pr_number_of_distinct_alleles {numberofalleles}

Compute the probability distribution of the number of distinct alleles observed in a DNA mixture for a locus

Description

For a given number of independent alleles, compute the probability distribution of the number of distinct alleles observed in a DNA mixture.

Usage

pr_number_of_distinct_alleles(
  number_of_independent_alleles,
  f,
  fst = 0,
  brute_force = FALSE
)

Arguments

number_of_independent_alleles

Integer. Number of independent alleles in the mixture.

f

Numeric vector with allele frequencies

fst

Numeric value for sub-population correction (also known as theta)

brute_force

Logical. Should a brute force algorithm be used?

Details

Due to allele sharing between DNA mixture contributors, the number of distinct alleles observed in a mixture is often less than the number of independent alleles in the mixture. For example, if mixture comprises two unrelated contributors, there are four independent alleles. Some of these four independent alleles may be of the same allelic type so that at least one and at most four distinct alleles are observed.

This function computes the probability distribution of the number of distinct alleles observed when the mixtures comprises a given number of independent alleles. Optionally, a sub-population correction may be applied by setting fst>0.

An efficient way of computing the probability distribution was given by Tvedebrink (2014) and was slightly adapted by Kruijver & Curran (2022) to handle the case of an odd number of independent alleles. A much slower brute force algorithm is also implemented (argument brute_force=TRUE) for testing purposes.

Value

A named numeric vector describing the probability distribution. Numeric values are the probabilities corresponding to the names describing integer values.

References

M. Kruijver & J.Curran (2022). 'The number of alleles in DNA mixtures with related contributors', manuscript submitted

T. Tvedebrink (2014). 'On the exact distribution of the number of alleles in DNA mixtures', International Journal of Legal Medicine; 128(3):427–37. doi: 10.1007/s00414-013-0951-3

Examples

f <- c(A = 0.1, B = 0.2, C = 0.7)

p <- pr_number_of_distinct_alleles(3, f)
p_by_hand <- c(sum(f^3), 1 - sum(f^3) - 6 * prod(f), 6 * prod(f))
stopifnot(all.equal(as.vector(p), p_by_hand))