Summary
This is largely a review paper, describing various statistical methods for analysing interactions in general and genotype-environment interactions in particular, and giving nearly 100 references to previous work. The joint regression analysis approach introduced by Yates and Cochran (1938) is considered in some detail; alternatives to regression are discussed, as are various stability parameters. Much work has been done on statistical methods for testing for interactions in general, and this also is reviewed, from Tukey's (1949) one degree of freedom for non-additivity to Milliken and Graybill's (1970) generalisation to testing for various types of possible interaction. The difficulties of testing and inference in the presence of interaction are discussed. Data from a two-way table may be regarded as a multivariate set, as first shown by Williams (1952) and later extended by others, particularly Mandel (1969b and 1971 ). These methods are only just beginning to be used in studies of genotype-environment interactions, and several recent references are given. External measurements may be used to measure the environment and these may be either physical or biological. Again, the appropriate methods of analysis are fairly new. The interpretation of interactions is considered in relation to the use to be made of the results. It is suggested that various multivariate techniques may be used to assist in the elucidation of interactions, especially when these are not easy to explain by simpler methods of analysis.
Similar content being viewed by others
Article PDF
References
Abou-El-Fittouh, H A, Rawlings, J O, and Miller, P A. 1969a. Classification of environments to control genotype by environment interactions with an application to cotton. Crop Sci, 9, 135–140.
Abou-El-Fittouh, H A, Rawlings, J O, and Miller, P A. 1969b. Genotype by environment interactions in cotton—their nature and related environmental variables. Crop Sci, 9, 377–381.
Allard, R W, and Bradshaw, A D. 1964. Implications of genotype-environmental interactions in applied plant breeding. Crop Sci, 4, 503–508.
Baker, R J. 1969. Genotype-environment interactions in yield of wheat. Can J Plant Sci, 49, 743–751.
Bartlett, M S. 1947. The use of transformations. Biometrics, 2, 39–52.
Bogyo, T P, and Russell, T S. 1972. Some properties of the statistics used in the analysis of genotype-environment interactions. Biometrics, 28, 1161–1162.
Bolton, A, and Scaife, M A. 1969. Maize variety trials in Western Tanzania, 1963–1966. E Afr agric for J, 35, 11–20.
Breese, E L. 1969. The measurement and significance of genotype-environment interactions in grasses. Heredity, 24, 27–44.
Bucio Alanis, L. 1966. Environmental and genotype-environmental components of variability. I. Inbred lines. Heredity, 21, 387–397.
Bucio Alanis, L, and Hill, J. 1966. Environmental and genotype-environmental com potents of variability. II. Heterozygotes. Heredity, 21, 399–405.
Bucio Alanis, L, Perkins, Jean M, and Jinks, J L. 1969. Environmental and genotype-environmental components of variability. V. Segregating generations. Heredity, 24, 115–127.
Corsten, L C A, and Van Eijnsbergen, A C. 1972. Multiplicative effects in two-way analysis of variance. Statist Neerlandica, 26, 61–68.
Dowker, B D. 1963. Rainfall reliability and maize yields in Machakos district. E Afr agric for J, 28, 134–138.
Dowker, B D. 1971. Variation studies in carrots as an aid to breeding. I. Concepts. J hort Sci, 46, 485–497.
Easton, H S, and Clements, R J. 1973. The interaction of wheat genotypes with a specific factor of the environment. J agric Sci, Camb, 80, 43–52.
Eberhart, S A, and Russell, W A. 1966. Stability parameters for comparing varieties. Crop Sci, 6, 36–40.
Elston, R C. 1961. On additivity in the analysis of variance. Biometrics, 17, 209–219.
Finlay, K W, and Wilkinson, G N. 1963. The analysis of adaptation in a plant-breeding programme. Aust J Agric Res, 14, 742–754.
Fisher, R A, and Mackenzie, W A. 1923. Studies in crop variation. II. The manurial response of different potato varieties. J agric Sci, Camb, 13, 311–320.
