Mixtures with relatives and linked markers


Mixture DNA profiles commonly appear in forensic genetics, and a large number of statistical methods and software are available for such cases. However, most of the literature concerns mixtures where the contributors are assumed unrelated and the genetic markers are unlinked. In this paper, we consider mixtures of linked markers and related contributors. If no relationships are involved, linkage can be ignored. While unlinked markers can be treated independently, linkage introduces dependencies. The use of linked markers presents statistical and computational challenges, but may also lead to a considerable increase in power since the number of markers available is much larger if we do not require the markers to be unlinked. In addition, some cases that cannot be solved with an unlimited number of unlinked autosomal markers can be solved with linked markers. We focus on two special cases of linked markers: pairs of linked autosomal markers and X-chromosomal markers. A framework is presented for calculation of likelihood ratios for mixtures with general relationships and with linkage between any number of markers. Finally, we explore the effect of linkage disequilibrium, also called allelic association, on the likelihood ratio.

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  1. 1.

    Abecasis G, Cherny S, Cookson W, Cardon L (2002) Merlin-rapid analysis of dense genetic maps using sparse gene flow trees. Nat Genet 30:97–101

    Article  CAS  PubMed  Google Scholar 

  2. 2.

    Boyles A, Scott W, Martin E, Schmidt S, Li Y, Ashley-Koch A, Bass M, Schmidt M, Pericak-Vance M, Speer M, Hauser E (2005) Linkage disequilibrium inflates type I error rates in multipoint linkage analysis when parental genotypes are missing. Hum Hered 59(4):220–227. doi:10.1159/000087122

    Article  PubMed  PubMed Central  Google Scholar 

  3. 3.

    Bright J-A, Curran JM, Buckleton JS (2013) Relatedness calculations for linked loci incorporating subpopulation effects. Forensic Sci Int: Genet 7(3):380–383. doi:10.1016/j.fsigen.2013.03.002

    Article  CAS  Google Scholar 

  4. 4.

    Buckleton J, Triggs C, Walsh S (eds) (2005) Forensic DNA evidence interpretation. CRC Press

  5. 5.

    Curran J, Triggs C, Buckleton J, Weir B (1999) Interpreting DNA mixtures in structured populations. J Forensic Sci 44(5):987– 995

    Article  CAS  PubMed  Google Scholar 

  6. 6.

    Daniel R, Santos C, Phillips C, Fondevila M, van Oorschot R, Carracedo Á., Lareu M, McNevin D (2015) A SNaPshot of next generation sequencing for forensic SNP analysis. Forensic Sci Int: Genet 14(0):50–60

    Article  CAS  Google Scholar 

  7. 7.

    Dawid A, Mortera J, Pascali VL (2001) Non-fatherhood or mutation?: a probabilistic approach to parental exclusion in paternity testing. Forensic Sci Int 124(1):55–61. doi:10.1016/S0379-0738(01)00564-3

    Article  CAS  PubMed  Google Scholar 

  8. 8.

    Egeland T, Sheehan N (2008) On identification problems requiring linked autosomal markers. Forensic Sci Int: Genet 2(3):219–225. doi:10.1016/j.fsigen.2008.02.006

    Article  Google Scholar 

  9. 9.

    Egeland T, Dørum G, Vigeland MD, Sheehan NA (2014) Mixtures with relatives: a pedigree perspective. Forensic Sci Int: Genet 10:49–54. doi:10.1016/j.fsigen.2014.01.007

    Article  Google Scholar 

  10. 10.

    Fung WK, Hu YQ (2004) Interpreting DNA mixtures with related contributors in subdivided populations. Scand J Stat 31(1):115–130. doi:10.1111/j.1467-9469.2004.00376.x

    Article  Google Scholar 

  11. 11.

    Fung WK, Hu YQ (2008) Statistical DNA Forensics: Theory, methods and computation. Wiley, England

    Google Scholar 

  12. 12.

    Hu YQ, Fung W (2005) Evaluation of DNA mixtures involving two pairs of relatives. Int J Legal Med 119 (5):251–259. doi:10.1007/s00414-004-0493-9

    Article  PubMed  Google Scholar 

  13. 13.

    Huang Q, Shete S, Amos C (2004) Ignoring linkage disequilibrium among tightly linked markers induces false-positive evidence of linkage for affected sib pair analysis. Am J Human Genet 75(6):1106–1112. doi:10.1086/426000

    Article  CAS  Google Scholar 

  14. 14.

    Kling D, Tillmar A, Egeland T, Mostad P (2014) A general model for likelihood computations of genetic marker data accounting for linkage, linkage disequilibrium, and mutations. International Journal of Legal Medicine, pp 1–12. doi:10.1007/s00414-014-1117-7

  15. 15.

    Kling D, Dell’Amico B, Tillmar AO (2015) Famlinkx—implementation of a general model for likelihood computations for x-chromosomal marker data. Forensic Sci Int: Genet 17:1–7. doi:10.1016/j.fsigen.2015.02.007

    Article  CAS  Google Scholar 

  16. 16.

    Kong A, Thorleifsson G, Gudbjartsson DF, Masson G, Sigurdsson A, Jonasdottir A, Walters GB, Jonasdottir A, Gylfason A, Kristinsson KT, Gudjonsson SA, Frigge ML, Helgason A, Thorsteinsdottir U, Stefansson K (2010) Fine-scale recombination rate differences between sexes, populations and individuals. Nature 467(7319):1099–1103. doi:10.1038/nature09525

    Article  CAS  PubMed  Google Scholar 

  17. 17.

    Kruijver M (2015) Efficient computations with the likelihood ratio distribution. Forensic Sci Int: Genet 14:116–124. doi:10.1016/j.fsigen.2014.09.018

    Article  Google Scholar 

  18. 18.

