Skip to main content

The area under the function: an index for selecting desirable genotypes

Abstract

The linear regression approach has been widely used for selecting high-yielding and stable genotypes targeted to several environments. The genotype mean yield and the regression coefficient of a genotype's performance on an index of environmental productivity are the two main stability parameters. Using both can often complicate the breeder's decision when comparing high-yielding, less-stable genotypes with low-yielding, stable genotypes. This study proposes to combine the mean yield and regression coefficient into a unified desirability index (D i). Thus, D i is defined as the area under the linear regression function divided by the difference between the two extreme environmental indexes. D i is equal to the mean of the ith genotype across all environments plus its slope multiplied by the mean of the environmental indexes of the two extreme environments (symmetry). Desirable genotypes are those with a large D i. For symmetric trials the desirability index depends largely on the mean yield of the genotype and for asymmetric trials the slope has an important influence on the desirability index. The use of D i was illustrated by a 20-environments maize yield trial and a 25-environments wheat yield trial. Three maize genotypes out of nine showed values of D i 's that were significantly larger than a hypothetical, stable genotype. These were considered desirable, even though two of them had slopes significantly greater than 1.0. The results obtained from ranking wheat genotypes on mean yield differ from a ranking based on D i .

This is a preview of subscription content, access via your institution.

References

  1. Crossa J (1988) A comparison of results obtained with two methods for assessing yield stability. Theor Appl Genet 75:460–467

    Google Scholar 

  2. Crossa J (1990) Statistical analyses of multilocation trials. Adv Agron 44:55–85

    Google Scholar 

  3. Draper NR, Smith H (1966) Applied regression analysis. John Wiley and Sons, New York

    Google Scholar 

  4. Eberhart SA, Russell WA (1966) Stability parameters for comparing varieties. Crop Sci 6:36–40

    Google Scholar 

  5. Finlay KW, Wilkinson GH (1963) The analysis of adaptation in a plant breeding program. Aust J Agric Res 14:742–754

    Google Scholar 

  6. Freeman GH (1973) Statistical methods for the analysis of genotype-environment interaction. Heredity 31:339–354

    Google Scholar 

  7. Hardwick RC, Wood JT (1972) Regression methods for studying genotype-environment interactions. Heredity 28:209–222

    Google Scholar 

  8. Hill J (1975) Genotype-environment interactions — a challenge for plant breeding. J Agric Sci 85:477–493

    Google Scholar 

  9. Lin CS, Binns MR, Lefkovitch LP (1986) Stability analysis: where do we stand? Crop Sci 26:894–900

    Google Scholar 

  10. Westcott B (1986) Some methods of analyzing genotype-environment interaction. Heredity 56:243–253

    Google Scholar 

  11. Yates F, Cochran WG (1938) The analysis of a group of experiments. J Agric Sci 28:556–580

    Google Scholar 

Download references

Author information

Affiliations

Authors

Additional information

Communicated by A. R. Hallauer

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Hernandez, C.M., Crossa, J. & Castillo, A. The area under the function: an index for selecting desirable genotypes. Theoret. Appl. Genetics 87, 409–415 (1993). https://doi.org/10.1007/BF00215085

Download citation

Key words

  • Genotype x environment interaction
  • Adaptation
  • Stability
  • Desirability index