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, Jean 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.
Fripp, Yvonne J. 1972. Genotype-environmental interactions in Schizophyllum commune. II. Assessing the environment. Heredity, 28, 223–238.
Fripp, Yvonne J, and Caten, C E. 1971. Genotype-environmental interactions in Schizophyllum commune. I. Analysis and character. Heredity, 27, 393–407.
Fripp, Yvonne J, and Caten, C E. 1973. Genotype-environmental interactions in Schizophyllum commune. III. The relationship between mean expression and sensitivity to change in environment. Heredity, 30, 341–349.
Ghosh, M N, and Sharma, D. 1963. Power of Tukey's test for non-additivity. Jl R statist Soc B, 25, 213–219.
Gollob, H F. 1968. A statistical model which combines features of factor analytic and analysis of variance techniques. Psychometrika, 33, 73–116.
Gower, J C. 1966. Some distance properties of latent root and vector methods used in multivariate analysis. Biometrika, 53, 325–338.
Grafius, J E, and Kiesling, R L. 1960. The prediction of the relative yields of different oat varieties based on known environmental variables. Agron J, 52, 396–399.
Graybill, F A, and Wortham, A W. 1956. A note on uniformly best unbiased estimators for variance components. J Am statist Ass, 51, 266–268.
Hamaker, H C. 1955. Experimental design in industry. Biometrics, 11, 257–286.
Hanson, W D. 1964. Genotype-environment interaction concepts for field experimentation. Biometrics, 20, 540–552.
Hanson, W D. 1970. Genotypic stability. Theoret Appl Genetics, 40, 226–231.
Hardwick, R C, and Wood, J T. 1972. Regression methods for studying genotype-environment interactions. Heredity, 28, 209–222.
Hill, J, and Perkins, Jean M. 1969. The environmental induction of heritable changes in Nicotiana rustica. Effects of genotype-environmental interactions. Genetics, 61, 661–675.
Hill, J, and Samuel, C J A. 1971. Measurement and inheritance of environmental response amongst selected material of Lolium perenne. Heredity, 27, 265–276.
Jinks, J L, and Perkins, Jean M. 1970. Environmental and genotype-environmental components of variability. VII. Simultaneous prediction across environments and generations. Heredity, 25, 475–480.
Johnson, D E, and Graybill, F A. 1972a. Estimation of σ2 in a two-way classification model with interaction. J Am statist Ass, 67, 388–394.
Johnson, D E, and Graybill, F A. 1972b. An analysis of a two-way model with interaction and no replication. J Am statist Ass, 67, 862–868.
Joppa, L R, Lebsock, K L, and Busch, R H. 1971. Yield stability of selected spring wheat cultivars (Triticum aestivum L. em Thell) in the uniform regional nurseries, 1959 to 1968. Crop Sci, 11, 238–241.
Jowett, D. 1972. Yield stability parameters for sorghum in East Africa. Crop Sci, 12, 314–317.
Knight, R. 1970. The measurement and interpretation of genotype-environment interactions. Euphytica, 19, 225–235.
Knight, R. 1971. A multiple regression analysis of hybrid vigour in single crosses of Dactylis glomerata L. Theoret Appl Genetics, 41, 306–311.
Mandel, J. 1959. The measuring process. Technometrics, 1, 251–267.
Mandel, J. 1961. Non-additivity in two-way analysis of variance. J Am statist Ass, 56, 878–888.
Mandel, J. 1969a. A method for fitting empirical surfaces to physical or chemical data. Technometrics, 11, 411–429.
Mandel, J. 1969b. The partitioning of interaction in analysis of variance. J Res natn Bur Stand, 73B, 309–328.
Mandel, J. 1971. A new analysis of variance model for non-additive data. Technometrics, 13, 1–18.
Mandel, J. 1972. Principal components, analysis of variance and data structure. Statist Neerlandica, 26, 119–129.
