Mutability of Y-Chromosomal Microsatellites: Rates, Characteristics, Molecular Bases, and Forensic Implications

Nonrecombining Y-chromosomal microsatellites (Y-STRs) are widely used to infer population histories, discover genealogical relationships, and identify males for criminal justice purposes. Although a key requirement for their application is reliable mutability knowledge, empirical data are only available for a small number of Y-STRs thus far. To rectify this, we analyzed a large number of 186 Y-STR markers in nearly 2000 DNA-confirmed father-son pairs, covering an overall number of 352,999 meiotic transfers. Following confirmation by DNA sequence analysis, the retrieved mutation data were modeled via a Bayesian approach, resulting in mutation rates from 3.78 × 10−4 (95% credible interval [CI], 1.38 × 10−5 − 2.02 × 10−3) to 7.44 × 10−2 (95% CI, 6.51 × 10−2 − 9.09 × 10−2) per marker per generation. With the 924 mutations at 120 Y-STR markers, a nonsignificant excess of repeat losses versus gains (1.16:1), as well as a strong and significant excess of single-repeat versus multirepeat changes (25.23:1), was observed. Although the total repeat number influenced Y-STR locus mutability most strongly, repeat complexity, the length in base pairs of the repeated motif, and the father's age also contributed to Y-STR mutability. To exemplify how to practically utilize this knowledge, we analyzed the 13 most mutable Y-STRs in an independent sample set and empirically proved their suitability for distinguishing close and distantly related males. This finding is expected to revolutionize Y-chromosomal applications in forensic biology, from previous male lineage differentiation toward future male individual identification. Nonrecombining Y-chromosomal microsatellites (Y-STRs) are widely used to infer population histories, discover genealogical relationships, and identify males for criminal justice purposes. Although a key requirement for their application is reliable mutability knowledge, empirical data are only available for a small number of Y-STRs thus far. To rectify this, we analyzed a large number of 186 Y-STR markers in nearly 2000 DNA-confirmed father-son pairs, covering an overall number of 352,999 meiotic transfers. Following confirmation by DNA sequence analysis, the retrieved mutation data were modeled via a Bayesian approach, resulting in mutation rates from 3.78 × 10−4 (95% credible interval [CI], 1.38 × 10−5 − 2.02 × 10−3) to 7.44 × 10−2 (95% CI, 6.51 × 10−2 − 9.09 × 10−2) per marker per generation. With the 924 mutations at 120 Y-STR markers, a nonsignificant excess of repeat losses versus gains (1.16:1), as well as a strong and significant excess of single-repeat versus multirepeat changes (25.23:1), was observed. Although the total repeat number influenced Y-STR locus mutability most strongly, repeat complexity, the length in base pairs of the repeated motif, and the father's age also contributed to Y-STR mutability. To exemplify how to practically utilize this knowledge, we analyzed the 13 most mutable Y-STRs in an independent sample set and empirically proved their suitability for distinguishing close and distantly related males. This finding is expected to revolutionize Y-chromosomal applications in forensic biology, from previous male lineage differentiation toward future male individual identification. IntroductionThe nonrecombining part of the human Y chromosome (NRY) is widely used in human population1Underhill P.A. Kivisild T. Use of y chromosome and mitochondrial DNA population structure in tracing human migrations.Annu. Rev. Genet. 2007; 41: 539-564Crossref PubMed Scopus (302) Google Scholar and forensic genetics2Kayser M. Uni-parental markers in human identity testing including forensic DNA analysis.Biotechniques. 2007; 43: 3042Crossref Google Scholar because it shows a male inheritance and substantial structuring in human populations.3Karafet T.M. Mendez F.L. Meilerman M.B. Underhill P.A. Zegura S.L. Hammer M.F. New binary polymorphisms reshape and increase resolution of the human Y chromosomal haplogroup tree.Genome Res. 2008; 18: 830-838Crossref PubMed Scopus (663) Google Scholar With its particular susceptibility to genetic drift caused by low effective population size4Jobling M.A. Tyler-Smith C. The human Y chromosome: An evolutionary marker comes of age.Nat. Rev. 