Relationship inference based on DNA mixtures


Today, there exists a number of tools for solving kinship cases. But what happens when information comes from a mixture? DNA mixtures are in general rarely seen in kinship cases, but in a case presented to the Norwegian Institute of Public Health, sample DNA was obtained after a rape case that resulted in an unwanted pregnancy and abortion. The only available DNA from the fetus came in form of a mixture with the mother, and it was of interest to find the father of the fetus. The mother (the victim), however, refused to give her reference data and so commonly used methods for paternity testing were no longer applicable. As this case illustrates, kinship cases involving mixtures and missing reference profiles do occur and make the use of existing methods rather inconvenient. We here present statistical methods that may handle general relationship inference based on DNA mixtures. The basic idea is that likelihood calculations for mixtures can be decomposed into a series of kinship problems. This formulation of the problem facilitates the use of kinship software. We present the freely available R package relMix which extends on the R version of Familias. Complicating factors like mutations, silent alleles, and θ-correction are then easily handled for quite general family relationships, and are included in the statistical methods we develop in this paper. The methods and their implementations are exemplified on the data from the rape case.

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  1. 1.

    Brenner C DNA-view.

  2. 2.

    Kling D, Tilmar A, Egeland T (2014) Familias 3—extensions and new functionality. Forensic Sci Int Genet 13:121–127

    Article  CAS  PubMed  Google Scholar 

  3. 3.

    Mostad P, Egeland T (2015) Familias, Probabilities for Pedigrees Given DNA Data., R version 2.2

  4. 4.

    Butler JM (2011) Advanced Topics in Forensic DNA Typing: Methodology. Academic Press

  5. 5.

    Buckleton JS, Triggs CM, Walsh SJ (2005) Forensic DNA evidence interpretation. CRC press

  6. 6.

    Team R (2014) Core: R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing; 2012, Open access available at:

  7. 7.

    Egeland T, Dørum G, Vigeland MD, Sheehan NA (2014) Mixtures with relatives: a pedigree perspective. Forensic Sci Int Genet 10:49–54

    Article  PubMed  Google Scholar 

  8. 8.

    Fung WK, Hu Y-Q (2008) Statistical DNA forensics: theory, methods and computation. Wiley, Statistics in practice

    Google Scholar 

  9. 9.

    Hu Y-Q, Fung WK, Choy YT (2011) Interpreting DNA mixtures with relatives of a missing suspect. In: Remote Sensing, Environment and Transportation Engineering (RSETE), 2011 International Conference on. IEEE, pp 7649–7652

  10. 10.

    Kling D, Egeland T, Mostad P (2012) Using object oriented bayesian networks to model linkage, linkage disequilibrium and mutations between STR markers. PloS one 7(9):e43873

    PubMed Central  Article  CAS  PubMed  Google Scholar 

  11. 11.

    Dawid AP, Mortera J, Vicard P (2007) Object-oriented Bayesian networks for complex forensic DNA profiling problems. Forensic Sci Int 169(2):195–205

    Article  CAS  PubMed  Google Scholar 

  12. 12.

    Balding DJ (2005) Weight-of-evidence for Forensic DNA Profiles. Statistics in practice. Wiley

  13. 13.

    Steele CD, Balding DJ (2014) Statistical evaluation of forensic DNA profile evidence. In: Annual Review of Statistics and Its Application, vol 1, pp 361–384

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Correspondence to Navreet Kaur.

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Kaur, N., Bouzga, M.M., Dørum, G. et al. Relationship inference based on DNA mixtures. Int J Legal Med 130, 323–329 (2016).

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  • DNA mixtures
  • Kinship analysis
  • Unknown reference profiles
  • Likelihood ratios