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Genetic Identity Coefficients

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Book cover Applied Probability

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Abstract

Genetic identity coefficients are powerful theoretical tools for genetic analysis. Geneticists have devised these indices to measure the degree of inbreeding of a single individual and the degree of relatedness of a pair of relatives. Since the degree of inbreeding of a single individual can be summarized by the relationship between his or her parents, we will focus on identity coefficients for relative pairs. These coefficients pertain to a generic autosomal locus and depend only on the relevant pedigree connecting two relatives and not on any phenotypes observed in the pedigree. In Chapter 6 we will investigate the applications of identity coefficients. Readers desiring motivation for the combinatorial problems attacked here may want to glance at Chapter 6 first.

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5.8 References

  1. Cotterman CW (1940) A Calculus for Statistico-Genetics. Ph.D. thesis, Ohio State University, in Genetics and Social Structure: Mathematical Structuralism in Population Genetics and Social Theory. (1974) Ballonoff PA, editor, Dowden, Hutchinson & Ross, Stroudsburg, PA, pp 155–272

    Google Scholar 

  2. Gillois M (1964) La relation d’identité en génétique. Ann Inst Henri Poincaré B 2:1–94

    MathSciNet  Google Scholar 

  3. Harris DL (1964) Genotypic covariances between inbred relatives. Genetics 50:1319–1348

    Google Scholar 

  4. Henderson CR (1976) A simple method for computing the inverse of the numerator relationship matrix used in prediction of breeding values. Biometrics 32:69–83

    Article  MATH  Google Scholar 

  5. Jacquard A (1966) Logique du calcul des coefficients d’identité entre deux individus. Population (Paris) 21:751–776

    Google Scholar 

  6. Jacquard A (1974) The Genetic Structure of Populations. Springer-Verlag, New York

    MATH  Google Scholar 

  7. Karigl G (1981) A recursive algorithm for the calculation of identity coefficients. Ann Hum Genet 45:299–305

    Article  MATH  MathSciNet  Google Scholar 

  8. Karigl G (1982) Multiple genetic relationships: joint and conditional genotype probabilities. Ann Hum Genet 46:83–92

    Article  MATH  MathSciNet  Google Scholar 

  9. Lange K, Sinsheimer JS (1992) Calculation of genetic identity coefficients. Ann Hum Genet 56:339–346

    Article  MATH  Google Scholar 

  10. Lange K, Westlake J, Spence MA (1976) Extensions to pedigree analysis. II. Recurrence risk calculation under the polygenic threshold model. Hum Hered 26:337–348

    Google Scholar 

  11. Lange K, Westlake J, Spence MA (1976) Extensions to pedigree analysis. III. Variance components by the scoring method. Ann Hum Genet 39:485–491

    Article  Google Scholar 

  12. Malécot G (1948) Les Mathématiques de I’Hérédité. Masson et Cie, Paris

    Google Scholar 

  13. Nadot R, Vaysseix G (1973) Apparentement et identityé. Algorithme du calcul des coefficients d’identité, Biometrics 29:347–359

    Article  Google Scholar 

  14. Thompson EA (1983) Gene extinction and allelic origins in complex genealogies. Proc R Soc London B 219:241–251

    Article  Google Scholar 

  15. Thompson EA (1986) Pedigree Analysis in Human Genetics. Johns Hopkins University Press, Baltimore

    Google Scholar 

  16. Thompson EA, Shaw RG (1990) Pedigree analysis for quantitative traits: Variance components without matrix inversion. Biometrics 46:399–413

    Article  MATH  Google Scholar 

  17. Weeks DE, Lange K (1988) The affected-pedigree-member method of linkage analysis. Amer J Hum Genet 42:315–326

    Google Scholar 

  18. Weeks DE, Valappil TI, Schroeder M, Brown DL (1995) An X-linked version of the affected pedigree member method of linkage analysis. Hum Hered 45:25–33

    Google Scholar 

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© 2003 Springer-Verlag New York, Inc.

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(2003). Genetic Identity Coefficients. In: Applied Probability. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-22711-5_5

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  • DOI: https://doi.org/10.1007/978-0-387-22711-5_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-00425-9

  • Online ISBN: 978-0-387-22711-5

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