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Genet. 2000; 26: 358-361Crossref PubMed Scopus (764) Google Scholar including estimation of demographic parameters,11Shi W. Ayub Q. Vermeulen M. Shao R.G. Zuniga S. van der Gaag K. de Knijff P. Kayser M. Xue Y. Tyler-Smith C. A worldwide survey of human male demographic history based on Y-SNP and Y-STR data from the HGDP-CEPH populations.Mol. Biol. Evol. 2010; 27: 385-393Crossref PubMed Scopus (84) Google Scholar as well as for genealogical relationships12Kayser M. Vermeulen M. Knoblauch H. Schuster H. Krawczak M. Roewer L. Relating two deep-rooted pedigrees from Central Germany by high-resolution Y-STR haplotyping.Forensic Sci. Int.; Genet. 2007; 1: 125-128Abstract Full Text Full Text PDF PubMed Scopus (34) Google Scholar and male lineage determination in forensic applications.13Kayser M. Caglià A. Corach D. Fretwell N. Gehrig C. Graziosi G. Heidorn F. Herrmann S. Herzog B. Hidding M. et al.Evaluation of Y-chromosomal STRs: A multicenter study.Int. J. 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Genealogical and evolutionary inference with the human Y chromosome.Science. 2001; 291: 1738-1742Crossref PubMed Scopus (70) Google Scholar Commonly, Y-chromosomal microsatellite or short tandem repeat (Y-STR) variation is used to infer temporal and spatial origins of the Y chromosome, particularly the nodes of a phylogenetic tree constructed from single-nucleotide polymorphism (SNP) or DNA sequences.17Novelletto A. Y chromosome variation in Europe: Continental and local processes in the formation of the extant gene pool.Ann. Hum. Biol. 2007; 34: 139-172Crossref PubMed Scopus (20) Google Scholar, 18Balaresque P. Bowden G.R. Adams S.M. Leung H.Y. King T.E. Rosser Z.H. Goodwin J. Moisan J.P. Richard C. Millward A. et al.A predominantly neolithic origin for European paternal lineages.PLoS Biol. 2010; 8: e1000285Crossref PubMed Scopus (171) Google Scholar As such, evolutionary inferences on timescales of tens to hundreds of generations, as usually applied, are highly dependent on the accuracy of the Y-STR mutation rate estimates used. Furthermore, for forensic applications of Y-STRs such as paternity testing, including deficiency cases involving male offspring and deceased alleged fathers,19Kayser M. Sajantila A. Mutations at Y-STR loci: Implications for paternity testing and forensic analysis.Forensic Sci. Int. 2001; 118: 116-121Abstract Full Text Full Text PDF PubMed Scopus (109) Google Scholar accurate knowledge of the mutability of the applied Y-STRs is needed to obtain reliable paternity probabilities. Such knowledge is also essential in genealogical studies aiming to establish the relationship between putatively closely or distantly related males.12Kayser M. Vermeulen M. Knoblauch H. Schuster H. Krawczak M. Roewer L. Relating two deep-rooted pedigrees from Central Germany by high-resolution Y-STR haplotyping.Forensic Sci. Int.; Genet. 2007; 1: 125-128Abstract Full Text Full Text PDF PubMed Scopus (34) Google ScholarHowever, current information about Y-STR mutability is limited, because empirical data are only available for a small set of particular loci. Commonly, either small pedigrees (both deep-rooting and immediate families) or observed repeat variation between isolated human populations has been used to estimate Y-STR mutation rates.20Heyer E. Puymirat J. Dieltjes P. Bakker E. de Knijff P. Estimating Y chromosome specific microsatellite mutation frequencies using deep rooting pedigrees.Hum. Mol. Genet. 1997; 6: 799-803Crossref PubMed Scopus (233) Google Scholar, 21Pollin T.I. McBride D.J. Agarwala R. Schäffer A.A. Shuldiner A.R. Mitchell B.D. O'Connell J.R. Investigations of the Y chromosome, male founder structure and YSTR mutation rates in the Old Order Amish.Hum. Hered. 2008; 65: 91-104Crossref PubMed Scopus (21) Google Scholar, 22Vermeulen M. Wollstein A. van der Gaag K. Lao O. Xue Y. Wang Q. Roewer L. Knoblauch H. Tyler-Smith C. de Knijff P. Kayser M. Improving global and regional resolution of male lineage differentiation by simple single-copy Y-chromosomal short tandem repeat polymorphisms.Forensic Sci. Int. Genet. 