The number of alleles in DNA mixtures with related contributors


      • The probability distribution of the Total Allele Count in a DNA mixture is obtained.
      • Mixtures of relatives can often be distinguished from mixtures of unrelated persons.
      • The R package numberofalleles implements the methods.


      The maximum allele count (MAC) across loci and the total allele count (TAC) are often used to gauge the number of contributors to a DNA mixture. Computational strategies that predict the total number of alleles in a mixture arising from a certain number of contributors of a given population have been developed. Previous work considered the restricted case where all of the contributors to a mixture are unrelated. We relax this assumption and allow mixture contributors to be related according to a pedigree. We introduce an efficient computational strategy. This strategy based on first determining a probability distribution on the number of independent alleles per locus, and then conditioning on this distribution to compute a distribution of the number of distinct alleles per locus. The distribution of the number of independent alleles per locus is obtained by leveraging the Identical by Descent (IBD) pattern distribution which can be computed from the pedigree. We explain how allelic dropout and a subpopulation correction can be accounted for in the calculations.


      To read this article in full you will need to make a payment

      Purchase one-time access:

      Academic & Personal: 24 hour online accessCorporate R&D Professionals: 24 hour online access
      One-time access price info
      • For academic or personal research use, select 'Academic and Personal'
      • For corporate R&D use, select 'Corporate R&D Professionals'


      Subscribe to Forensic Science International: Genetics
      Already a print subscriber? Claim online access
      Already an online subscriber? Sign in
      Institutional Access: Sign in to ScienceDirect