Mandel, J, and Lashof, T W. 1959. The interlaboratory evaluation of testing methods. ASTM Bulletin, 239, 53–61.
Mandel, J, and McCrackin, F L. 1963. Analysis of families of curves. J Res natn Bur Stand, 67A, 259–267.
Mather, K. 1971. On Biometrical Genetics. Heredity, 26, 349–364.
Mather, K, and Jinks, J L. 1971. Biometrical Genetics. 2nd edition. Chapman and Hall, London.
Mather, K, and Morley Jones, R. 1958. Interaction of genotype and environment in continuous variation. I. Description. Biometrics, 14, 343–359.
Miller, P A, Robinson, H F, and Pope, O A. 1962. Cotton variety testing: additional information on variety × environment interactions. Crop Sci, 2, 349–352.
Miller, P A, Williams, J C, and Robinson, H F. 1959. Variety × environment interactions in cotton variety tests and their implications on testing methods. Agron J, 51, 132–134.
Milliken, G A, and Graybill, F A. 1970. Extensions of the general linear hypothesis model. J Am statist Ass, 65, 797–807.
Morley Jones, R, and Mather, K. 1958. Interaction of genotype and environment in continuous variation. II. Analysis. Biometrics, 14, 489–498.
Paroda, R S, and Hayes, J D. 1971. An investigation of genotype-environment interactions for rate of ear emergence in spring barley. Heredity, 26, 157–175.
Perkins, Jean M. 1970. Environmental and genotype-environmental components of variability. VI. Diallel sets of crosses. Heredity, 25, 29–40.
Perkins, Jean M. 1972. The principal component analysis of genotype-environmental interactions and physical measures of the environment. Heredity, 29, 51–70.
Perkins, Jean M, and Jinks, J L. 1968a. Environmental and genotype-environmental components of variability. III. Multiple lines and crosses. Heredity, 23, 339–356.
Perkins, Jean M, and Jinks, J L. 1968b. Environmental and genotype-environmental components of variability. IV. Non-linear interactions for multiple inbred lines. Heredity, 23, 525–535.
Perkins, Jean M, and Jinks, J L. 1971. Specificity of the interaction of genotypes with contrasting environments. Heredity, 26, 463–474.
Perkins, Jean M, and Jinks, J L. 1973. The assessment and specificity of environmental and genotype-environmental components of variability. Heredity, 30, 111–126.
Plackett, R L. 1960. Models in the analysis of variance. Jl R statist Soc B, 22, 195–217.
Porceddu, E. 1970. The environmental component and the genotype × environment interaction in plant selection work. Genet, agr, 24, 129–144.
Qualset, C O, and Granger, R M. 1970. Frequency dependent stability of performance in oats. Crop Sci, 10, 386–389.
Reich, V H, and Atkins, R E. 1970. Yield stability of four population types of grain sorghum, Sorghum bicolor (L.) Moench, in different environments. Crop Sci, 10, 511–517.
Rojas, B A. 1973. On Tukey's test of additivity. Biometrics, 29, 45–52.
Rowe, P R, and Andrew, R A. 1964. Phenotypic stability for a systematic series of corn genotypes. Crop Sci, 4, 563–567.
Russell, W A, and Eberhart, S A. 1968. Testcrosses of one-and two-ear types of corn belt maize inbreds. II. Stability of performance in different environments. Crop Sci, 8, 248–251.
St-Pierre, C A, Klinck, H R, and Gauthier, F M. 1967. Early generation selection under different environments as it influences adaptation of barley. Can J Plant Sci, 47, 507–517.
Salmon, S C. 1951. Analysis of variance and long-time variety tests of wheat. Agron J, 43, 562–570.
Sampford, M R. 1960. Discussion on “Models in the analysis of variance”by R. L. Plackett. Jl R statist Soc B, 22, 211–212.
Samuel, C J A, Hill, J, Breese, E L, and Davies, Alison. 1970. Assessing and predicting environmental response in Lolium perenne. J agric Sci, Comb, 75, 1–9.
