## Compute the smaller clade spectrum of a tree.

### Description

`smaller.clade.spectrum` returns a n*2 matrix where n is the number of internal nodes of the tree. For each i in 1:n, the [i,1] element of the matrix is the size of the clade rooted at the 'i'th node of the tree. [i,2] is the size of the smaller daughter clade of the 'i'th node of the tree.

### Usage

```smaller.clade.spectrum(tree)
```

### Arguments

 `tree` An object of class `"treeshape"`.

### Value

A n*2 matrix (where n is the number of internal nodes of the tree) containing the size of the clades and the smaller clades. `smaller.clade.spectrum(tree)[1,1]` contains the number of tips of the tree. `smaller.clade.spectrum(tree)[i,1]` contains the number of tips of the subtree whose root is the node number `n-i+1`. `smaller.clade.spectrum(tree)[1,2]` contains the number of tips of the smaller daughter clade at the root.

### Author(s)

Michael Blum <michael.blum@imag.fr>
Nicolas Bortolussi <nicolas.bortolussi@imag.fr>
Eric Durand <eric.durand@imag.fr>
Olivier Francois <olivier.franois@imag.fr>

`spectrum.treeshape`

### Examples

```
# computes the log-likelihood for Aldous' model
shape.new <- function(tree){
h <- function(n){sum(1/(1:n))}
parent <- mat[,1]
daughter <- mat[,2]
nh.n <- sapply(parent, FUN = function(x){x*h(x-1)} )
s <- sum(log(daughter/parent) + log(1 - daughter/parent) + log(nh.n))
return(s)}

# distribution over 200 replicates

tr <- rtreeshape(200, 100, FUN =
function(n,i){if((i>0)&(i<n))return(1/i/(n-i)) else return(0)})
res <- sapply( tr, FUN = shape.new)
hist(res)```

[Package apTreeshape version 1.5-0.1 Index]