---
title: "Getting started"
author: "Maarten Kruijver and James Curran"
output: rmarkdown::html_vignette
date: "`r Sys.Date()`"
vignette: >
  %\VignetteIndexEntry{getting_started-vignette}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

# 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.
```{r setup}
library(numberofalleles)
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.
```{r TAC}
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.
```{r fig.asp = 0.4, fig.width = 7}
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()
```