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

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 withk

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`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

`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.

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.

`Pevid.rel`

, `Pevid.gen`

## 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)