7/16/97 The following is an example calculation for the program DNAMIX. Suppose we have a sample with the alleles A, B, and C from the locus HBGG present. We want to calculate the probabilities for the numerator of the likelihood ratio under the explanation of zero alleles whose sources are unknown and zero to one unknown contributors. We want to calculate the probabilities for the denominator of the likelihood ratio under the explanation that alleles A and C have unknown sources and the possibility of one to three unknown contributors. We have the following databases to use: African-American Caucasian Hispanic f(A) = 0.420 f(A) = 0.558 f(A) = 0.375 f(B) = 0.230 f(B) = 0.437 f(B) = 0.580 f(C) = 0.350 f(C) = 0.005 f(C) = 0.045 The following is the input and output to the screen during execution of the program: ****************************************************** * This program performs calculations for the methods * * and formulas presented in: * * * * Weir BS, Triggs CM, Starling L, Stowell LI, * * Walsh KAJ, Buckleton J. Interpreting DNA * * Mixtures. J Forensic Sci 1997; 42(2):213-222. * ****************************************************** ENTER THE NUMBER OF ALLELES IN THE MIXTURE (maximum of 12): 3 ENTER THE NAMES OF THE ALLELES (one name per line): A B C ENTER THE NUMBER OF DATABASES TO BE USED (maximum of 12): 3 ENTER THE NAME FOR DATABASE NUMBER 1: Afr-Amer ENTER THE FREQUENCY OF A .420 ENTER THE FREQUENCY OF B .230 ENTER THE FREQUENCY OF C .350 ENTER THE NAME FOR DATABASE NUMBER 2: Caucasia ENTER THE FREQUENCY OF A .558 ENTER THE FREQUENCY OF B .437 ENTER THE FREQUENCY OF C .005 ENTER THE NAME FOR DATABASE NUMBER 3: Hispanic ENTER THE FREQUENCY OF A .375 ENTER THE FREQUENCY OF B .580 ENTER THE FREQUENCY OF C .045 DO YOU WANT TO USE THE "p^2" FORMULAS OR THE "2p" MODIFICATION? ("p^2" = 0, "2p" = 1) 0 DO YOU WANT A SUMMARY FILE? ( 0=No, 1=Yes ) 1 ENTER THE FILE NAME TO WRITE THE SUMMARY: example ENTER A TITLE FOR THE SUMMARY (such as a locus name): HBGG ************************************************************************ THE FOLLOWING INPUT IS FOR THE NUMERATOR OF THE LIKELIHOOD RATIO ************************************************************************ ENTER THE NUMBER OF ALLELES WHOSE SOURCES ARE UNKNOWN: 0 ENTER THE LOWER BOUND ON THE NUMBER OF UNKNOWN CONTRIBUTORS: (maximum of 12) 0 ENTER THE UPPER BOUND ON THE NUMBER OF UNKNOWN CONTRIBUTORS: (maximum of 12) 1 Unknown Contributors: 0 Database Numerator Probability ------------------------------------ Afr-Amer 0.100000E+01 Caucasia 0.100000E+01 Hispanic 0.100000E+01 Unknown Contributors: 1 Database Numerator Probability ------------------------------------ Afr-Amer 0.100000E+01 Caucasia 0.100000E+01 Hispanic 0.100000E+01 ************************************************************************ THE FOLLOWING INPUT IS FOR THE DENOMINATOR OF THE LIKELIHOOD RATIO ************************************************************************ ENTER THE NUMBER OF ALLELES WHOSE SOURCES ARE UNKNOWN: 2 ENTER THE NUMBER(S) CORRESPONDING TO THE UNKNOWN ALLELE(S): 1 = A 2 = B 3 = C (one entry per line) 1 3 ENTER THE LOWER BOUND ON THE NUMBER OF UNKNOWN CONTRIBUTORS: (maximum of 12) 1 ENTER THE UPPER BOUND ON THE NUMBER OF UNKNOWN CONTRIBUTORS: (maximum of 12) 3 Unknown Contributors: 1 Database Denominator Probability ------------------------------------ Afr-Amer 0.294000E+00 