    Lancia M, Severini S, Coletti A, Margiotta G, Dobosz M, Carnevali E (2011) Using x-chromosomal markers in rape investigation. Forensic Sci Int: Genet Suppl Ser 3(1):e55 – e56. doi:10.1016/j.fsigss.2011.08.027

    Google Scholar 

  19. 19.

    Mayor LR, Balding DJ (2006) Discrimination of half-siblings when maternal genotypes are known. Forensic Sci Int 159:141–147. doi:10.1016/j.forsciint.2005.07.007

    Article  CAS  PubMed  Google Scholar 

  20. 20.

    Nothnagel M, Szibor R, Vollrath O, Augustin C, Edelmann J, Geppert M, Alves C, Gusmao L, Vennemann M, Hou Y, Immel U-D, Inturri S, Luo H, Lutz-Bonengel S, Robino C, Roewer L, Rolf B, Sanft J, Shin K-J, Sim JE, Wiegand P, Winkler C, Krawczak M, Hering S (2012) Collaborative genetic mapping of 12 forensic short tandem repeat (STR) loci on the human X chromosome. Forensic Sci Int: Genet 6(6):778–784. doi:10.1016/j.fsigen.2012.02.015

    Article  CAS  Google Scholar 

  21. 21.

    O’Connor KL, Tillmar AO (2012) Effect of linkage between vWA and D12s391 in kinship analysis. Forensic Sci Int: Genet 6(6):840–844. doi:10.1016/j.fsigen.2012.03.008

    Article  CAS  Google Scholar 

  22. 22.

    Phillips C, Fernandez-Formoso L, Garcia-Magariños M, Porras L, Tvedebrink T, Amigo J, Fondevila M, Gomez-Tato A, Alvarez-Dios J, Freire-Aradas A, Gomez-Carballa A, Mosquera-Miguel A, Carracedo Á, Lareu M (2011) Analysis of global variability in 15 established and 5 new european standard set (ESS) STRs using the CEPH human genome diversity panel. Forensic Sci Int: Genet 5(3):155–169. doi:10.1016/j.fsigen.2010.02.003

    Article  CAS  Google Scholar 

  23. 23.

    Skare O, Sheehan N, Egeland T (2009) Identification of distant family relationships. Bioinformatics 25 (18):2376–2382. doi:10.1093/bioinformatics/btp418

    Article  CAS  PubMed  Google Scholar 

  24. 24.

    Slooten K-J, Egeland T (2015) Exclusion probabilities and likelihood ratios with applications to mixtures. Int J Legal Med:1–19. doi:10.1007/s00414-015-1217-z

  25. 25.

    Szibor R (2007) X-chromosomal markers: Past, present and future. Forensic Sci Int: Genet 1(2, SI):93–99. doi:10.1016/j.fsigen.2007.03.003

    Article  Google Scholar 

  26. 26.

    Szibor R, Krawczak M, Hering S, Edelmann J, Kuhlisch E, Krause D (2003) Use of x-linked markers for forensic purposes. Int J Legal Med 117(2):67–74. doi:10.1007/s00414-002-0352-5

    Article  CAS  PubMed  Google Scholar 

  27. 27.

    Thompson E (1986) Pedigree analysis in human genetics. The Johns Hopkins University Press, Baltimore

    Google Scholar 

  28. 28.

    Thompson EA (1975) The estimation of pairwise relationships. Ann Human Genet 39(2):173–88

    Article  CAS  Google Scholar 

  29. 29.

    Thompson EA (2000) Statistical Inference from Genetic Data on Pedigrees, volume 6 of NSF-CBMS Regional Conference Series in Probability and Statistics. IMS, Beachwood, Ohio

    Google Scholar 

  30. 30.

    Thompson EA, Meagher TR (1998) Genetic linkage in the estimation of pairwise relationship. Theor Appl Genet 97(5-6):857–864. doi:10.1007/s001220050965

    Article  CAS  Google Scholar 

  31. 31.

    Tillmar AO (2012) Population genetic analysis of 12 X-STRs in Swedish population. Forensic Sci Int: Genet 6(2):e80 – e81. doi:10.1016/j.fsigen.2011.07.008

    Article  CAS  Google Scholar 

  32. 32.

    Tillmar AO, Mostad P (2014) Choosing supplementary markers in forensic casework. Forensic Sci Int: Genet 13(0):128–133. doi:10.1016/j.fsigen.2014.06.019

    Article  CAS  Google Scholar 

  33. 33.

    Tillmar AO, Mostad P, Egeland T, Lindblom B, Holmlund G, Montelius K (2008) Analysis of linkage and linkage disequilibrium for eight X-STR markers. Forensic Sci Int: Genet 3(1):37–41. doi:10.1016/j.fsigen.2008.09.006

    Article  CAS  Google Scholar 

  34. 34.

    Tillmar AO, Egeland T, Lindblom B, Holmlund G, Mostad P (2011) Using X-chromosomal markers in relationship testing: Calculation of likelihood ratios taking both linkage and linkage disequilibrium into account. Forensic Sci Int: Genet 5(5):506–511. doi:10.1016/j.fsigen.2010.11.004

    Article  CAS  Google Scholar 

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Correspondence to Guro Dørum.

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Dørum, G., Kling, D., Tillmar, A. et al. Mixtures with relatives and linked markers. Int J Legal Med 130, 621–634 (2016). https://doi.org/10.1007/s00414-015-1288-x

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  • DNA mixtures
  • Kinship
  • Linkage
  • Linkage disequilibrium
  • Likelihood ratio
  • Forensics