Theoretical and Applied Genetics

, Volume 86, Issue 4, pp 437–441 | Cite as

Estimation of heritability from varietal trials data

  • M. Singh
  • S. Ceccarelli
  • J. Hamblin


We present the estimation of heritabilities of an observed trait in situations where evaluation of several pure breeding lines is performed in a trial at a single location and in trials from several locations. For the single location situation, we evaluate exact confidence intervals, the probability of invalid estimates, and the percentage points of the distribution of heritability. Simulations were performed to numerically verify the results. Additionally, approximations to the bias and standard error of the estimate were obtained and are presented along with their simulated values and coefficients of skewness and kurtosis. For trials in several locations, explicit expressions for exact values of confidence limits are not available. Further, one would require knowledge of one more parameter, represented by the ratio of genotype x environment (G x E) interaction variance to error variance, in addition to the number of genotypes, replication and true heritability value. Approximations were made for bias and the standard error of estimates of heritability. The evaluation of the distribution of heritability and its moments was recognized as a problem of the linear function of an independent chi-square. The methods have been illustrated by data from experiments on grain and straw yield of 64 barley genotypes evaluated at three locations.

Key words

Heritability Standard error Genotype x environment interaction Confidence interval Invalid estimates 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bogyo TP, Becker WA (1963) Exact confidence intervals for heritability estimated from parental half-sib correlations. Biometrics 19:494–496Google Scholar
  2. Bridges Jr, Knapp SJ, Cornelius SJ (1991) Standard errors and confidence interval estimators for expected selection response. Crop Sci 31:253–255Google Scholar
  3. Broemeling LD (1969) Confidence intervals for measures of heritability. Biometrics 25:424–427PubMedGoogle Scholar
  4. Falconer DS (1982) Introduction to quantitative genetics. Longman Inc., New YorkGoogle Scholar
  5. Gill JL, Jensen EL (1968) Probability of obtaining negative estimates of heritability. Biometrics 24:517–526PubMedGoogle Scholar
  6. Graybill FA, Chih-Ming Wang (1979) Confidence intervals for proportions of variability in two-factor nested variance component models. J Am Stat Assoc 74:368–374Google Scholar
  7. Graybill FA, Martin F, Godfrey G (1956) Confidence intervals for variance ratios specifying genetic heritability. Biometrics 12:99–109Google Scholar
  8. Kendall MG, Stuart A (1969) Advanced theory of statistics vol I. Charles Griffin and Co., LondonGoogle Scholar
  9. Knapp SJ, Stroup WW, Ross WM (1985) Exact confidence intervals for heritability on a progeny mean basis. Crop Sci 25:192–194Google Scholar
  10. Imhoff JP (1961) Computing the distribution of quadratic forms in normal variables. Biometrika 48:419–425Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • M. Singh
    • 1
  • S. Ceccarelli
    • 1
  • J. Hamblin
    • 1
  1. 1.International Center for Agricultural Research in the Dry Areas (ICARDA)AleppoSyria

Personalised recommendations