Biometrical Models in Behavioral Genetics

The main goal of this chapter is to describe the research designs and statistical methods that are in popular use in behavioral genetics (BG). We begin with a brief overview of the historical background to BG in general and twin studies in particular. Next, we describe some elementary statistics required for understanding biometrical modeling. Then follows a statistical model for genetic variation, as articulated by Fisher in his classic 1918 paper, in which additive and dominance genetic variance terms are defined. The coefficients of resemblance between relatives derived from this model are then implemented in structural equation models for the analysis of data from twins and other relatives. Overall the intent is to provide a general and extensible infrastructure for the modeling of genetically informative data.


Twin Pair Behavior Genetic Path Diagram Behavioral Genetic Twin Data 


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  1. Aitken, A. C. (1934). Note on selection from a multivariate normal population. Proceedings of the Edinburgh Mathematical Society B, 4, 106–110.CrossRefGoogle Scholar
  2. Bodmer, W. F. (1987). HLA, immune response, and disease. In F. Vogel & K. Sperling (Eds.), Human genetics: Proceedings of the 7th international congress (pp. 107–113). New York: Springer-Verlag.Google Scholar
  3. Bollen, K. A. (1989). Structural equations with latent variables. New York: John Wiley.Google Scholar
  4. Busjahn, A., & Hur, Y.-M. (2006). Twin registries: An ongoing success story. Twin Res Hum Genet, 9(6), 705.PubMedCrossRefGoogle Scholar
  5. Carey, G. (1986). A general multivariate approach to linear modeling in human genetics. American Journal of Human Genetics, 39, 775–786.PubMedGoogle Scholar
  6. Casella, G., & George, E. I. (1992). Explaining the gibbs sampler. The American Statistician, 46, 167–174.CrossRefGoogle Scholar
  7. Caspi, A., Harrington, H., Moffitt, T. E., Milne, B. J., & Poulton, R. (2006). Socially isolated children 20 years later: Risk of cardiovascular disease. Archives of Pediatrics Adolescent Medicine, 160(8), 805–811.PubMedCrossRefGoogle Scholar
  8. Castle, W. E. (1903). The law of heredity of Galton and Mendel and some laws governing race improvement by selection. Proceedings of the American Academy of Sciences, 39, 233–242.Google Scholar
  9. Crow, J. F., & Kimura, M. (1970). Introduction to population genetics theory. New York: Harper and Row.Google Scholar
  10. Cudeck, R., du Toit, S. H. C., & Sorbom, D. (2001). Structural equation modeling: Present and future. Chicago: Scientific Software International.Google Scholar
  11. Darwin, C. (1859). On the origin of species by means of natural selection. London: John Murray.Google Scholar
  12. Darwin, C. (1871). The descent of man, and selection in relation to sex. London: John Murray.Google Scholar
  13. Defries, J., Gervais, M., & Thomas, E. (1978). Response to 30 generations of selection for open-field activity in laboratory mice. Behavior Genetics, 8(1), 3–13.PubMedCrossRefGoogle Scholar
  14. DeFries, J. C., & Fulker, D. W. (1988). Multiple regression analysis of twin data: Etiology of deviant scores versus individual differences. Acta Genet Med Gemellol (Roma), 37(3–4), 205–216.Google Scholar
  15. Duffy, D. L., & Martin, N. G. (1994). Inferring the direction of causation in cross-sectional twin data: Theoretical and empirical considerations. Genetic Epidemiology, 11(6), 483–502.PubMedCrossRefGoogle Scholar
  16. Eaves, L., & Erkanli, A. (2003). Markov chain monte carlo approaches to analysis of genetic and environmental components of human developmental change and g x e interaction. Behavior Genetics, 33(3), 279–299.PubMedCrossRefGoogle Scholar
  17. Eaves, L., Foley, D., & Silberg, J. (2003). Has the ‘equal environments’ assumption been tested in twin studies? Twin Research, 6(6), 486–489.PubMedCrossRefGoogle Scholar
  18. Eaves, L. J. (1976). A model for sibling effects in man. Heredity, 36, 205–214.PubMedCrossRefGoogle Scholar
