Hereditary Variance: Mating Designs

  • Arnel R. Hallauer
  • J. B. Miranda Filho
  • Marcelo J. Carena
Part of the Handbook of Plant Breeding book series (HBPB, volume 6)


Average allele frequency at segregating loci of F2 populations derived from pure line crosses is expected to be p = q = 0.5. From now on, however, we will use as source material genetic broad-based populations with arbitrary allele frequencies. This means that special case of p = q = 0.5 often does not apply. Therefore, p is not equal to q.


Inbred Line Reference Population General Combine Ability Specific Combine Ability Epistatic Effect 
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  1. Baker, R. J. 1978. Issues in diallel analysis. Crop Sci. 18:533–36.CrossRefGoogle Scholar
  2. Bernardo, R. 2002. Breeding for Quantitative Traits in Plants. Stemma Press, Woodbury, MN.Google Scholar
  3. Bernardo, R. 2008. Molecular markers and selection for complex traits in plants: learning from the past 20 years. Crop Sci. 48:1649–64.CrossRefGoogle Scholar
  4. Bernardo, R., and J. Yu. 2007. Prospects for genomewide selection for quantitative traits in maize. Crop Sci. 47:1082–90.CrossRefGoogle Scholar
  5. Brim, C. A. 1966. A modified pedigree method of selection in soybeans. Crop Sci. 6:220.CrossRefGoogle Scholar
  6. Buckler, E. S., J. B. Holland, P. J. Bradbury, C. B. Acharya, P. J. Brown, C. Browne, E. Ersoz, S. Flint-Garcia, A. Garcia, J. C. Glaubitz, M. M. Goodman, C. Harjes, K. Guill, D. E. Kroon, S. Larsson, N. K. Lepak, H. Li, S. E. Mitchell, G. Pressoir, J. A. Peiffer, M. O. Rosas, T. R. Rocherford, M. C. Romay, S. Romero, S. Salvo, H. S. Villeda, H. S. da Silva, Q. Sun, F. Tian, N. Upadyayula, D. Ware, H. Yates, J. Yu, Z. Zhang, S. Kresovich, and M. D. McMullen. 2009. The genetic architecture of maize flowering time. Science 325:714–18.PubMedCrossRefGoogle Scholar
  7. Carena, M. J. 2005. Maize commercial hybrids compared to improved population hybrids for grain yield and agronomic performance. Euphytica 141:201–8.CrossRefGoogle Scholar
  8. Carena, M. J., and Z. W. Wicks III. 2006. Maize early maturing hybrids: an exploitation of U.S. temperate public genetic diversity in reserve. Maydica 51:201–8.Google Scholar
  9. Carena, M. J., G. Bergman, N. Riveland, E. Eriksmoen, and M. Halvorson. 2009a. Breeding maize for higher yield and quality under drought stress. Maydica 54:287–98.Google Scholar
  10. Carena, M. J., J. Yang, J. C. Caffarel, M. Mergoum, and A. R. Hallauer. 2009b. Do different production environments justify separate maize breeding programs? Euphytica 169: 141–50.CrossRefGoogle Scholar
  11. Chi, R. K., S. A. Eberhart, and L. H. Penny. 1969. Covariances among relatives in a maize variety (Zea mays L.). Genetics 63:511–20.PubMedGoogle Scholar
  12. Cockerham, C. C. 1954. An extension of the concept of partitioning hereditary variance for analysis of covariance among relatives when epistasis is present. Genetics 39:859–82.PubMedGoogle Scholar
  13. Cockerham, C. C. 1956a. Analysis of quantitative gene action. Brookhaven Symp. Biol. 9:53–68.Google Scholar
  14. Cockerham, C. C. 1956b. Effects of linkage on the covariances between relatives. Genetics 41:138–41.PubMedGoogle Scholar
  15. Cockerham, C. C. 1961. Implications of genetic variances in a hybrid breeding program. Crop Sci. 1:47–52.CrossRefGoogle Scholar
  16. Cockerham, C. C. 1963. Estimation of genetic variances. In Statistical Genetics and Plant Breeding, W. D. Hanson and H. F. Robinson, (eds.), pp. 53–94. NAS–NRC Publ. 982. Washington, DC.Google Scholar
  17. Comstock, R. E., and H. F. Robinson. 1948. The components of genetic variance in populations of biparental progenies and their use in estimating the average degree of dominance. Biometrics 4:254–66.PubMedCrossRefGoogle Scholar
  18. Comstock, R. E., and H. F. Robinson. 1952. Estimation of average dominance of genes. In Heterosis, J. W. Gowen, (ed.), pp. 494–516. Iowa State University Press, Ames, IA.Google Scholar
  19. Dickerson, G. E. 1969. Techniques for research in quantitative animal genetics. In Techniques and Procedures in Animal Science Research. Am. Soc. Anim. Sci., Albany, New York, NY.Google Scholar
  20. Dudley, J. W., and G. R. Johnson. 2009. Epistatic models improve prediction of performance in corn. Crop Sci. 49:763–70.CrossRefGoogle Scholar
