forensic (version 0.2)

Pevid.gen: Probability of DNA Evidence (Allowing for Population Substructure and Dependence)

Description

Calculates conditional probability of DNA evidence, given proposition about who the known and unknown contributors to the mixture were. All the individuals involved in a case are assumed to come from the same subpopulation with a given coancestry coefficient. Independence of alleles in the subpopulation (i.e., relatives are excluded) and dependence in the whole population is assumed.

Usage

Pevid.gen(alleles, prob, x, T = NULL, V = NULL, theta = 0)

Arguments

alleles

vector of distinct alleles (from one specific locus) found in the crime sample.

prob

vector of corresponding allele proportions in a population. The allele proportions are estimated from the whole population.

x

nonnegative integer. The number of unknown contributors to the mixture.

T

object of class genotype (package genetics), or a vector of strings where each string contains two alleles seperated by '/', corresponding to one known contributor. The length of the vector equals the number of known contributors. Default is NULL.

V

object of class genotype (package genetics), or a vector of strings where each string contains two alleles seperated by '/', corresponding to one known noncontributor. The length of the vector equals the number of known noncontributors. Default is NULL.

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 are 0.01 for large subpopulations such as USA, and 0.03 for small isolated subpopulations (National Research Council, 1996).

Value

probability of the DNA evidence

Details

The general formula for the evaluation of the probability of DNA evidence (and its derivation) can be found in Zoubkova and Zvarova (2004).

If theta = 0, Pevid.gen returns the same numerical result as Pevid.ind.

References

Curran JM, Triggs CM, Buckleton J, Weir BS (1999), Interpreting DNA mixtures in structured populations, Journal of Forensic Sciences 44, 987-995.

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

Fung WK, Hu YQ (2000), Interpreting forensic DNA mixtures: allowing for uncertainty in population substructure and dependence, Journal of the Royal Statistical Society A 163, 241-254. National Research Council (1996), The evaluation of forensic DNA evidence National Academy Press, Washington, DC.

Zoubkova K, Zvarova J (2004), Statisticke metody ve forenzni genetice, Master's thesis, Charles University, Prague.

See Also

Pevid.ind, LR.ind, Pmatch

Examples

   ## Rape case 
   ## The evidence profile: 
   m <- c(13, 14, 15) 
   ##  the victim's genotype:
   victim <- "13/14"
   ## the suspect's genotype 
   suspect <- "15/15"
   ## frequencies of alleles {13, 14, 15}:
   p <- c(0.042, 0.166, 0.106) 
   ## consensual partner of the victim
   partner <- "15/16"
   ## Prosecution proposition: 
   ## Contributors were the victim and the suspect.
   Pevid.gen( alleles = m, prob = p, T = c(victim, suspect), 
     V = partner, x = 0, theta = 0.03)
   ## Defence proposition: 
   ## Contributors were the victim and one unknown person.
   ## 
   ## Likelihood ratio for DNA evidence:
   ## structured population
   1/Pevid.gen( alleles = m, prob = p, T = victim, 
     V = c(suspect, partner), x = 1, theta = 0.03)
   ## Note: a person carrying both alleles different from the alleles 
   ## in the crime sample (e.g., with genotype "16/16") has no effect 
   ## on the value of LR: 
   1/Pevid.gen( alleles = m, prob = p, T = victim, 
     V = c(suspect, partner, "16/16"), x = 1, theta = 0.03)
   ## But the consensual partner of the victim having genotype "15/16" 
   ## influences the value of LR, compare:
   1/Pevid.gen( alleles = m, prob = p, T = victim, V = suspect, 
     x = 1, theta = 0.03)
   ## 
   ## population in Hardy - Weinberg equilibrium      
   1/Pevid.gen( alleles = m, prob = p, T = victim, 
     V = c(suspect, partner), x = 1)
   1/Pevid.gen( alleles = m, prob = p, T = victim, x = 1)
   ## compare
   1/Pevid.ind( alleles = m, prob = p, u = 15, x = 1)