2009; 3: 205-213Abstract Full Text Full Text PDF PubMed Scopus (78) Google Scholar However, population diversity-based estimates are often indirectly assumed with the help of calibration dates from other sources, such as archeological investigations.23Zhivotovsky L.A. Underhill P.A. Cinnioğlu C. Kayser M. Morar B. Kivisild T. Scozzari R. Cruciani F. Destro-Bisol G. Spedini G. et al.The effective mutation rate at Y chromosome short tandem repeats, with application to human population-divergence time.Am. J. Hum. Genet. 2004; 74: 50-61Abstract Full Text Full Text PDF PubMed Scopus (327) Google Scholar Usually, and for the limited set of Y-STRs studied so far, resulting rates are a magnitude lower than family-based rates, which is explained by noninclusion of multistep mutations and back mutations, as well as variation in calibration dates.23Zhivotovsky L.A. Underhill P.A. Cinnioğlu C. Kayser M. Morar B. Kivisild T. Scozzari R. Cruciani F. Destro-Bisol G. Spedini G. et al.The effective mutation rate at Y chromosome short tandem repeats, with application to human population-divergence time.Am. J. Hum. Genet. 2004; 74: 50-61Abstract Full Text Full Text PDF PubMed Scopus (327) Google Scholar The more accurate method of estimating Y-STR mutation rates is the direct observation of transmission between father and son, as long as large numbers of genetic transfers (meioses) are covered by testing a large number of father-son pairs. However, reasonably large family data are only available for a small number of particular Y-STRs often used for forensic purposes.24Kayser M. Roewer L. Hedman M. Henke L. Henke J. Brauer S. Krüger C. Krawczak M. Nagy M. Dobosz T. et al.Characteristics and frequency of germline mutations at microsatellite loci from the human Y chromosome, as revealed by direct observation in father/son pairs.Am. J. Hum. Genet. 2000; 67: 1526-1543Abstract Full Text Full Text PDF PubMed Scopus (479) Google Scholar, 25Dupuy B.M. Stenersen M. Flønes A.G. Egeland T. Olaisen B. Y-chromosomal microsatellite mutation rates: Differences in mutation rate between and within loci.Hum. Mutat. 2004; 23: 117-124Crossref PubMed Scopus (96) Google Scholar, 26Gusmão L. Sánchez-Diz P. Calafell F. Martín P. Alonso C.A. Alvarez-Fernández F. Alves C. Borjas-Fajardo L. Bozzo W.R. Bravo M.L. et al.Mutation rates at Y chromosome specific microsatellites.Hum. 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Legal Med. 2009; 123: 471-482Crossref PubMed Scopus (107) Google Scholar A recent large study on 17 Y-STRs, which also provided a summary of the most relevant published data covering over 135,000 meiotic transfers, revealed variation in the mutation rates between loci of about 1 magnitude from 2 × 10−4 (95% credible interval [CI], 2 × 10−5 to 8 × 10−3) to 6.5 × 10−3 (2.3 × 10−3 to 1.3 × 10−2) per locus per generation.28Goedbloed M. Vermeulen M. Fang R.N. Lembring M. Wollstein A. Ballantyne K. Lao O. Brauer S. Krüger C. Roewer L. et al.Comprehensive mutation analysis of 17 Y-chromosomal short tandem repeat polymorphisms included in the AmpFlSTR Yfiler PCR amplification kit.Int. J. Legal Med. 2009; 123: 471-482Crossref PubMed Scopus (107) Google Scholar Such noticeable variation in mutation rates between just 17 loci predicts that even higher variation in mutation rates will be found when increased numbers of Y-STRs are examined. However, the lack of reliable mutation rate data for most of the currently known Y-STRs29Kayser M. Kittler R. Erler A. Hedman M. Lee A.C. Mohyuddin A. Mehdi S.Q. Rosser Z. Stoneking M. Jobling M.A. et al.A comprehensive survey of human Y-chromosomal microsatellites.Am. J. Hum. Genet. 