Caucasia 0.558000E-02 Hispanic 0.337500E-01 Unknown Contributors: 2 Database Denominator Probability ------------------------------------ Afr-Amer 0.711127E+00 Caucasia 0.181526E-01 Hispanic 0.128787E+00 Unknown Contributors: 3 Database Denominator Probability ------------------------------------ Afr-Amer 0.886660E+00 Caucasia 0.291355E-01 Hispanic 0.219851E+00 ************************************************************************ THE FOLLOWING ARE THE LIKELIHOOD RATIOS FOR EACH DATABASE ************************************************************************ (Press return after each database) Numerator Unknown Denominator Unknown Database Contributors Contributors Likelihood Ratio ------------------------------------------------------------------------ Afr-Amer 0 1 3.40 Afr-Amer 0 2 1.41 Afr-Amer 0 3 1.13 Afr-Amer 1 1 3.40 Afr-Amer 1 2 1.41 Afr-Amer 1 3 1.13 Caucasia 0 1 179.21 Caucasia 0 2 55.09 Caucasia 0 3 34.32 Caucasia 1 1 179.21 Caucasia 1 2 55.09 Caucasia 1 3 34.32 Hispanic 0 1 29.63 Hispanic 0 2 7.76 Hispanic 0 3 4.55 Hispanic 1 1 29.63 Hispanic 1 2 7.76 Hispanic 1 3 4.55 DO YOU WANT TO COMPUTE ANOTHER LR? ( 0=No, 1=Yes ) 0 Program written by John Storey on July 7, 1997. Questions and/or comments should be sent to: storey@statgen.ncsu.edu --end The following is the content of the file "example" to which we wrote our results: Title: HBGG Form : p^2 Database: Afr-Amer Database: Caucasia Database: Hispanic Allele Freq Allele Freq Allele Freq ------------------ ------------------ ------------------ A 0.420000 A 0.558000 A 0.375000 B 0.230000 B 0.437000 B 0.580000 C 0.350000 C 0.005000 C 0.045000 ------------------ ------------------ ------------------ **************************************************************************** Unknown Alleles in the Numerator: None Unknown Contributors: 0 Database Numerator Probability ------------------------------------ Afr-Amer 0.100000E+01 Caucasia 0.100000E+01 Hispanic 0.100000E+01 Unknown Contributors: 1 Database Numerator Probability ------------------------------------ Afr-Amer 0.100000E+01 Caucasia 0.100000E+01 Hispanic 0.100000E+01 Unknown Alleles in the Denominator: A 0.420000 C 0.350000 Unknown Contributors: 1 Database Denominator Probability ------------------------------------ Afr-Amer 0.294000E+00 Caucasia 0.558000E-02 Hispanic 0.337500E-01 Unknown Contributors: 2 Database Denominator Probability ------------------------------------ Afr-Amer 0.711127E+00 Caucasia 0.181526E-01 Hispanic 0.128787E+00 Unknown Contributors: 3 Database Denominator Probability ------------------------------------ Afr-Amer 0.886660E+00 Caucasia 0.291355E-01 Hispanic 0.219851E+00 Numerator Unknown Denominator Unknown Database Contributors Contributors Likelihood Ratio ------------------------------------------------------------------------ Afr-Amer 0 1 3.40 Afr-Amer 0 2 1.41 Afr-Amer 0 3 1.13 Afr-Amer 1 1 3.40 Afr-Amer 1 2 1.41 Afr-Amer 1 3 1.13 Caucasia 0 1 179.21 Caucasia 0 2 55.09 Caucasia 0 3 34.32 Caucasia 1 1 179.21 Caucasia 1 2 55.09 Caucasia 1 3 34.32 Hispanic 0 1 29.63 Hispanic 0 2 7.76 Hispanic 0 3 4.55 Hispanic 1 1 29.63 Hispanic 1 2 7.76 Hispanic 1 3 4.55 **************************************************************************** --end We could have calculated more likelihood ratios under different scenarios. These would have been written in the same file after this first result. John Storey