  19. Eaves, L. J., Long, J., & Heath, A. C. (1986). A theory of developmental change in quantitative phenotypes applied to cognitive development. Behavior Genetics, 16, 143–162.PubMedCrossRefGoogle Scholar
  20. Eaves, L. J., Neale, M. C., & Maes, H. (1996). Multivariate multipoint linkage analysis of quantitative trait loci. Behavior Genetics, 26, 519–525.PubMedCrossRefGoogle Scholar
  21. Edwards, A. L. (1979). Multiple regression and the analysis of variance and covariance. San Francisco, CA: W. H. Freeman.Google Scholar
  22. Falconer, D. S. (1960). Quantitative genetics. Edinburgh: Oliver and Boyd.Google Scholar
  23. Falconer, D. S. (1990). Introduction to quantitative genetics (3rd ed.). New York: Longman Group Ltd.Google Scholar
  24. Fisher, R. A. (1912). On an absolute criterion for fitting frequency curves. Messenger of Mathematics, 41, 155–160.Google Scholar
  25. Fisher, R. A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Translations of the Royal Society, Edinburgh, 52, 399–433.Google Scholar
  26. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A, 222, 309–368.CrossRefGoogle Scholar
  27. Fulker, D. W. (1988). Genetic and cultural transmission in human behavior. In B. S. Weir, E. J. Eisen, M. M. Goodman, & G. Namkoong (Eds.), Proceedings of the second international conference on quantitative genetics (pp. 318–340). Sunderland, MA: Sinauer.Google Scholar
  28. Fulker, D. W., Baker, L. A., & Bock, R. D. (1983). Estimating components of covariance using LISREL. Data Analyst, 1, 5–8.Google Scholar
  29. Fulker, D. W., & Cardon, L. R. (1994). A sib-pair approach to interval mapping of quantitative trait loci. American Journal of Human Genetics, 54(6), 1092–1103.PubMedGoogle Scholar
  30. Fulker, D. W., & Cherny, S. S. (1996). An improved multipoint sib-pair analysis of quantitative traits. Behavior Genetics, 26, 527–532.PubMedCrossRefGoogle Scholar
  31. Fuller, J. L., & Herman, B. H. (1974). Effect of genotype and practice upon behavioral development in mice. Developmental Psychobiology, 7, 21–30.PubMedCrossRefGoogle Scholar
  32. Fuller, J. L., & Thompson, W. R. (1978). Foundations of behavior genetics. St. Louis: C. V. Mosby.Google Scholar
  33. Gale, J. S. (1980). Population genetics. New York: J. Wiley.Google Scholar
  34. Galton, F. (1875). The history of twins, as a criterion of the relative powers of nature and nurture. Journal of the Anthropological Institute, 12, 566–576.Google Scholar
  35. Geman, S., & Geman, D. (1984). Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741.CrossRefGoogle Scholar
  36. Gillespie, N. A., Kendler, K. S., Prescott, C. A., Aggen, S. H., Gardner, C. O. J., Jacobson, K., et al. (2007). Longitudinal modeling of genetic and environmental influences on self-reported availability of psychoactive substances: Alcohol, cigarettes, marijuana, cocaine and stimulants. Psychological Medicine, 37(7), 947–959.PubMedCrossRefGoogle Scholar
  37. Goldsmith, H. H., Lemery-Chalfant, K., Schmidt, N. L., Arneson, C. L., & Schmidt, C. K. (2007). Longitudinal analyses of affect, temperament, and childhood psychopathology. Twin Research and Human Genetics, 10(1), 118–126.PubMedCrossRefGoogle Scholar
  38. Gordon, K (1919). Report on psychological tests of orphan children. Journal of Deliquency, 4, 45–55.Google Scholar
  39. Gottesman, I. I., & Gould, T. D. (2003). The endophenotype concept in psychiatry: Etymology and strategic intentions. American Journal of Psychiatry, 160(4), 636–645.PubMedCrossRefGoogle Scholar
  40. Heath, A. C. (1987). The analysis of marital interaction in cross-sectional twin data. Acta Geneticae Medicae et Gemellologiae, 36, 41–49.PubMedGoogle Scholar
  41. Heath, A. C., Kessler, R. C., Neale, M. C., Hewitt, J. K., Eaves, L. J., & Kendler, K. S. (1993). Testing hypotheses about direction of causation using cross-sectional family data. Behavior Genetics, 23(1), 29–50.PubMedCrossRefGoogle Scholar
  42. Jöreskog, K. G. (1967). Some contributions to maximum likelihood factor analysis. Psychometrika, 32, 443–482.CrossRefGoogle Scholar
