R: Probability of DNA Evidence With the Presence of Relatives
Pevid.rel
R Documentation
Probability of DNA Evidence With the Presence of Relatives
Description
Computes probability of DNA evidence, given the proposition about who the
contributors to the mixture were. Two main cases are considered:
tested suspect (noncontributor) with an unknown relative (contributor),
or unknown suspect (contributor) with a tested relative (noncontributor)
and two unknown related people as contributors.
Usage
Pevid.rel(alleles, prob, x, u = NULL, k = c(1, 0, 0), S = NULL)
Arguments
alleles
vector of distinct alleles (from one specific locus)
found in the crime sample.
prob
vector of corresponding allele proportions in a population
x
nonnegative integer. The number of unknown contributors to
the mixture.
u
vector of alleles from the mixture, which are not carried by
known contributors (and have to be carried by some unknown contributors).
If u=NULL (default), all alleles from the crime sample are carried
by known contributors.
k
vector of kinship coefficients (k_0, k_1, k_2), where
k_i is the probability that two people will share i alleles
identical by descent, i = 0, 1, 2.
S
object of class genotype (package genetics), or a string
of length 1 with two alleles seperated by '/'.
Genotype of the typed person (declared noncontributor) whose untyped
relative is assumed to be a contributor to the sample.
If S = NULL (default), we consider two related unknown contributors.
Details
Table of kinship coefficients for commonly encountered relationships:
Relationship
k_0
k_1
k_2
Parent - child
0
1
0
Grandparent - grandchild
1/2
1/2
0
Full sibs
1/4
1/2
1/4
Halfsibs
1/2
1/2
0
Uncle - nephew
1/2
1/2
0
First cousins
3/4
1/4
0
Second cousins
15/16
1/16
0
Unrelated
1
0
0
The formulas (and their derivations) for the evaluation of the probabilities
of DNA evidence with the presence of at most 2 relatives can be found in
Hu and Fung (2003).
The work was supported by the project 1M06014 of the
Ministry of Education, Youth and Sports of the Czech Republic.
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.
Fung WK, Hu YQ (2000), Interpreting DNA mixtures based on the NRC-II recommendation
4.1. Forensic Sci Commun. Available at http://www.fbi.gov/hq/lab/fsc/backissu/oct2000/fung.htm
Hu YQ, Fung WK (2003), Interpreting DNA mixtures with the presence of relatives.
International Journal od Legal Medicine 117, 39-45.
Evett IW, Weir BS (1998), Interpreting DNA evidence.
Statistical genetics for forensic scientists. Sinauer, Sunderland, MA.
See Also
Pmatch
Examples
## Rape case in Hong Kong (Fung and Hu (2000))
## mixture (loci: D3S1358, vWA, FGA)
m1 <- c(14, 15, 17, 18)
m2 <- c(16, 18)
m3 <- c(20, 24, 25)
## genotype of the victim (loci: D3S1358, vWA, FGA):
victim_1 = "15/18"
victim_2 = "18/18"
victim_3 = "20/24"
## genotype of the suspect (loci: D3S1358, vWA, FGA):
suspect_1 = "14/17"
suspect_2 = "16/16"
suspect_3 = "25/25"
## allele proportions
p1 <- c(0.033, 0.331, 0.239, 0.056)
p2 <- c(0.155, 0.158)
p3 <- c(0.042, 0.166, 0.106)
##
## Likelihood ratio for DNA evidence:
## Prosecution proposition:
## Contributors were the victim and the suspect.
## Defence proposition 1:
## Contributors were the victim and one relative of the suspect (sibling).
print(LR11 <- 1 / Pevid.rel(alleles = m1, prob = p1, x = 1,
k = c(1/4, 1/2, 1/4), S = suspect_1, u = c(14, 17)))
print(LR12 <- 1 / Pevid.rel(alleles = m2, prob = p2, x = 1,
k = c(1/4, 1/2, 1/4), S = suspect_2, u = 16))
print(LR13 <- 1 / Pevid.rel(alleles = m3, prob = p3, x = 1,
k = c(1/4, 1/2, 1/4), S = suspect_3, u = 25))
##
## Defence proposition 2:
## Contributors were one relative of the suspect (sibling) and one unknown.
print(LR21 <- 1 / Pevid.rel(alleles = m1, prob = p1, x = 2,
k = c(1/4, 1/2, 1/4), S = suspect_1, u = m1))
print(LR22 <- 1 / Pevid.rel(alleles = m2, prob = p2, x = 2,
k = c(1/4, 1/2, 1/4), S = suspect_2, u = m2))
print(LR23 <- 1 / Pevid.rel(alleles = m3, prob = p3, x = 2,
k = c(1/4, 1/2, 1/4), S = suspect_3, u = m3))
##
## Defence proposition 3:
## Contributors were two related people (siblings).
print(LR31 <- 1 / Pevid.rel(alleles = m1, prob = p1, x = 2,
k = c(1/4, 1/2, 1/4), u = m1))
print(LR32 <- 1 / Pevid.rel(alleles = m2, prob = p2, x = 2,
k = c(1/4, 1/2, 1/4), u = m2))
print(LR33 <- 1 / Pevid.rel(alleles = m3, prob = p3, x = 2,
k = c(1/4, 1/2, 1/4), u = m3))
##
## Likelihood ratios overall:
## for defence proposition 1
LR11*LR12*LR13
## for defence proposition 2
LR21*LR22*LR23
## for defence proposition 3
LR31*LR32*LR33