Acta Mathematica Hungarica

, Volume 139, Issue 1–2, pp 160–182 | Cite as

Multifactorial inheritance with selection

  • Balázs Gerencsér
  • Balázs Ráth
  • Gábor Tusnády
Article

Abstract

We present an alternative model for multifactorial inheritance. By changing the way the malformation (and selection) is determined from the genetic information, we arrive at a model that can be properly handled in the mathematical sense. This includes the proof of population convergence and computation of conditional malformation probabilities in a closed form. We also present a comparison to similar models and results of fitting our model to Hungarian data.

Key words and phrases

multifactorial inheritance birth defect balance of selection and mutation 

Mathematics Subject Classification

62P10 92D25 

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References

  1. [1]
    E. Czeizel and G. Tusnády, Aetiological Studies of Isolated Common Congenital Abnormalities in Hungary, Akadémiai Kiadó (Budapest, 1984). Google Scholar
  2. [2]
    J. Edwards, The genetic basis of common disease, Am. J. Med., 34 (1963), 627–638. CrossRefGoogle Scholar
  3. [3]
    L. Hatvani, F. Toókos and G. Tusnády, A mutation-selection-recombination model in population genetics, Dyn. Syst. Appl., 18 (2009), 335–362. MATHGoogle Scholar
  4. [4]
    S. Karlin, Models of multifactorial inheritance: I, multivariate formulations and basic convergence results* 1, Theor. Popul. Biol., 15 (1979), 308–355. MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    A. Mukherjea, M. Rao and S. Suen, A note on moment generating functions, Stat. Probab. Lett., 76 (2006), 1185–1189. MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    K. Sankaranarayanan, N. Yasuda, R. Chakraborty, G. Tusnády and A. Czeizel, Ionizing radiation and genetic risks. V. Multifactorial diseases: A review of epidemiological and genetic aspects of congenital abnormalities in man and of models on maintenance of quantitative traits in populations, Mutat. Res., Rev. Genet. Toxicol., 317 (1994), 1–23. CrossRefGoogle Scholar
  7. [7]
    G. Tusnády, Mutation and selection, Magy. Tud., 7 (1997), 792–805 (in Hungarian). Google Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  • Balázs Gerencsér
    • 1
  • Balázs Ráth
    • 2
  • Gábor Tusnády
    • 1
  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.ETH ZürichZürichSwitzerland

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