forensic (version 0.2)

Pmatch: Match Probabilities of Genotype

Description

Calculates match probability of the genotype of the suspect and that of the crime stain presumed to have come from an offender other than the suspect. Possible assumptions: the suspect and an unknown offender are unrelated, or are members of the same subpopulation with a given coancestry coefficient, or are close relatives.

Usage

Pmatch(prob, k = c(1, 0, 0), theta = 0)

Arguments

prob

matrix with 2 rows and L columns (L is the number of loci, each locus has 2 alleles). Contains frequencies of alleles in a population found in the crime stain. For homozygous locus just one entry is nonzero. prob can also be a vector with

k

vector of kinship coefficients $(k_0, k_1, k_2)$, where $k_i$ is the probability that two people (the suspect and an unknown offender) will share $i$ alleles identical by descent, $i = 0, 1, 2$.

theta

number from the interval [0,1). Coancestry coefficient theta describes variation in allele proportions among subpopulations. Default is 0 (no variation, whole population in Hardy-Weinberg equilibrium). The recommended values of theta

Value

• Pmatch returns a list with the following components:
• prob
  matrix of allele proportions at each locus (input value in Pmatch)
• match
  single locus match probabilities
• total_match
  match probability of genotype = multiplication of single locus match probabilities

Details

The match probability is calculated as $$k_2 + k_1 Z_1 + k_0 Z_2,$$ where $k_0, k_1, k_2$ are the kinship coefficients (for more information see Details of Pevid.rel), $$Z_2=\frac{\left[2\theta+(1-\theta)p_i\right] \left[3\theta+(1-\theta)p_i \right]}{(1+\theta)(1+2\theta)},$$ $$Z_2=\frac{2\left[\theta+(1-\theta)p_i\right] \left[\theta+(1-\theta)p_j \right]}{(1+\theta)(1+2\theta)}$$ are the match probabilities in the unrelated case for homozygotes and heterozygotes, respectively, and $$Z_1=\frac{2\theta + (1-\theta)p_i}{1+\theta}$$ for the homozygote case and $$Z_1=\frac{2\theta + (1-\theta)(p_i+p_j)}{2(1+\theta)}$$ for the heterozygote case. The quantity $\theta$ is the coancestry population theta. The formula is derived in Balding and Nichols (1994).

The match probability at all loci is calculated as a product of all single locus probabilities. We assume independence across loci.

References

Balding DJ, Nichols RA (1994), DNA profile match probability calculation: how to allow for population stratification, relatedness, database selection and single bands. Forensic Science International 64, 125-140.

Evett IW, Weir BS (1998), Interpreting DNA evidence; Statistical genetics for forensic scientists. Sinauer, Sunderland, MA.

National Research Council (1996), The evaluation of forensic DNA evidence National Academy Press, Washington, DC.

See Also

Pevid.rel, Pevid.gen

Examples

## match probability of thirteen-locus genotype 
    ## (11 heterozygous and 2 homozygous loci)
    p<-c(0.057,0.160,0.024,0.122,0.078,0.055,0.035,0.150,
      0.195,0.027,0.084,0.061,0.122,0.083,0.164,0.065,0.143,
      0.151,0.167,0.180,0.099,0.182,0.120,0,0.182,0)
    ## suspect and offender are unrelated 
    Pmatch(p)
    ## suspect and offender are unrelated but members of the same 
    ## subpopulation with the coancestry coefficient theta 
    Pmatch(p, theta = 0.03)
    ## suspect and offender are close relatives (cousins) 
    Pmatch(p, k = c(3/4, 1/4, 0))
    ## suspect and offender are close relatives (cousins) and 
    ## members of the same subpopulation with the coancestry 
    ## coefficient theta 
    Pmatch(p, k = c(3/4, 1/4, 0), theta = 0.03)
    ##
    ## one locus
    Pmatch(p[1:2], theta = 0.03)
    Pmatch(p[25:26], theta = 0.03)
    ## compare
    Pevid.gen(alleles = c(1, 2), prob = p[1:2], V = "1/2", x = 1, 
      theta = 0.03)
    Pevid.gen(alleles = "a", prob = p[25], V = "a/a", x = 1, 
      theta = 0.03)