Scheffe, H. 1959. The Analysis of Variance. John Wiley, New York.
Shukla, G K. 1972a. Some statistical aspects of partitioning genotype-environmental components of variability. Heredity, 29, 237–245.
Shukla, G K. 1972b. Application of some multivariate techniques in the analysis and interpretation of the genotype-environment interaction. Paper presented at the Symposium on Genotype × Environment Interactions, Birmingham University, September, 1972.
Snee, R D. 1972a. On the analysis of response curve data. Technometrics, 14, 47–62.
Snee, R D. 1972b. A useful method for conducting carrot shape studies. J hort Sci, 47, 267–277.
Sprague, G F, and Federer, W T. 1951. A comparison of variance components in corn yield trials. II. Error, year × variety, location × variety, and variety components. AgronJ, 43, 535–541.
Tai, G C C. 1971. Genotypic stability analysis and its application-to potato regional trials. Crop Sci, 11, 184–190.
Troughton, A. 1970. Intra-varietal variation of yield in two varieties of Lolium perenne L. Euphytica, 19, 382–389.
Tukey, J W. 1949. One degree of freedom for non-additivity. Biometrics, 5, 232–242.
Tukey, J W. 1962. The future of data analysis. Ann math Statist, 33, 1–67.
Utz, H F. 1972. Die Zerlegung der Genotyp × Umwelt-Interaktionen. EDV Med&Biol, 3, 52–59.
Ward, G C, and Dick, I D. 1952. Non-additivity in randomized block designs and balanced incomplete block designs. NZ Jl Sci Technol, 33, 430–435.
Westerman, Jane M. 1971. Genotype-environment interaction and developmental regulation in Arabidopsis thaliana. II. Inbred lines; analysis. Heredity, 26, 93–106.
Westerman, Jane M, and Lawrence, M J. 1970. Genotype-environment interaction and developmental regulation in Arabidopsis thaliana. I. Inbred lines; description. Heredity, 25, 609–627.
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 environment interaction shown by germinating seeds of Brassica napus. Heredity, 26, 397–411.
Wood, J T. 1972. The multivariate approach to genotype-environment interactions. Paper presented to the Symposium on Genotype × Environment Interactions, Birmingham University, September, 1972.
Wricke, G. 1962. Uber eine Methode zur Erfassung der ökologischen Streubreite in Feldversuchen. Z Pflzücht, 47, 92–96.
Wright, A J. 1971. The analysis and prediction of some two factor interactions in grass breeding. J agric Sci, Camb, 76, 301–306.
Yates, F. 1967. A fresh look at the basic principles of the design and analysis of experiments. Proc 5th Berkeley Symp math Statist Probab, 4, 777–790.
Yates, F, and Cochran, W G. 1938. The analysis of groups of experiments. J agric Sci, Camb, 28, 556–580.
Author information
Authors and Affiliations
Additional information
Based on a paper presented at the Symposium on Genotype × Environment Interactions, Birmingham University, September, 1972.
Rights and permissions
About this article
Cite this article
Freeman, G. Statistical methods for the analysis of genotype-environment interactions. Heredity 31, 339–354 (1973). https://doi.org/10.1038/hdy.1973.90
Received:
Issue Date:
DOI: https://doi.org/10.1038/hdy.1973.90
This article is cited by
-
Multi-environment Genomic Selection in Rice Elite Breeding Lines
Rice (2023)
-
Clustering stability methods towards selecting best performing and stable durum wheat genotypes
Euphytica (2023)
-
Improvement of bacterial blight resistance of the high yielding, fine-grain, rice variety, Gangavati sona through marker-assisted backcross breeding
3 Biotech (2023)
-
Improvement of bacterial blight resistance of the popular variety, Nellore Mahsuri (NLR34449) through marker-assisted breeding
Journal of Genetics (2022)
-
Statistical methods to explore genotype-by-environment interaction for loblolly pine clonal trials
Tree Genetics & Genomes (2017)