        • Paoletti D.R.
        • Doom T.E.
        • Krane C.M.
        • Raymer M.L.
        • Krane D.E.
        Empirical analysis of the STR profiles resulting from conceptual mixtures.
        J. Forensic Sci. 2005; 50: 1361-1366
        • Buckleton J.S.
        • Curran J.M.
        • Gill P.
        Towards understanding the effect of uncertainty in the number of contributors to DNA stains.
        Forensic Sci. Int.: Genet. 2007; 1: 20-28
        • Curran J.M.
        • Buckleton J.S.
        Uncertainty in the number of contributors for the European standard set of loci.
        Forensic Sci. Int.: Genet. 2014; 11: 205-206
        • Coble M.D.
        • Bright J.
        • Buckleton J.S.
        • Curran J.M.
        Uncertainty in the number of contributors in the proposed new CODIS set.
        Forensic Sci. Int.: Genet. 2015; 19: 207-211
        • Noël J.
        • Noël S.
        • Mailly F.
        • Granger D.
        • Lefebvre J-F.
        • Milot E.
        • Séguin D.
        Total allele count distribution (TAC curves) improves number of contributor estimation for complex DNA mixtures.
        Can. Soc. Forensic Sci. J. 2022; : 1-15
        • Paoletti David R.
        • Krane Dan E.
        • Doom Travis E.
        • Raymer Michael
        Inferring the number of contributors to mixed DNA profiles.
        IEEE/ACM Trans. Comput. Biol. Bioinform. 2011; 9: 113-122
        • Tvedebrink T.
        On the exact distribution of the numbers of alleles in DNA mixtures.
        Int. J. Legal Med. 2014; 128: 427-437
        • Norsworthy Sarah
        • Lun Desmond S.
        • Grgicak Catherine M.
        Determining the number of contributors to DNA mixtures in the low-template regime: exploring the impacts of sampling and detection effects.
        Legal Med. 2018; 32: 1-8
        • Perez Jaheida
        • Mitchell Adele A.
        • Ducasse Nubia
        • Tamariz Jeannie
        • Caragine Theresa
        Estimating the number of contributors to two-, three-, and four-person mixtures containing DNA in high template and low template amounts.
        Croat. Med. J. 2011; 52: 314-326
        • Alfonse Lauren E.
        • Garrett Amanda D.
        • Lun Desmond S.
        • Duffy Ken R.
        • Grgicak Catherine M.
        A large-scale dataset of single and mixed-source short tandem repeat profiles to inform human identification strategies: PROVEDIt.
        Forensic Sci. Int.: Genet. 2018; 32: 62-70
        • Gill Peter
        • Whitaker Jonathan
        • Flaxman Christine
        • Brown Nick
        • Buckleton John
        An investigation of the rigor of interpretation rules for STRs derived from less than 100 pg of DNA.
        Forensic Sci. Int. 2000; 112: 17-40
        • Curran J.M.
        • Gill Peter
        • Bill M.R.
        Interpretation of repeat measurement DNA evidence allowing for multiple contributors and population substructure.
        Forensic Sci. Int. 2005; 148: 47-53
        • Haned H.
        • Slooten K.
        • Gill P.
        Exploratory data analysis for the interpretation of low template DNA mixtures.
        Forensic Sci. Int.: Genet. 2012; 6: 762-774
        • Slooten K.
        Familial searching on DNA mixtures with dropout.
        Forensic Sci. Int.: Genet. 2016; 22: 128-138
        • Balding David J.
        • Nichols Richard A.
        DNA profile match probability calculation: how to allow for population stratification, relatedness, database selection and single bands.
        Forensic Sci. Int. 1994; 64: 125-140
        • Johnson N.
        • Kotz S.
        • Balakrishnan N.
        Discrete Multivariate Distributions.
        John Wiley and Sons Inc., New York1997
        • Martin G.E.
        Counting: The Art of Enumerative Combinatorics. Undergraduate Texts in Mathematics. Springer New York, 2013
        • Buckleton J.S.
        • Bright J.-A.
        • Taylor D.
        Forensic DNA Evidence Interpretation.
        CRC Press, 2018
        • Green P.J.
        • Mortera J.
        Inference about complex relationships using peak height data from DNA mixtures.
        J. R. Stat. Soc. Ser. C. Appl. Stat. 2021; 70: 1049-1082
        • R. Core Team
        R: A language and environment for statistical computing.
        2021 (R Foundation for Statistical Computing, Vienna, Austria)
        • Vigeland M.D.
        Ribd: Pedigree-based relatedness coefficients.
        2021 (R package version 1.3.1)
        • Balding David J.
        • Buckleton John
        Interpreting low template DNA profiles.
        Forensic Sci. Int.: Genet. 2009; 4: 1-10
        • Moretti T.R.
        • Moreno L.I.
        • Smerick J.B.
        • Pignone M.L.
        • Hizon R.
        • Buckleton J.S.
        • Bright J.-A.
        • Onorato A.J.
        Population data on the expanded CODIS core STR loci for eleven populations of significance for forensic DNA analyses in the verenigde staten.
        Forensic Sci. Int.: Genet. 2016; 25: 175-181
        • Vigeland M.D.
        Pedtools: Creating and working with pedigrees and marker data.
        2021 (R package version 1.1.0)
        • Kruijver M.
        • Curran J.M.
        Numberofalleles: Number of alleles in a DNA mixture.
        2022 (R package version 1.0.1)
        • Ruckdeschel P.
        • Kohl M.
        • Stabla T.
        • Camphausen F.
        S4 classes for distributions.
        R News. 2006; 6: 2-6
        • Marciano Michael A.
        • Adelman Jonathan D.
        PACE: PRobabilistic assessment for contributor estimation—A machine learning-based assessment of the number of contributors in DNA mixtures.
        Forensic Sci. Int.: Genet. 2017; 27: 82-91
        • Benschop Corina C.G.
        • van der Linden Jennifer
        • Hoogenboom Jerry
        • Ypma Rolf
        • Haned Hinda
        Automated estimation of the number of contributors in autosomal short tandem repeat profiles using a machine learning approach.
        Forensic Sci. Int.: Genet. 2019; 43102150
        • Kruijver Maarten
        • Kelly Hannah
        • Cheng Kevin
        • Lin Meng-Han
        • Morawitz Judi
        • Russell Laura
        • Buckleton John
        • Bright Jo-Anne
        Estimating the number of contributors to a DNA profile using decision trees.
        Forensic Sci. Int.: Genet. 2021; 50102407
        • Lin M.-H.
        • Bright J.-A.
        • Pugh S.N.
        • Buckleton J.S.
        The interpretation of mixed DNA profiles from a mother, father, and child trio.
        Forensic Sci. Int.: Genet. 2020; 44102175
        • Kalafut T.
        • Bright J.-A.
        • Taylor D.
        • Buckleton J.
        Investigation into the effect of mixtures comprising related people on non-donor likelihood ratios, and potential practises to mitigate providing misleading opinions.
        Forensic Sci. Int.: Genet. 2022; 102691
        • Green P.J.
        • Mortera J.
        • Prieto L.
        Casework applications of probabilistic genotyping methods for DNA mixtures that allow relationships between contributors.
        Forensic Sci. Int.: Genet. 2021; 52102482
        • Slooten K.
        Identifying common donors in DNA mixtures, with applications to database searches.
        Forensic Sci. Int.: Genet. 2017; 26: 40-47