Summary
Methods of regression analysis of genotype-environment interaction are considered in relation to existing theory dealing with the relative efficiencies of selection for general or specific adaptation to the environment, and the choice of environments for assessment. The two alternative models involving regression on to environmental effects (model 2) or genotypic effects (model 3) are equivalent when regression lines are concurrent, but are shown to be mutually exclusive when concurrence is absent. Formulae relating the rates of advance under selection for general and specific adaptation are given, and can be used as a guide to the choice of an effective breeding strategy. When model (3) regression is important, then selection for general adaptation will be an efficient strategy but may be further enhanced by the use of environments with high regression coefficients (γ) for assessment. The advance following assessment in a single environment (kth) is expected to be better than that under n randomly chosen environments if γk>√n−1. If model (2) regression is also important (i.e. regression is concurrent), then the best selector environments can be chosen on the basis of their means. If, on the other hand, model (3) regression does not hold, then selection for general adaptation will be inefficient and it is preferable to group the environments to achieve more homogeneity. When model (2) regression holds, then this grouping can be carried out on the basis of the mean expression of the environments.
Similar content being viewed by others
Article PDF
References
Bliss, C I. 1967. Statistics in Biology McGraw-Hill, New York.
Comstock, R E, and Moll, R H. 1963. Genotype-environment interactions. In Statistical Genetics and Plant Breeding, NAS-NRC982, Washington, D.G., pp. 164–196.
Digkerson, G E. 1962. Implications of genetic-environmental interactions in animal breeding. An Prod, 4, 47–64.
Eberhart, S A, and Russell, W A. 1966. Stability parameters for comparing varieties. Crop Sci, 6, 36–40.
Falconer, D S. 1952. The problem of environment and selection. Am Nat, 86, 293.
Finlay, K W, Wilkinson, and G N. 1963. The analysis of adaptation in a plant breeding programme. Austr J Agric Res, 14, 742–754.
Freeman, G H. 1973. Statistical methods for the analysis of genotype-environment interactions. Heredity, 31, 339–354.
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.
Geidel, H. 1971. Zur Interpretation von Interaktionen bei Versuchsserien. EDV in Medizen und Biologie, 2, 13–18.
Hill, J. 1976. Genotype-environment interactions—a challenge for plant breeders. J Agric Sci, Camb, 85, 477–494.
Mather, K, and Caligari P D S. 1974. Genotype and environment interactions. I. Regression of interaction on overall effect of the environment. Heredity, 33, 43–59.
Moav, R, and Wohlfarth, G W. 1974. Magnification through competition of genetic differences in Carp. Heredity, 33, 181–202.
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.
Perkins, J M, and Jinks, J L. 1971. Specificity of the interaction of genotypes with contrasting environments. Heredity, 26, 463–474.
Perkins, J M, and Jinks, J L. 1973. The assessment and specificity of environmental and genotype-environmental components of variability. Heredity, 30, 111–126.
Robertson, A. 1959. The sampling variance of the genetic correlation coefficient. Biometrics, 15, 469–485.
Utz, H F. 1972. Die Zerlegung der Genotyp × Umwelt-Interationen. EDV in Medezin und Biologie, 3, 52–59.
Wricke, G. 1971. Eine orthogonale Aufterlung der Interaktion fur ein eingeschranktes Modeli. In Rdsehr Arb-Gem Biom DLG1.
Wright, A J. 1971. The analysis and prediction of some two factor interactions in grass breeding. J agric Sci, Camb, 76, 301–306.
Wright, A J. 1976. Bias in the estimation of regression coefficients in the analysis of genotype-environmental interaction. Heredity, in press.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wright, A. The significance for breeding of linear regression analysis of genotype-environment interactions. Heredity 37, 83–93 (1976). https://doi.org/10.1038/hdy.1976.67
Received:
Issue Date:
DOI: https://doi.org/10.1038/hdy.1976.67
This article is cited by
-
A comprehensive multisite recurrent selection strategy in perennial ryegrass
Euphytica (1996)
-
Potential gain from selection for yield stability in two grain sorghum populations
Theoretical and Applied Genetics (1992)
-
Some methods of analysing genotype—environment interaction
Heredity (1986)
-
Genotype by environment interactions and genetic correlations involving two environmental factors
Theoretical and Applied Genetics (1983)
-
The analysis of genotype � environment interactions: What does it mean if varietal stability is linearly related to varietal performance?
Euphytica (1981)