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Getting started

Maarten Kruijver and James Curran

2022-04-28

Introduction

In forensic genetics, the number of alleles in a mixed DNA profile is often used to gauge the number of contributors to the mixture. Two statistics are relevant: the total allele count (TAC) across all loci and the maximum allele count (MAC) across the loci. TAC is informative of the number of contributors. MAC can be used as a lower bound: if a mixture has more than \(2n\) alleles at a locus (MAC exceeds \(2n\)) then there are at least \(n+1\) mixture donors. For example, if there is a locus with five alleles (MAC=5), then the mixture can not have originated from two donors.

TAC curves

The numberofalleles package has functionality to compute the probability distribution of the TAC for a given number of contributors. Optionally, subpopulation correction and dropout can be modelled. First, we load the package and read the allele frequencies.

library(numberofalleles)
#> 
#> Attaching package: 'numberofalleles'
#> The following object is masked from 'package:stats':
#> 
#>     var
library(ggplot2)

freqs <- read_allele_freqs(system.file("extdata","FBI_extended_Cauc.csv", 
                                       package = "numberofalleles"))

gf_loci <- c("D3S1358", "vWA", "D16S539", "CSF1PO", "TPOX", "D8S1179", "D21S11", 
             "D18S51", "D2S441", "D19S433", "TH01", "FGA", "D22S1045", "D5S818", 
             "D13S317", "D7S820", "SE33", "D10S1248", "D1S1656", "D12S391", 
             "D2S1338")

Then, we call the pr_total_number_of_distinct_alleles function for \(n=1,\ldots,6\) contributors and obtain the TAC curve.

p_by_n <- list()

for (i in 1:6){
  p <- pr_total_number_of_distinct_alleles(contributors = paste0("U", seq(i)), 
                                           freqs = freqs, loci = gf_loci)
  
  p_by_n[[i]] <- data.frame(n = factor(i),
             number_of_alleles = p$noa,
             p = p$pf)
}

We use ggplot2 to plot the curves.

ggplot(subset(do.call(rbind, p_by_n), p > 1e-5)) + 
  aes(x = number_of_alleles, y = p, colour = n) + 
  geom_point() + geom_line() + xlim(0, 150) + theme_bw()

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