Theoretical and Applied Genetics

, Volume 91, Issue 3, pp 544–552 | Cite as

The beta-binomial model for estimating heritabilities of binary traits

  • S. Magnussen
  • A. Kremer
Article

Abstract

Calculations of individual narrow-sense heritability and family mean heritability of a binary trait in stochastically simulated sib trials in completely randomized block experiments showed that in some situations estimates of “realized” heritabilities obtained from the mixed linear threshold model could be improved by application of a proposed beta-binomial model. The proposed model adopts the beta-binomial as the conjugate-prior for the distribution of probabilities of observing the binary trait in a genetic entry. Estimation of the beta parameters allows an estimation of selection response and, by linkage to a threshold model for the individual observations, the desired heritabilities can be obtained. The average bias in the betabinomial estimates of heritability and family mean heritability was less than 2%. Improvements over existing procedures were especially manifest at heritabilities above 0.3 and at low overall probabilities of observing the trait (p < 0.30). The lowest root mean square errors were consistently obtained with the algorithm proposed by Harville and Mee (1984). The beta-binomial framework, although restricted to a single random additive genetic effect, further facilitates general analysis, estimation of selection response, and calculation of reliable family mean heritability. Intraclass correlations can be estimated directly from the beta-binomial parameters.

Key words

Simulation Genetic response Family mean heritability Sib analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Breslow NE, Clayton DG (1993) Approximate inference in generalized linear mixed models. J Am Stat Assoc 88:9–25Google Scholar
  2. Dempster ER, Lerner IM (1950) Heritability of threshold characters. Genetics 35:212–236Google Scholar
  3. Falconer DS (1981) Introduction to quantitative genetics, 2nd edn. Longman, LondonGoogle Scholar
  4. Foulley JL, Gianola D, Thompson R (1983) Prediction of genetic merit from data on binary and quantitative variates with an application to calving difficulty, birth weight, and pelvic opening. Genet Sel Evol 15:401–424Google Scholar
  5. Foulley JL, Gianola D, Im S (1987) Genetic evaluation of traits distributed as Poisson-binomial with reference to reproductive characters. Theor Appl Genet 73:870–877Google Scholar
  6. Gianola D (1979) Heritability of polychotomous characters. Genetics 93:1051–1055Google Scholar
  7. Gianola D (1980) Genetic evaluation of animals for traits with categorical responses. J Anim Sci 51:1272–1276Google Scholar
  8. Hallauer AR, Miranda JB (1981) Quantitative genetics in maize breeding. Iowa State University PressGoogle Scholar
  9. Harville DA, Mee RW (1984) A mixed-model procedure for analyzing ordered categorical data. Biometrics 40:393–408Google Scholar
  10. Henderson CR (1984) Applications of linear models in animal breeding. University of Guelph, CanadaGoogle Scholar
  11. Johnson NL, Kotz S (1970) Continuous univariate distributions, 2. John Wiley and Sons, New YorkGoogle Scholar
  12. Landis JR, Koch GG (1977) A one-way components of variance model for categorical data. Biometrics 33:671–679CrossRefGoogle Scholar
  13. Magnussen S (1990) Alternative analyses of parent-offspring correlations for stem straightness in jack pine. Silvae Genet 3:237–244Google Scholar
  14. McCullagh P, Nelder A (1989) Generalized linear models. Chapman and Hall, LondonGoogle Scholar
  15. Prentice RL (1986) Binary regression using an extended beta-binomial distribution, with discussion of correlation induced by covariate measurement errors. J Am Stat Assoc 81:321–327Google Scholar
  16. Quaas RL, Van Vleck LD (1980) Categorical trait sire evaluation by best linear unbiased prediction of future progeny category frequencies. Biometrics 36:117–122Google Scholar
  17. Ripley BD (1987) Stochastic simulation. John Wiley and Sons, New YorkGoogle Scholar
  18. Santner TJ, Duffy DE (1989) The statistical analysis of discrete data. Springer-Verlag, New YorkGoogle Scholar
  19. Searle SR (1982) Matrix algebra useful for statistics. John Wiley and Sons, New YorkGoogle Scholar
  20. Searle SR, Casella G, McCulloch CE (1992) Variance components. John Wiley and Sons, New YorkGoogle Scholar
  21. Siegel S (1956) Non-parametric statistics for the behavioral sciences. McGraw-Hill, New YorkGoogle Scholar
  22. Simianer H, Schaeffer LR (1989) Estimation of covariance components between one continuous and one binary trait. Genet Sel Evol 21:303–315MathSciNetMATHGoogle Scholar
  23. Stiratelli R, Laird N, Ware JH (1984) Random-effects models for serial observations with binary response. Biometrics 40:961–971Google Scholar
  24. Van Vleck LD (1971) Estimation of heritability of threshold characters. J Dairy Sci 55:218–222Google Scholar
  25. Wright S (1978) Evolution and the genetics of populations. The University of Chicago Press, ChicagoGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • S. Magnussen
    • 1
  • A. Kremer
    • 2
  1. 1.Natural Resources Canada, Canadian Forest ServicePetawawa National Forestry InstituteChalk RiverCanada
  2. 2.Laboratoire d'amélioration des arbres forestieresInstitut national de la recherche agronomiqueCestasFrance

Personalised recommendations