2004; 74: 1183-1197Abstract Full Text Full Text PDF PubMed Scopus (175) Google Scholar precludes their accurate use for evolutionary inference of population parameters, as well as for others, such as forensic applications.Just as there is a lack of accurate mutation rate data, there is a lack of consensus regarding the molecular causes of Y-STR mutations because of the limited number of loci studied thus far. Although most research on autosomal STRs confirms that the stepwise mutation model (SMM)30Ota T. Kimura M. A model of mutation appropriate to estimate the number of electrophoretically detectable alleles in a finite population.Genet. Res. 1973; 22: 201-204Crossref PubMed Scopus (856) Google Scholar is too simplistic to explain the lack of long STRs, questions remain about the exact mechanism in operation for STRs in general. Mutation biases between alleles are commonly observed, with increasing repeat numbers increasing the probability of mutation.31Lai Y. Sun F. The relationship between microsatellite slippage mutation rate and the number of repeat units.Mol. Biol. Evol. 2003; 20: 2123-2131Crossref PubMed Scopus (174) Google Scholar, 32Ellegren H. Heterogeneous mutation processes in human microsatellite DNA sequences.Nat. Genet. 2000; 24: 400-402Crossref PubMed Scopus (266) Google Scholar, 33Xu X. Peng M. Fang Z. Xu X. The direction of microsatellite mutations is dependent upon allele length.Nat. Genet. 2000; 24: 396-399Crossref PubMed Scopus (301) Google Scholar A proportional bias of expansion versus contraction mutations appears to operate, with longer alleles tending to contract and vice versa,32Ellegren H. 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Every microsatellite is different: Intrinsic DNA features dictate mutagenesis of common microsatellites present in the human genome.Mol. Carcinog. 2009; 48: 379-388Crossref PubMed Scopus (76) Google Scholar with higher heterozygosities between human populations39Pemberton T.J. Sandefur C.I. Jakobsson M. Rosenberg N.A. Sequence determinants of human microsatellite variability.BMC Genomics. 2009; 10: 612Crossref PubMed Scopus (38) Google Scholar and greater sequence diversity between humans and chimpanzee STRs.40Kelkar Y.D. Tyekucheva S. Chiaromonte F. Makova K.D. The genome-wide determinants of human and chimpanzee microsatellite evolution.Genome Res. 2008; 18: 30-38Crossref PubMed Scopus (186) Google Scholar However, most conclusions regarding the causes of STR mutation have been formed from either comparative genomic analyses35Kruglyak S. Durrett R.T. Schug M.D. Aquadro C.F. Equilibrium distributions of microsatellite repeat length resulting from a balance between slippage events and point mutations.Proc. Natl. Acad. Sci. USA. 1998; 95: 10774-10778Crossref PubMed Scopus (335) Google Scholar, 37Pumpernik D. Oblak B. Borštnik B. Replication slippage versus point mutation rates in short tandem repeats of the human genome.Mol. Genet. Genomics. 2008; 279: 53-61Crossref PubMed Scopus (39) Google Scholar, 40Kelkar Y.D. Tyekucheva S. Chiaromonte F. Makova K.D. The genome-wide determinants of human and chimpanzee microsatellite evolution.Genome Res. 2008; 18: 30-38Crossref PubMed Scopus (186) Google Scholar or indirect polymorphism analyses,31Lai Y. Sun F. The relationship between microsatellite slippage mutation rate and the number of repeat units.Mol. Biol. Evol. 2003; 20: 2123-2131Crossref PubMed Scopus (174) Google Scholar, 39Pemberton T.J. Sandefur C.I. Jakobsson M. Rosenberg N.A. Sequence determinants of human microsatellite variability.BMC Genomics. 2009; 10: 612Crossref PubMed Scopus (38) Google Scholar both of which may miss substantial numbers of mutations. Instead, sequence-based analysis of a large number of Y-STR mutations would allow a more direct investigation of the molecular processes in action. The strict paternal inheritance of STRs on the NRY allows the unequivocal determination of the mutational event in father-son pair studies, which is difficult for autosomal STRs in family studies. Thus, using Y-STRs allows the retrieval of more accurate knowledge about STR mutability in general.Furthermore, Y-STR markers currently applied to evolutionary, genealogical, and forensic studies have low to midrange mutation rates,27Ge J. Budowle B. Aranda X.G. Planz J.V. Eisenberg A.J. Chakraborty R. Mutation rates at Y chromosome short tandem repeats in Texas populations.Forensic Sci. Int. Genet. 