517.
Tai, G C C. 1971. Genotypic stability analysis and its application to potato regional trials. Crop Science, 11, 184–190.
Takane, Y, Young, F W, and De Leeuw, J. 1977. Nonmetric individual differences multidimensional scaling: an alternating least squares method with optimal scaling features. Psychometrika, 42, 7–67.
Ten Berge, J M F. 1977. Orthogonal procrustes rotation for two or more matrices. Psychometrika, 42, 267–276.
Torgerson, W S. 1952. Multidimensional scaling. I. Theory and method. Psychometrika, 17, 401–419.
Tukey, J W. 1949. One degree of freedom for non-additivity. Biometrics, 5, 232–242.
Weisberg, S. 1980. Applied Linear Regression. Wiley, New York.
Williams, E J. 1952. The interpretation of interactions in factorial experiments. Biometrika, 39, 65–81.
Witcombe, J R, and Whittington, W J. 1971. A Study of the genotype by environmental interaction shown by germinating seeds of Brassica napus. Heredity, 26, 397–411.
Wood, J T. 1976. The use of environmental variables in the interpretation of genotype-environment interaction. Heredity, 37, 1–7.
Wricke, G. 1962. Uber eine methode zur erfassung der ökologischen streubreite in feldversuchen. Zeitschrift für Pflanzenzüchtung, 47, 92–96.
Wricke, G. 1964. Zur berechnung der ökovalenz bei sommer-weizen und hafer. Zeitschrift für Pflanzenzüchtung, 52, 127–138.
Wright, A J. 1976. The significance for breeding of linear regression analysis of genotype-environment interactions. Heredity, 37, 83–93.
Yates, F, and Cochran, W G. 1938. The analysis of groups of experiments. Journal of Agricultural Science, 28, 556–580.
Young, G, and Householder, A S. 1938. Discussion of a set of points in terms of mutual distances. Psychometrika, 3, 19–22.
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Westcott, B. Some methods of analysing genotype—environment interaction. Heredity 56, 243–253 (1986). https://doi.org/10.1038/hdy.1986.37
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