## Node_Prob_Functions

The file `Node_Prob_Functions.R`

is a compilation of methods which include a coalescence simulator for trees sampled at the same time, conversion of the simulator into a phylo object accepted by apein R, simulation of where an additional unknown sample would fall for an ultrametric tree,and the proportion of samples expected under any internal node in a given phylogenetic tree with a known effective population size.

Methods Included:

### For Ultrametric Trees

#### cosim(n, popsize)

- Description: Uses the coalescent framework to simulate an ultrametric tree structure. Returns an object with a list of branch lengths, descendants, number of lineages from each node, hash table mapping parent nodes to descendants, total generations, and intervals between branches.
- Arguments: n-number of samples, popsize-effective population size.

#### traverse(xhash, node=0)

- Description: Recursively performs in-order tree traversal.
- Arguments: xhash-the hash table with key value pairs of nodes and their descendants, node-node to start traversal at, default at 0.

#### create.phylo(n, popsize)

- Description: Creates a phylo object accepted by ape using cosim() and traverse() functions for ultrametric trees.
- Arguments: n-number of samples, popsize-effective population size

#### interval.sort(tr)

- Description: returns a matrix with three columns corresponding to length of current interval, origin node for that interval, and number of lineages in that interval respectively.
- Arguments:
`tr`

- a phylo object tree.

#### interval.pcoal.sort(tr, popsize)

- Description: Returns the probability of coalescence within an interval for each internal node using an exponential distribution to model probabilities of coalescence.
- Arguments: tr-a phylo object tree, popsize-effective population size.

#### one.lin.p(t, popsize)

- Description: Returns a list of conditional probabilities for each interval of the probability of landing on a specific lineage in an interval given that it didn't coalesce to the tree in a previous interval.
- Arguments: t-a phylo object tree, popsize- effective population size.

#### node.prob(t, subtree, popsize)

- Description: for an internal node, returns the proportion of samples expected to coalesce under this subtree rooted at the internal node.
- Arguments: t-a phylo object tree, subtree- a phylo object subtree rooted at the node of interest, popsize- effective population size.

#### drop.t(tr, ndtips, p=TRUE)

- Description: Returns a phylo object tree with ndtips randomly dropped tips. If p=TRUE, plots the difference between trees.
- Arguments: t-a phylo object tree, ndtips- number of tips to drop, p-whether to plot the change between trees.

#### tree.overlay(tr, ndtips)

- Description: Plots the overerlay between a tree and the resulting tree with ndtips fewer tips.
- Arguments: tr- a phylo object tree, ndtips- number of tips to drop.

### For Simulation (of Ultrametric Trees)

#### lins.in.interval(t, ints=interval.sort(t))

- Description: Returns a hash table with the lineage names in each interval. The interval serves as the key and is denoted by the node at the left boundary of the interval. The lineages in it are values, denoted to the first top or node to the right of the interval boundary.
- Arguments: t-a phylo object tree, ints-a matrix of sorted intervals returned by the interval.sort(t) method.

#### interval.sim(t, popsize, numsim=1000)

- Description: Returns a list of average proportion of times a new, unknown sample would land under a particular node. Does this through storing a matrix of numsim rows and number of nodes columns and recording where a randomly added sample falls.
- Arguments: t-a phylo object tree, popsize- effective population size, numsim- number of simulations desired.

### For Time Sampled Trees

#### dist.to.root(t)

- Description: Returns a matrix of node or tip label and the corresponding distance to the root of the tree, ordered by decreasing distance.
- Arguments: t-a phylo object tree.

#### nu.interval.sort(t)

- Description: returns a matrix with three columns corresponding to length of current interval, origin node for that interval, and number of lineages in that interval respectively.
- Arguments: tr-a phylo object tree.

#### nu.pcoal.cont(t, popsize)

- Description: Returns the probability of coalescence within an interval for each internal node using an exponential distribution to model probabilities of coalescence.
- Arguments: tr-a phylo object tree, popsize-effective population size.

#### nu.one.lin.p(t, popsize)

- Description: Returns a list of conditional probabilities for each interval of the probability of landing on a specific lineage in an interval given that it didn't coalesce to the tree in a previous interval.
- Arguments: t-a phylo object tree, popsize- effective population size.

#### nu.node.prob(t, subtree, popsize)

- Description: for an internal node, returns the proportion of samples expected to coalesce under this subtree rooted at the internal node.
- Arguments: t-a phylo object tree, subtree- a phylo object subtree rooted at the node of interest, popsize- effective population size.