2009; 3: 179-184Abstract Full Text Full Text PDF PubMed Scopus (68) Google Scholar, 28Goedbloed M. Vermeulen M. Fang R.N. Lembring M. Wollstein A. Ballantyne K. Lao O. Brauer S. Krüger C. Roewer L. et al.Comprehensive mutation analysis of 17 Y-chromosomal short tandem repeat polymorphisms included in the AmpFlSTR Yfiler PCR amplification kit.Int. J. Legal Med. 2009; 123: 471-482Crossref PubMed Scopus (107) Google Scholar which makes them ideal tools to distinguish male lineages (i.e., groups of closely and distantly related males sharing almost identical Y chromosomes) in applications involving comparatively recent timescales.12Kayser M. Vermeulen M. Knoblauch H. Schuster H. Krawczak M. Roewer L. Relating two deep-rooted pedigrees from Central Germany by high-resolution Y-STR haplotyping.Forensic Sci. Int.; Genet. 2007; 1: 125-128Abstract Full Text Full Text PDF PubMed Scopus (34) Google Scholar, 15Roewer L. Y chromosome STR typing in crime casework.Forensic Sci. Med. Pathol. 2009; 5: 77-84Crossref PubMed Scopus (161) Google Scholar However, these particular Y-STR markers usually fail to differentiate members of the same male lineage, and as such, the current forensic use of NRY suffers from the strong limitation that conclusions cannot be made on an individual level, as is usually required in forensic investigations. Also, for microevolutionary studies, investigating male genealogies for historical and other purposes,12Kayser M. Vermeulen M. Knoblauch H. Schuster H. Krawczak M. Roewer L. Relating two deep-rooted pedigrees from Central Germany by high-resolution Y-STR haplotyping.Forensic Sci. Int.; Genet. 2007; 1: 125-128Abstract Full Text Full Text PDF PubMed Scopus (34) Google Scholar or for investigating histories of populations that underwent strong bottleneck or founder effects,9Kayser M. Brauer S. Weiss G. Underhill P.A. Roewer L. Schiefenhövel W. Stoneking M. Melanesian origin of Polynesian Y chromosomes.Curr. Biol. 2000; 10: 1237-1246Abstract Full Text Full Text PDF PubMed Scopus (163) Google Scholar, 41Hedman M. Neuvonen A.M. Sajantila A. Palo J.U. Dissecting the Finnish male uniformity: The value of additional Y-STR loci.Forensic Sci. Int. Genet. 2010; (in press. Published online April 28, 2010)Google Scholar the amount of diversity offered by currently used Y-STRs with midrange mutation rates is usually not sufficient. One could speculate that if Y-STRs with substantially higher mutation rates than are currently known for the limited number of markers investigated were available, it may become possible to differentiate male relatives at the individual level, which would solve the current dilemma of Y chromosome applications in forensics.To address three main issues—(1) the lack of knowledge on Y-STR mutability based on a reasonably large number of loci, as required for evolutionary and genealogical applications, (2) the limited knowledge about the molecular basis of Y-STR mutability, and (3) the lack of Y-STRs for familial differentiation in forensic, genealogical, and particular population applications—we have investigated 186 Y-STRs in ∼2000 DNA-confirmed father-son pairs. We not only describe in this study mutation rates and characteristics for the largest number of different Y-STRs ever studied so far, including the first mutation rate estimates for most of these markers, but we also use the diversity and DNA sequence data generated for all loci to investigate the underlying causes of Y-STR mutability. Finally, we empirically tested the suitability of the identified most mutable Y-STRs for male relative differentiation, as well as their implication for Y chromosome applications in forensic science.Material and MethodsDNA SamplesAll father-son pairs used in the mutation rate study were confirmed in their paternity by molecular analyses, utilizing autosomal STRs, Y-STRs, HLA and RFLP genotyping, and blood grouping, in addition to familial or governmental documentation. A threshold for paternity probability of 99.9% was set for inclusion in the study. Samples were obtained from the Berlin, Leipzig, and Cologne areas of Germany and the Warsaw and Wroclaw areas of Poland. Whole-genome amplification (WGA) with the GenomiPhi DNA Amplification kit (GE Healthcare) was performed on the Leipzig samples because of low DNA quantities. WGA reactions were performed as recommended by the manufacturer, and products were purified with Invisorb 96 Filter Microplates (Invitek GmbH). To verify the value of the smaller set of RM Y-STRs, we obtained an additional independent set of samples from male relatives from the Greifswald, Kiel, and Berlin areas of Germany, the Leuven area of Belgium, the Warsaw area of Poland, and Canada and Central Germany, as described elsewhere.12Kayser M. Vermeulen M. Knoblauch H. Schuster H. Krawczak M. Roewer L. Relating two deep-rooted pedigrees from Central Germany by high-resolution Y-STR haplotyping.Forensic Sci. Int.; Genet. 