DNA Analysis

• Anton Lucassen; Karen Ehlers; Paul J. Grobler; Charles H. Brenner (2021) Evaluating Mixture Solution™ — rapid and non-MCMC probabilistic mixture analysis
  International Journal of Legal Medicine https://doi.org/10.1007/s00414-021-02680-2 Accepted August 2021

• Kijeong Kim; Munkhtsetseg Bazarragchaa; Charles H Brenner; Byung-Sun Choi; Kyung-Yong Kim (2015) Extensive evaluation of DNA polymerase performance for highly degraded human DNA samples
  Forensic Science International Ms. No. FSI-D-14-00930R1 Accepted April 2015

• Brenner CH (2017) Fairness in evaluating DNA mixtures
  Forensic Sci. Int. Genet.27 186

• Brenner CH (2014) Understanding Y haplotype matching probability
  Forensic Sci. Int. Genet. 8 233–243

• Brenner CH (2010) Fundamental problem of forensic mathematics – The evidential value of a rare haplotype
  Forensic Sci. Int. Genet. 4 281–291
  abstract and comments on this paper
  presentation for Berlin 2010

• Brenner CH (2007 letter) Counterexample to a conjecture of Krawczak For Sci International: Genetics, 2 2008 p75

• Brenner CH (2006July15) Forensic Genetics: Mathematics In: Encyclopedia of Life Sciences
  John Wiley & Sons, Ltd: Chichester http://www.els.net/ [doi: 10.1038/npg.els.0005451] Standard Article
  draft version for download Basic concepts of using DNA for evidence including

  • Mathematical model of decision making – Likelihood ratios & hypotheses; prior and posterior odds/probabilities; thresholds, standards for proof
  • DNA profile probabilities – product rule, verbal explanation
  • Fallacies – prosecutor's, defense, laboratory error
  • Limitations – relatives, population substructure, linkage

• Gill P, Brenner CH, Buckleton JS, et al. (2006July13) DNA commission of the International Society of Forensic Genetics: Recommendations on the interpretation of mixtures For Sci International,160 (2-3), 90-101
  Download from ISFG site

• Brenner CH, Bieber FR, Lazer D (2006June2) Finding Criminals Through DNA of Their Relatives Science
  Supporting on-line materials detail the simulations & results.

  If a crime stain isn't matched in the offender database, there's still a good chance that its relative is there. The relative can likely be found by "kinship" searching if you know how to search. If the search results in a list of even dozens of potential relatives, sort them out with Y-haplotyping. This approach could significantly increase the effective reach of offender database. It could also raise some hackles and some eyebrows.

  my comments on this paper

• Brenner CH (Mar 2006) Some mathematical problems in the DNA identification of victims in the 2004 tsunami and similar mass fatalities For Sci International,157, 172-180
  Abstract and links

  • Related victims missing, one found
  • Related victims missing, several found
  • Distinguishing race using DNA
  Forensic STR markers are powerful for racial estimation
  • Which races to calculate in disaster identifcation?
  • Combining DNA and other identification information

• Biescker LG, et al (2005Nov18) DNA Identifications After the 9/11 Trade Center Attack Science 310, 1122-1123

• Brenner CH, Inman K (Jan 2004) Commentary on: Thompson WC, Taroni F, Aitken CGG, How the Probability of a False Positive Affects the Value of DNA Evidence J For Sci

• Brenner CH (2004) Multiple mutations, covert mutations and false exclusions in paternity casework Progress in Forensic Genetics 10, 112-114. Eds. Doutremépuich, Morling, Elsevier Science B.V.

• Brenner CH, Weir BS (May 2003) Issues and strategies in the identification of World Trade Center victims Theor Pop Bio 63 (2003)173-178

• Brenner CH (1992-2020) DNA·VIEW User's Manual

• Buard J, Brenner CH, Jeffreys AJ (April 2002) Evolutionary fate of an unstable human minisatellite deduced from sperm mutation spectra of individual alleles Am J Hum Genet 70:1038-1043
  Online appendix

• Brenner CH (2001) Family secrets revealed, Progress in Forensic Genetics 9, Eds B Brinkmann et al.

• Gill P, Brenner C, Brinkmann B, Budowle B, Carracedo A, Jobling MA, de Knijff P, Kayser M, Krawczak M, Mayr WR, Morling N, Olaisen B, Pascali V, Prinz M, Roewer L, Schneider PM, Sajantila A, Tyler-Smith C (2001) technical note: DNA Commission of the International Society of Forensic Genetics: recommendations on forensic analysis using Y-chromosome STRs Int J Leg Med 114:(6)305-309 abstract

• Tamaki K, Brenner CH, Jeffreys AJ (2000) Distinguishing minisatellite mutation from non-paternity by MVR-PCR, Forensic Science International 113:55-62 (as the Proceedings of the 4th International Symposium on Advances in Legal Medicine (ISALM))

• Brenner CH (1999) Kinship Analysis by DNA When There Are Many Possibilities, Progress in Forensic Genetics 8, Eds G Sensabaugh et al.