  43. Keller, M. C., & Coventry, W. L. (2005). Quantifying and addressing parameter indeterminacy in the classical twin design. Twin Research and Human Genetics, 8(3), 201–213.PubMedCrossRefGoogle Scholar
  44. Kempthorne, O. (1960). Biometrical genetics. New York: Pergammon Press.Google Scholar
  45. Kendler, K. S., & Kidd, K. K. (1986). Recurrence risks in an oligogenic threshold model: The effect of alterations in allele frequency. Annals of Human Genetics, 50 (Pt 1), 83–91.PubMedCrossRefGoogle Scholar
  46. LaBuda, M. C., DeFries, J. C., & Fulker, D. W. (1986). Multiple regression analysis of twin data obtained from selected samples. Genetic Epidemiology, 3, 425–433.PubMedCrossRefGoogle Scholar
  47. Lawley, D. (1940). The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society of Edinburgh, 60, 64–82.Google Scholar
  48. Lehmann, E. L. (1998). Elements of large-sample theory. New York: Springer.Google Scholar
  49. Li, T.-K., Lumeng, L., & Doolittle, D. (1993). Selective breeding for alcohol preference and associated responses. Behavior Genetics, 23(2), 163–170.PubMedCrossRefGoogle Scholar
  50. Loehlin, J. (1996). The cholesky approach: A cautionary note. Behavior Genetics, 26, 65–69.CrossRefGoogle Scholar
  51. Lynch, M., & Walsh, B. (1998). Genetics and analysis of quantitative traits. Sunderland, MA: Sinauer.Google Scholar
  52. Maes, H. H., Neale, M. C., Kendler, K. S., Martin, N. G., Heath, A. C., & Eaves, L. J. (2006). Genetic and cultural transmission of smoking initiation: an extended twin kinship model. Behavior Genetics, 36(6), 795–808.PubMedCrossRefGoogle Scholar
  53. Mann, C. C. (1994). Behavioral genetics in transition. Science, 264(5166), 1686–1689.PubMedCrossRefGoogle Scholar
  54. Martin, N. G., & Eaves, L. J. (1977). The genetical analysis of covariance structure. Heredity, 38, 79–95.PubMedCrossRefGoogle Scholar
  55. Mather, K., & Jinks, J. L. (1971). Biometrical genetics. London: Chapman and Hall.Google Scholar
  56. Mather, K., & Jinks, J. L. (1977). Introduction to biometrical genetics. Ithaca, New York: Cornell University Press.Google Scholar
  57. Mather, K., & Jinks, J. L. (1982). Biometrical genetics: The study of continuous variation (3rd ed.). London: Chapman and Hall.Google Scholar
  58. Maxwell, A. E. (1977). Multivariate analysis in behavioral research. New York: John Wiley.Google Scholar
  59. McArdle, J. J., & Boker, S. M. (1990). Rampath path diagram software. Denver, CO: Data Transforms Inc.Google Scholar
  60. McArdle, J. J., & Goldsmith, H. H. (1990). Alternative common factor models for multivariate biometric analyses. Behavior Genetics, 20(5), 569–608.PubMedCrossRefGoogle Scholar
  61. McArdle, J. J., & Prescott, C. A. (2005). Mixed-effects variance components models for biometric family analyses. Behavior Genetics, 35(5), 631–652.PubMedCrossRefGoogle Scholar
  62. Merriman, C. (1924). The intellectual resemblance of twins. Psychological Monographs, 33, 1–58.Google Scholar
  63. Mullis, K. (1990). The unusual origin of the polymerase chain reaction. Scientific American, 262(4), 56–61, 64–5.PubMedCrossRefGoogle Scholar
  64. Nance, W. E., & Neale, M. C. (1989). Partitioned twin analysis: A power study. Behavior Genetics, 19, 143–150.PubMedCrossRefGoogle Scholar
  65. Neale, M. C. (2000). Individual fit, heterogeneity, and missing data in multigroup sem. In T. D. Little, K. U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multiple-group data: Practical issues, applied approaches, and specific examples. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  66. Neale, M. C. (2003a). Twins studies: Software and algorithms. In D. N. Cooper & N. J. Hoboken (Eds.), Encyclopedia of the human genome. Macmillan Publishers Ltd, Nature Publishing Group, London, p.88–96.Google Scholar
  67. Neale, M. C. (2003b). A finite mixture distribution model for data collected from twins. Twin Research, 6(3), 235–239.Google Scholar
  68. Neale, M., Boker, S., Bergeman, C., & Maes, H. (2005). The utility of genetically informative data in the study of development. In S. Boker & C. Bergeman (Eds.), Notre dame quantitative methods in psychology. New York: Erlbaum.Google Scholar