2007; 1: 125-128Abstract Full Text Full Text PDF PubMed Scopus (34) Google Scholar All families and pedigrees were confirmed by the same methods as the father-son pairs; pairs with complete genotypes for both the rapidly mutating (RM) Y-STRs and Yfiler Y-STRs were considered for analysis, or, in the case of partial genotypes, only those that showed a mutation at one or more loci were included. The use of all samples for the purpose of this study was in agreement with the institutional regulations and was under informed consent.Y-STR Markers and Genotyping ProtocolsY-STR markers were mostly selected from a previous study detailing a large number of 167 previously unknown Y-STRs,29Kayser M. Kittler R. Erler A. Hedman M. Lee A.C. Mohyuddin A. Mehdi S.Q. Rosser Z. Stoneking M. Jobling M.A. et al.A comprehensive survey of human Y-chromosomal microsatellites.Am. J. Hum. Genet. 2004; 74: 1183-1197Abstract Full Text Full Text PDF PubMed Scopus (175) Google Scholar with the additional inclusion of Y-STRs known at the time of project commencement.42Hanson E.K. Berdos P.N. Ballantyne J. Testing and evaluation of 43 "noncore" Y chromosome markers for forensic casework applications.J. Forensic Sci. 2006; 51: 1298-1314Crossref PubMed Scopus (23) Google Scholar The focus was on single-copy Y-STR markers in order to be able to fully confirm genotype differences by DNA sequence analysis when identifying mutations. However, given our aim to find RM Y-STRs, we included some additional multicopy Y-STRs, especially those with high diversities (for which mutation confirmation was performed by independent genotyping). A complete list of loci, primer sequences, and protocols can be found in Table S1 available online. Seventeen of the 186 Y-STRs were genotyped with a commercially available kit, the AmpFlSTR Yfiler PCR Amplification kit (Applied Biosystems), following the manufacturer's instructions. Full descriptions of protocols and markers can be found in 28Goedbloed M. Vermeulen M. Fang R.N. Lembring M. Wollstein A. Ballantyne K. Lao O. Brauer S. Krüger C. Roewer L. et al.Comprehensive mutation analysis of 17 Y-chromosomal short tandem repeat polymorphisms included in the AmpFlSTR Yfiler PCR amplification kit.Int. J. Legal Med. 2009; 123: 471-482Crossref PubMed Scopus (107) Google Scholar. The remaining 169 Y-STRs were genotyped via 54 multiplex assays, including 1–5 markers each. PCRs were performed via three differing protocols, and details are provided in Table S1. In addition, 13 Y-STRs identified during the study as RM Y-STRs were genotyped via three multiplex assays in an independent sample set of male relatives. All PCRs were performed on GeneAmp PCR System 9700 machines (Applied Biosystems) at the Department of Forensic Molecular Biology, Erasmus MC Rotterdam. Fragment length analysis was performed with the 3130xl Genetic Analyzer (Applied Biosystems). Profiles generated were genotyped with GeneMapper software (ID v. 3.2, Applied Biosystems). Genotype differences were identified with in-house-developed Microsoft Excel 2007 macros. All mutations were confirmed by DNA sequence analysis in Rotterdam of both the father and son at the Y-STR locus, as described in 28Goedbloed M. Vermeulen M. Fang R.N. Lembring M. Wollstein A. Ballantyne K. Lao O. Brauer S. Krüger C. Roewer L. et al.Comprehensive mutation analysis of 17 Y-chromosomal short tandem repeat polymorphisms included in the AmpFlSTR Yfiler PCR amplification kit.Int. J. Legal Med. 2009; 123: 471-482Crossref PubMed Scopus (107) Google Scholar. Multicopy Y-STR loci with three or more alleles were not able to be sequenced, but mutations were confirmed by at least two independent fragment length analysis amplifications.Statistical Data AnalysesMutation rates for individual markers were estimated via a binomial hierarchical Bayesian model43Ge