003-infinite-sites-mutation.Rmd

---
title: "Infinite Sites Mutation"
output: 
  html_notebook:
    toc: true
    toc_float: true
author: "Eric C. Anderson"
bibliography: references.bib
---


```{r, message=FALSE, warning=FALSE}
library(tidyverse)
library(GSImulator)
library(ape)
library(ggtree)
```

`ms` will simulate infinite sites mutation very readily.  There are two
options.  

First we can tell it to simulate an exact number of segregating sites (like 7, for
example):
```{r}

cat("101 203", file = "seedms")  # this sets the seed for ms
system2(command = ms_binary(), args = "10 1 -s 7 -T")
```

Notice that the samples can be thought of as being labeled 1--10, and the mutations
can be thought of as being labeled 1--7.  Each line like 0010010 is an individual
gene sequence sample.  A 1 means it inherited the mutation, and a 0 means it inherited
the non-mutated base.

## In class exercise 1

Pair up with your partner. Each group will be assigned a site (i.e. 
a mutation).  Figure out which branch in the tree below that mutation must have occurred.  Each
group will then stick their mutation to their branch with some tape.
```{r echo=FALSE}
cat("101 203", file = "seedms")  # this sets the seed for ms
system2(command = ms_binary(), args = "10 1 -s 7 -T", stdout = "out.tree", stderr = FALSE)
ctree <- read.tree("out.tree") 
ggtree(ctree, layout = "rectangular") +
  geom_tiplab(size = 5)
```


## In class excerise 2

This exercise will get us thinking about what is called the 
"four-gamete test".  Each group will take their site and one other site
that they can choose from amongst the 7, and count up the number of
different pairs of mutations at the two sites are found by looking at the 
segretating sites output above, and then write that on the board.  
For example, for sites 1 and 2 the result that gets written on the board should
look like:

  Pair  |   n 
--------|----
00 | 5
01 | 4
10 | 1

Each group will do this with two pairs of sites.  For example, if your
group is assigned site 1, you might to it for sites 1 and 2 and sites 1 and 5.

Write each little table on the board with a title like "Sites 1,2" above each.
When that is done, we will talk about it.



### Sprinkling mutations at rate $\theta = 4N\mu$

Instead of using the `-s` option to specify the exact number of segregating sites,
you can also use the `-t` option to specify $\theta = 4N\mu L$ where $\nu$ is the 
per-base-pair per-generation mutation rate and $L$ is the length of the DNA sequence
in number of base pairs.  Under the infinite sites model, each mutation is an entirely
novel mutation.