  21. Eberhart, S. A., R. H. Moll, H. F. Robinson, and C. C. Cockerham. 1966. Epistatic and other genetic variances in two varieties of maize. Crop Sci. 6:275–80.CrossRefGoogle Scholar
  22. Falconer, D. S., and T. F. C. Mackay. 1996. Introduction to quantitative genetics. 4th ed., Longman Group, Ltd., Essex, England.Google Scholar
  23. Federer, W. T. 1961. Augmented designs with one-way elimination of heterogeneity. Biometrics 17:447–73.CrossRefGoogle Scholar
  24. Gardner, C. O. 1963. Estimates of genetic parameters in cross-fertilizing plants and their implications in plant breeding. In Statistical Genetics and Plant Breeding, W. D. Hanson and H. F. Robinson, (eds.), pp. 225–52. NAS–NRC Publ. 982. NAS–NRC. Washington, DC.Google Scholar
  25. Gardner, C. O., and S. A. Eberhart. 1966. Analysis and interpretation of the variety cross diallel and related populations. Biometrics 22:439–52.PubMedCrossRefGoogle Scholar
  26. Gardner, C. O., and J. H. Lonnquist. 1959. Linkage and the degree of dominance of genes controlling quantitative characters in maize. Agron. J. 51:524–28.CrossRefGoogle Scholar
  27. Gardner, C. O., P. H. Harvey, R. C. Comstock, and H. F. Robinson. 1953. Dominance of genes controlling quantitative characters in maize. Agron. J. 45:186–91.CrossRefGoogle Scholar
  28. Graybill, F. A., and W. H. Robertson. 1957. Calculating confidence intervals for genetic heritability. Poult. Sci. 36:261–65.CrossRefGoogle Scholar
  29. Graybill, F. A., F. Martin, and G. Godfrey. 1956. Confidence intervals for variance ratios specifying genetic heritability. Biometrics 12:99–109.CrossRefGoogle Scholar
  30. Griffing, B. 1956. Concept of general and specific combining ability in relation to diallel crossing systems. Australian J. Biol. Sci. 9:463–93.Google Scholar
  31. Hallauer, A. R. 1970. Genetic variability for yield after four cycles of reciprocal recurrent selections in maize. Crop Sci. 10:482–85.CrossRefGoogle Scholar
  32. Hallauer, A. R., and J. H. Sears. 1973. Changes in quantitative traits associated with inbreeding in a synthetic variety of maize. Crop Sci. 13:327–30.CrossRefGoogle Scholar
  33. Hanson, W. D. 1959. The breakup of initial linkage blocks under selected mating systems. Genetics 44:857–68.PubMedGoogle Scholar
  34. Holland, J. B. 2001. Epistasis and plant breeding. In Plant Breeding Reviews, Vol. 21, J. Janick, (ed.), pp. 27–92. Wiley, Hoboken, NJ.Google Scholar
  35. Holland, J. B. 2009. Epistasis? 3rd Plant Breeding Workshop. Aug 3–5. Madison, WI.Google Scholar
  36. Holland, J. B., W. E. Nyquist, and C. T. Cervantes-Martinez. 2003. Estimating and interpreting heritability for plant breeding: an update. In Plant Breeding Reviews, J. Janick, (ed.), pp. 9–111. Wiley, Hoboken, NJ.Google Scholar
  37. Jensen, S. D. 1959. Combining ability of unselected inbred lines of corn from incomplete diallel and topcross tests. Ph.D. dissertation, Iowa State University, Ames, IA.Google Scholar
  38. Jumbo, M.B., and Carena, M.J. 2008. Combining ability, maternal, and reciprocal effects of elite early-maturing maize population hybrids. Euphytica 162:325–33.CrossRefGoogle Scholar
  39. Kearsey, M. J., and J. L. Jinks. 1968. A general model of detecting additive, dominance, and epistatic variation for metrical traits. I. Theory. Heredity 23:403–9.PubMedCrossRefGoogle Scholar
  40. Kempthorne, O. 1957. An Introduction to Genetic Statistics. Wiley, New York, NY.Google Scholar
  41. Kempthorne, O., and R. N. Curnow. 1961. The partial diallel cross. Biometrics 17:229–50.CrossRefGoogle Scholar
  42. Knapp, S. J. 1986. Confidence intervals for heritability for two-factor mating design single environment linear models. Theoret. Appl. Genet. 72:857–91.CrossRefGoogle Scholar
  43. Knapp, S. J., W. W. Stroup, and W. M. Ross. 1985. Exact confidence intervals for heritability on a progeny mean basis. Crop Sci. 25:192–94.CrossRefGoogle Scholar
  44. Lamkey, K. R., and A. R. Hallauer. 1987. Heritability estimated from recurrent selection experiments in maize. Maydica 32:61–78.Google Scholar
  45. Lindsey, M. F., J. H. Lonnquist, and C. O. Gardner. 1962. Estimates of genetic variance in open-pollinated varieties of Corn Belt corn. Crop Sci. 2:105–8.CrossRefGoogle Scholar