  69. Neale, M., Boker, S., Xie, G., & Maes, H. (2003). Mx: Statistical modeling (6th ed.). Box 980126 Richmond VA: Department of Psychiatry, Virginia Commonwealth University.Google Scholar
  70. Neale, M. C., & Cardon, L. R. (1992). Methodology for genetic studies of twins and families. Dordrecht: Kluwer Academic Publishers.Google Scholar
  71. Neale, M. C., & Kendler, K. S. (1995). Models of comorbidity for multifactorial disorders. American Journal of Human Genetics, 57(4), 935–953.PubMedGoogle Scholar
  72. Neale, M. C., & McArdle, J. J. (2000). Structured latent growth curves for twin data. Twin Research, 3, 165–77.PubMedCrossRefGoogle Scholar
  73. Neale, M.C., Walters, E., Health, A. C., Kessler, R. C., Perusse, D., Eaves, L. J.; et al. (1994). Depression and parental bonding: cause, consequence, or genetic covariance? Genetic Epidemiology, 11(6), 503–522.PubMedCrossRefGoogle Scholar
  74. Pearson, K. (1901). Mathematical contributions to the theory of evolution. VII. On the correlation of characters not quantitatively measurable. Proceedings of the Royal Society, 66, 241–244.CrossRefGoogle Scholar
  75. Pearson, K. (1904). On a generalized theory of alternative inheritance, with special references to Mendel’s laws. Philosophical Transactions of the Royal Society A, 203, 53–86.CrossRefGoogle Scholar
  76. Purcell, S. (2002). Variance components models for gene-environment interaction in twin analysis. Twin Research, 5(6), 554–571.PubMedCrossRefGoogle Scholar
  77. Rabe-Hesketh, S., Skrondal, A., & Gjessing, H. (2008). Biometrical modeling of twin and family data using standard mixed model software. Biometrics, 64, 280–288.PubMedCrossRefGoogle Scholar
  78. Rende, R. D., Polmin, R., & Vandenberg, S. G. (1990). Who discovered the twin method? Behavior Genetics, 20(2), 277–285.PubMedCrossRefGoogle Scholar
  79. Risch, N. (2001). The genetic epidemiology of cancer: Interpreting family and twin studies and their implications for molecular genetic approaches. Cancer Epidemiology Biomakers Prevention, 10(7), 733–741.Google Scholar
  80. Sörbom, D. (1974). A general method for studying differences in factor means and factor structures between groups. British Journal of Mathematical and Statistical Psychology, 27, 229–239.Google Scholar
  81. Steiger, J. H. (1990). Structural model evaluation and modification: An interval estimation approach. Multivariate Behavioral Research, 25, 173–180.CrossRefGoogle Scholar
  82. Thorndike, E. L. (1905). Measurement of twins. Archieves of Philosophy, Psychology and Scientific Methods, 1, 1–64.Google Scholar
  83. Tryon, R. C. (1941). Studies in individual differences in maze ability. x. ratings and other measures of initial emotional responses of rats to novel inanimate objects. Journal of Comparative Psychology, 32, 447–473.CrossRefGoogle Scholar
  84. Visscher, P. M., Medland, S. E., Ferreira, M. A., Morley, K. I., Zhu, G., Cornes, B. K., et al. (2006). Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings. PLoS Genetics, 2(3), e41.Google Scholar
  85. Watson, J. D., & Crick, F. H. (1953). Genetical implications of the structure of deoxyribonucleic acid. Nature, 171(4361), 964–967.PubMedCrossRefGoogle Scholar
  86. Wright, S. (1921). Correlation and causation. Journal of Agricultural Research, 20, 557–585.Google Scholar
  87. Wright, S. (1934). The method of path coefficients. Annals of Mathematical Statistics, 5, 161–215.CrossRefGoogle Scholar
  88. Wright, S. (1968). Evolution and the genetics of populations. Volume 1. Genetic and Biometric foundations. Chicago: University of Chicago Press.Google Scholar
  89. Yule, G. U. (1902). Mendel’s laws and their probable relation to intra-racial heredity. New Phytology, 1, 192–207.Google Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Departments of Psychiatry and Human GeneticsVirginia Institute for Psychiatric and Behavioral Genetics, Virginia Commonwealth UniversityRichmondUSA

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