• Yoshida K, Kasai K, Sato H, Brenner CH, Sensabaugh GF (1998) Genetic Variation at 6 STR Loci in the Japanese Population, Progress in Forensic Genetics 7, Eds. B Olaisen, B Brinkmann, PJ Lincoln, Elsevier Science B.V. 360-362

• Brenner CH (1998) Difficulties in estimating ethnic affiliation, Am J Hum Genet 62:1558-1560
       disputing unbelievable claims published in the AJHG

• Brenner CH (1998) Mixed Stain Calculator, Progress in Forensic Haemogenetics 7, Ed B Olaisen, B Brinkmann, PJ Lincoln. Elsevier Science B.V. 556-558
       software tool

• Brenner CH (1997) Probable Race of a Stain Donor, Proceedings from the Seventh Human Identification Symposium, Promega Corp 48-52
      Can you tell the race of a DNA sample? Yes.

  • 4-d graphs of racial likelihoods Jan98

• Brenner CH (1997) Proof of a mixed stain formula of Weir, (Appendix) J For Sci 42(2)221-222

• Brenner CH, Fimmers R, Baur MP (1996) Likelihood Ratios for Mixed Stains When the Number of Donors Cannot be Agreed, Int J Legal Med 109(4):218-219

• Brenner CH (1996) Hardy-Weinberg Equilibrium in RFLP Databases, Advances in Forensic Haemogenetics 6, Ed A Carracedo, B Brinkmann, W Bär, Springer Verlag 96-98

• Brenner CH (1994) Clouding the Simpson DNA Issue, (Op-Ed) Los Angeles Times, September 4

• Brenner CH (1994) Evaluation of the Product Rule, Advances in Forensic Haemogenetics 5, Ed W. Bär, A. Fiori and U. Rossi, Springer Verlag 453-455

• Brenner CH, Morris JW (1990) Paternity Index Calculations in Single Locus Hypervariable DNA Probes: Validation and Other Studies Proceedings for The International Symposium on Human Identification 1989, Promega Corporation 21-53

  has a lot of meat —

  • We cracked the mystery of apparent excess homozygysity in RFLP systems, a big deal because many experts had drawn incorrect and consequential conclusions from misunderstanding the phenomenon,
  • useful identities and approximations for typical paternity index and exclusion,
  • validation methods, Hardy-Weinberg and linkage independence analysis years ahead of its time, behavior of gel migration.

Paternity Attribution

• Gjertson DW, Brenner CH, Baur MP, Carracedo A, Guidet F, Luque JA, Lessig R, Mayr WR, Pascali VL, Prinz M, Schneider PM, Morling N (2007) ISFG: Recommendations on Biostatistics in Paternity Testing, Review Article for Forensic Science International: Genetics 1(3)223-231

  Abstract: The Paternity Commission of the International Society for Forensic Gentics has formulated recommendations on the use of biostatistics in the evaluation of results of genetic analyses in paternity cases and other situations with disputed genetic (family) relations.

• Sawaguchi T, Brenner CH, Sawaguchi A (1998) Application of DNA·VIEW & PATER to a kinship paternity case Rom J Leg Med 6(1)66-70

• Brenner CH (1997) Symbolic Kinship Program, Genetics 145:535-542
  Kinship web page

• Brenner CH (1993) A Note on Motherless Paternity Case Computation, pdf of the paper Transfusion 33:51-54
        The situation is simple, but popularly misunderstood

• Morris JW, Garber RA, D'Autremont J, Brenner CH (1988) The Avuncular Index and the Incest Index, Advances in Forensic Haemogenetics 2, Springer-Verlag, 607-611
        This is Jeff's paper. I get my name on it for inventing the term “Avuncular Index” which has stuck although as Ronnie Garner pointed out according to Latin it should refer to the maternal uncle.

• Brenner CH (1985) Evidence, Probability, and Paternity, (letter) Am J Hum Genet 826-827

• Brenner CH (1983) Calculation of paternity index, in Inclusion Probabilities in Paternity Testing 632-638, Amer. Assoc. of Blood Banks, Arlington

Pure Mathematics

• Brenner CH (1986) Asymptotic analogues of the Rogers-Ramanujan identities, J. of Combinatorial Theory, Ser. A, 42(2):303-319.
        This is my PhD thesis. One result:

  p(n|2, 3, 6, 9, 10 mod 12) ~ q(n|2, 3, 4, 6, 7, 8, 9, 10, 11, 12 mod 12), where p(n|S) is the number of partitions of n into parts belonging to S, q(n|T) is the number of partitions of n into distinct parts belonging to T, and ~ here denotes asymptotic equality. For example with n=10 and S, T the sets stated, e.g. S is positive numbers that are 2, 3, 6, 9, or 10 greater than a multiple of 12: p(10|S)=5 by counting (10) (5+5) (5+3+2) (3+3+2+2) (2+2+2+2+2); q(10|T)=4 by counting (10) (8+2) (7+3) (6+4). Of course 5≠4, but as n→∞, p(n|S)/q(n|T)→1.

• Brenner CH & JL (1962) The popularity of small integers as primitive roots, Numer. Math. 4:336-342