  46. Malécot, G. 1948. Les Mathématiques de l'Hérédité. Masson et Cie, Paris.Google Scholar
  47. Mather, K. 1949. Biometrical Genetics. Methuen, London.Google Scholar
  48. Mather, K., and J. L. Jinks. 1971. Biometrical Genetics. Cornell Univ. Press, Ithaca, NY.Google Scholar
  49. Matzinger, D. F., G. F. Sprague, and C. C. Cockerham. 1959. Diallel crosses of maize in experiments repeated over locations and years. Agron. J. 51: 346–50.CrossRefGoogle Scholar
  50. Melani, M. D., and M. J. Carena. 2005. Alternative heterotic patterns for the northern Corn Belt. Crop Sci. 45:2186–94.CrossRefGoogle Scholar
  51. Nyquist, W. E. 1991. Estimation of heritability and prediction of selection response in plant populations. Crit. Rev. Plant Sci. 10:235–322.CrossRefGoogle Scholar
  52. Patterson, H. D., and E. R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83–92.CrossRefGoogle Scholar
  53. Perkins, J. M., and J. L. Jinks. 1970. Detection and estimation of genotype-environmental linkage and epistatic components of variation for a metrical trait. Heredity 25:157–77.CrossRefGoogle Scholar
  54. Rawlings, J., and C. C. Cockerham. 1962a. Triallel analysis. Crop Sci. 2:228–31.CrossRefGoogle Scholar
  55. Rawlings, J., and C. C. Cockerham. 1962b. Analysis of double cross hybrid populations. Biometrics 18:229–44.CrossRefGoogle Scholar
  56. Robinson, H. F., and C. C. Cockerham. 1961. Heterosis and inbreeding depression in populations involving two open-pollinated varieties of maize. Crop Sci. 1:68–71.CrossRefGoogle Scholar
  57. Robinson, H. F., R. E. Comstock, and P. H. Harvey. 1949. Estimates of heritability and the degree of dominance in corn. Agron. J. 41:353–59.CrossRefGoogle Scholar
  58. Satterthwaite, F. E. 1946. An approximate distribution of estimates of variance components. Biom. Bull. 2:110–14.CrossRefGoogle Scholar
  59. Schnell, F. W. 1963. The covariance between relatives in the presence of linkage. In Statistical Genetics and Plant Breeding, W. D. Hanson and H. F. Robinson, (eds.), pp. 468–83. NAS-NRC Publ. 982. NAS-NRC.Google Scholar
  60. Searle, S. R. 1971. Topics in variance component estimation. Biometrics 27:1–74.CrossRefGoogle Scholar
  61. Silva, J. C., and A. R. Hallauer. 1975. Estimation of epistatic variance in Iowa Stiff Stalk Synthetic maize. J. Hered. 66:290–96.Google Scholar
  62. Smith, J. D., and M. L. Kinman. 1965. The use of parent-offspring regression as an estimator of heritability. Crop Sci. 5:595–96.CrossRefGoogle Scholar
  63. Snedecor, G. W. 1956. Statistical Methods. Iowa State University Press, Ames, IA.Google Scholar
  64. Sokol, M. J., and R. J. Baker. 1977. Evaluation of the assumptions required for the genetic interpretation of diallel experiments in self-pollinated crops. Canadian J. Plant Sci. 57:1185–91.CrossRefGoogle Scholar
  65. Sprague, G. F., and L. A. Tatum. 1942. General vs. specific combining ability in single crosses of corn. J. Am. Soc. Agron. 34:923–32.CrossRefGoogle Scholar
  66. Stuber, C. W. 1970. Estimation of genetic variances using inbred relatives. Crop Sci. 10:129–35.CrossRefGoogle Scholar
  67. Warner, J. N. 1952. A method for estimating heritability. Agron. J. 44:427–30.CrossRefGoogle Scholar
  68. Wolf, D. P., and A. R. Hallauer. 1997. Triple testcross analysis to detect epistasis in maize. Crop Sci. 37:763–70.CrossRefGoogle Scholar
  69. Wolf, D. P., L. A. Peternelli, and A. R. Hallauer. 2000. Estimates of genetic variance in an F2 maize population. J. Hered. 91:384–91.PubMedCrossRefGoogle Scholar
  70. Wright, J. A., A. R. Hallauer, L. H. Penny, and S. A. Eberhart. 1971. Estimating genetic variance in maize by use of single and three-way crosses among unselected inbred lines. Crop Sci. 11:690–95.CrossRefGoogle Scholar
  71. Yang, J., M. J. Carena, and J. Uphaus. 2010. AUDCC: A method to evaluate rate of dry down in maize. Crop Sci. (in press).Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Arnel R. Hallauer
    • 1
  • J. B. Miranda Filho
    • 2
  • Marcelo J. Carena
    • 3
  1. 1.Department of AgronomyIowa State UniversityAmesUSA
  2. 2.University of São PauloSão PauloBrazil
  3. 3.Department of Plant Sciences #7670North Dakota State UniversityFargoUSA

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