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The System for Random Man not ExcludedNataša GlišovićMathematical Institute of the SerbianAcademy of Sciences and Artsnatasaglisovic@gmail.comMilan BožićMathematical Institute of the SerbianAcademy of Sciences and Artsmilan@sezampro.rsThe aim of this paper is to present a system for calculating Random Man not Excluded (RMNE). RMNE is a typeof measure in population genetics to estimate the probability that an individual randomly picked out of the generalpopulation would not be excluded from matching a given piece of genetic data. RMNE is frequently employed in caseswhere other types of tests such as random match possibility are not possible because the sample in question is degradedor contaminated with multiple sources of DNA.I INTRODUCTIONThis paper explains a methodology for analyzing the problem of identification of DNA profiles. Assume that it is necessaryto calculate the percentage of random men in the population to be excluded from paternity of the child. The probability ofexcluding a random man from paternity is another quantity that may be used by some scientists and paternity laboratories.The exclusion probability can be calculated even before the collection of the genotype of the alleled father. [1]Part II of the paper presents some genetic background material. System for random man not excluded is presented inpart III. Part IV illustrates the model through the real forensic casework examples and shows this in implemented systemin C#. Finally, part V discusses further work.II Genetic backgroundAn individual’s DNA profile comprises a collection of genotypes, one for each marker. Each genotype consists of anunordered pair of alleles, one inherited from the father and one from the mother (though one can not distinguish whichis which). When both alleles are identical the individual is homozygous at that marker, and only a single allele value isobserved; else the individual is heterozygous.Databases have been gathered from calculated allele frequency distributions. These allele frequency distributions can becalculated for various populations and can be estimated for each forensic marker. Calculations presented in this paper aregathered from self developed software.III Statistical modelRandom Man Not Excluded (RMNE) is a type of measure in population genetics to estimate the probability that anindividual randomly picked out of the general population would not be excluded from matching a given piece of geneticdata. RMNE is frequently employed in cases where other types of tests such as random match possibility are not possiblebecause the sample in question is degraded or contaminated with multiple sources of DNA.Suppose that the mother and the child have genotypes M = A i A j and C = A i A k at a particular locus l, respectively.A man without allele A k (i.e. both of his alleles are not A k ) will be excluded as the true father of the child. Thus,the probability that a random individual in the male population is excluded from paternity in this case is (1-p k ) 2 . Thisexclusion probability at locus l isEP l = (1-p k ) 2 ,and so the inclusion probability or the ‘random man not excluded’ probability would be IPl = 1 - EPl. The EP l ’s forvarious combinations of genotypes of the mother and child can be derived similarly and are given in Table 1.M C EP lA i A i A i A i (1-p i ) 2A i A i A i A j (1-p j ) 2A i A j A i A i (1-p i ) 2A i A j A i A j (1-p i -p j ) 2A i A j A i A k (1-p k ) 2Table 1. Probability (EPl) that a random man is excluded from paternity of the child, given genotypes of the mother Mand child C at a particular locus l.IV System for random man not excluded to forensic caseworkA mixed DNA profile has been collected and the genotypes of one or more unknown individuals who have contributed tothe mixture are desired, for example with the purpose of searching for a potential perpetrator among an existing databaseof DNA profiles.36
For a two-person mixture, the easiest case to consider is clearly that of separation of a single unknown profile, i.e. whenthe genotype of one of the contributors to the mixture is known. The case when both contributors are unknown is moredificult. In the latter situation this is only possible to a reasonable accuracy when the contributions to the DNA mixturehave taken place in quite diferent proportions.In the system for random match probability to forensic casework is implemented the above-mentioned model. First arecalculated the frequency of certain alleles in the corresponding locus. The database used does not bring up reference as peoplewho are related and contain 4756 people. As for the number of loci for which allele frequencies are calculated-no.System from the input file base and locus with alleles, calculated for each locus allele frequencies p i .Random man not excluded used .txt file that contains data about the mother and child, their loci andallele values??. Theoutput also given in .txt file.V DISSCUSIONFurther research is planned upgrade the system to calculate other probability forensic methods.AcknowledgmentThe work presented here was supported by the Serbian Ministry of Education and Science (project III44006).References[1] Colin Aitken, and Franco Taroni, “Statistics and the Evaluation of evidence for Forensic Scientists,” John Wiley &Song Inc, England, ISBN 0-470-84367-5.[2] Chromosomal Laboratories, Inc, “Lawyer’s Guide to Forensic Statistics”, Technical Bulletin 40-021[3] Yun S. Song, “Forensic DNA analysis and multi-locus match probability in ?nite populations: A fundamental differencebetween the Moran and Wright-Fisher models,” Departments of EECS and Statistics UC Berkeley, 2009.[4] Koehler, J. J., Chia, A. & Lindsey, J. S, “The random match probability (RMP) in DNA evidence: Irrelevant andprejudicial?,” Jurimetrics Journal, 35, 1995, 201-219.37
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