Theoretical and Applied Genetics

, Volume 110, Issue 7, pp 1236–1243 | Cite as

The distribution of genetic parameter estimates and confidence intervals from small disconnected diallels

Original Paper


The distributions of genetic variance components and their ratios (heritability and type-B genetic correlation) from 105 pairs of six-parent disconnected half-diallels of a breeding population of loblolly pine (Pinus taeda L.) were examined. A series of simulations based on these estimates were carried out to study the coverage accuracy of confidence intervals based on the usual t-method and several other alternative methods. Genetic variance estimates fluctuated greatly from one experiment to another. Both general combining ability variance (σ2g) and specific combining ability variance (σ2s) had a large positive skewness. For σ2g and σ2s, a skewness-adjusted t-method proposed by Boos and Hughes-Oliver (Am Stat 54:121–128, 2000) provided better upper endpoint confidence intervals than t-intervals, whereas they were similar for the lower endpoint. Bootstrap BCa-intervals (Efron and Tibshirani, An introduction to the bootstrap. Chapman & Hall, London 436 p, 1993) and Hall’s transformation methods (Zhou and Gao, Am Stat 54:100–104, 2000) had poor coverages. Coverage accuracy of Fieller’s interval endpoint(J R Stat Soc Ser B 16:175–185, 1954) and t-interval endpoint were similar for both h2 and rB for sample sizes n≤10, but for n=30 the Fieller’s method is much better.


  1. Baker RJ (1978) Issues in diallel analysis. Crop Sci 18:533–536Google Scholar
  2. Balocchi CE, Bridgwater FE, Zobel BJ, Jahromi S (1993) Age trends in genetic parameters for tree height in non-selected population of loblolly pine. For Sci 39:231–251Google Scholar
  3. Boos DD, Hughes-Oliver J (2000) How large does n have to be for Z and t intervals? Am Stat 54:121–128Google Scholar
  4. Boyle TA (1987) A diallel cross in black spruce. Genome 29:180–189Google Scholar
  5. Burdon RD (1977) Genetic correlation as a concept for studying genotype-environment interaction in forest tree breeding. Silvae Genet 26:168–175Google Scholar
  6. Chaffin WW, Rhiel GS (1993) The effect of skewness and kurtosis on the one-sample t test and the impact of knowledge of the population standard deviation. J Stat Comput Simul 46:79–90Google Scholar
  7. Chen L (1995) Testing the mean of skewed distributions. J Am Stat Assoc 90:767–772Google Scholar
  8. Christensen R (1996) Exact tests for variance components. Biometrics 52:309–314Google Scholar
  9. Cisar G, Brown CM, Jedlinksi H (1982) Diallel analyses for tolerance in winter wheat to the barley yellow dwarf virus. Crop Sci 22:328–333Google Scholar
  10. Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, LondonGoogle Scholar
  11. Fayyad R, Graybill FA, Burdick RK (1996) A note on exact tests for variance components in unbalanced random and mixed linear models. Biometrics 52:306–308Google Scholar
  12. Fieller EC (1954) Symposium on interval estimation: some problems in interval estimation. J R Stat Soc Ser B 16:175–185Google Scholar
  13. Hill WG (1985) Effect of population size on response to short term and long term selection. J Anim Breeding Genet 102:161–173Google Scholar
  14. Johnson GR, King JN (1998) An analysis of half-diallel mating designs. Silvae Genet 47:74–79Google Scholar
  15. Knapp SJ, Ross WM, Stroup WW (1987) Precision of genetic variance and heritability estimates from sorghum populations. Crop Sci 27:265–268Google Scholar
  16. Knapp SJ, Bridges WC Jr, Yang MH (1989) Nonparametric confidence interval estimators for heritability and expected selection response. Genetics 121:891–898Google Scholar
  17. Li B, McKeand SE, Weir RJ (1996) Genetic parameter estimates and selection efficiency for the loblolly pine breeding in the south-eastern US. In: Tree improvement for sustainable tropical forestry. In: Dieters MJ, Matherson DG, Nikles DG, Harwood CE, Walker SM (eds) Proc QFRI-IUFRO Conf. Caloundra, Queensland, Australia, pp 164–168Google Scholar
  18. Li B, Weir R, Hatcher A, McKeand SE (1999) Third cycle loblolly pine breeding plan. Technical Report 99–2. NC State University-Industry Cooperative Tree Improvement Program, 16 pGoogle Scholar
  19. Lu TFC, Graybill FA (1987) Confidence intervals on the ratio of expected mean squares theta-1 plus d-theta-2-theta-3. Biometrics 43:535–544Google Scholar
  20. Öfversten FA (1993) Matrices with applications in statistics, 2nd edn. Belmont, Calif.Google Scholar
  21. Wilson ND, Weibel DE, Mcnew RW (1978) Diallel analysis of grain yield, percent protein, and yield in gain sorghum. Crop Sci 18:491–494Google Scholar
  22. Wright AJ (1985) Diallel designs, analyses, and reference populations. Heredity 54:307–311Google Scholar
  23. Xiang B, Li B (2001) A new mixed analytical method for genetic analysis of diallel data. Can J For Res 31:2252–2259Google Scholar
  24. Xiang B, Li B, Isik F (2003) Time trend of genetic parameter estimates in growth traits of Pinus Taeda L. Silvae Genet 52:114–121Google Scholar
  25. Yamada Y (1962) Genotype by environment interaction and genetic correlation of the same trait under different environments. Jpn J Genet 6:498–509Google Scholar
  26. Yanchuk AD (1996) General and specific combining ability from disconnected partial diallels of coastal Douglas fir. Silvae Genet 45:37–44Google Scholar
  27. Yeh FC, Heaman JC (1987) Estimating genetic parameters of height growth in seven year-old coastal Douglas-fir from disconnected diallels. For Sci 33:946–957Google Scholar
  28. Zhou XH, Gao S (2000) One-sided confidence intervals for means of positively skewed distributions. Am Stat 54:100–104Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of Forestry and Environmental ResourcesNorth Carolina State UniversityRaleighUSA
  2. 2.Department of StatisticsNorth Carolina State UniversityRaleighUSA

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