DNAprofiles (version 0.3.1)

rmp: Random match probability of profile(s)

Description

Computes the random/conditional match probability.

Usage

rmp(x, freqs = get.freqs(x), markers = get.markers(x), theta = 0,
  cmp = FALSE, ret.per.marker = FALSE)

Arguments

x

Integer matrix with the profile(s) for which random match probability is computed.

freqs

A list specifying the allelic frequencies. Should contain a vector of allelic frequencies for each locus, named after that locus.

markers

Character vector stating the markers to use in the rmp computation. Defaults to all markers of the profile.

theta

Numeric value specifying the amount of background relatedness.

cmp

Logical conditional match probability. If TRUE, the Balding-Nichols formula is used to compute the conditional match probability in the same subpopulation.

ret.per.marker

Logical. If TRUE, return a matrix of random match probabilities, where the columns correspond to markers.

Value

• numeric matrix of random match probabilities. When ret.per.matrix is TRUE, the columns contain rmps per marker.

Details

When $\theta=0$, the simple product rule is used. Assuming Hardy-Weinberg and Linkage Equilibrium, the random match probability (rmp) for unordered is computed as the product of $$2^H f_a f_b$$ over the loci, where $f_a$ and $f_b$ are respectively the population frequencies of allele $a$ and $b$ and $H$ is the indicator function for heterozygosity (alleles $a$ and $b$ are not the same).

When $\theta>0$ and cmp=FALSE, the product rule is used that incorporates a correction for inbreeding as measured by $theta$.

When $\theta>0$ and cmp=TRUE, a product rule involving a subpopulation correction is used, as given by Balding & Nichols. The match probability for homozygotes is given by: $$\frac{(2 \theta+(1-\theta)f_a)(3 \theta+(1-\theta)f_a)}{(1+\theta)(1+2 \theta)},$$and for heterozygotes by: $$\frac{2(\theta+(1-\theta)f_a)(\theta+(1-\theta)f_b)}{(1+\theta)(1+2\theta)}.$$

If x contains missing values (NAs) at a marker, then the returned match probability equals one for persons with both alleles missing. If a single allele is missing, then the match probability is equal to the frequency of the single allele that is seen, unless the conditional match probability is computed.

Examples

## compute the conditional match probability for two markers
data(freqsNLngm)
y <- sample.profiles(N=1,freqsNLngm)
rmp(y,markers = c("FGA","TH01"),theta=0.03,cmp=TRUE,ret.per.marker = TRUE)
rmp(y,markers = c("FGA","TH01"),ret.per.marker = TRUE) # compare to product rule estimate

## make a plot of density estimates of RMPs of profiles on the 10 SGMplus

data(freqsNLsgmplus)

#sample profiles
x <- sample.profiles(N=1e3,freqsNLsgmplus)

#compute RMPs
x.rmp <- rmp(x)

 plot(density(log10(x.rmp)),
    xlab=expression(log[10](RMP)),
    main="Random match probabilities for SGMplus profiles")