# howmanytrees

##### Calculate Numbers of Phylogenetic Trees

This function calculates the number of possible phylogenetic trees for a given number of tips.

##### Usage

```
howmanytrees(n, rooted = TRUE, binary = TRUE,
labeled = TRUE, detail = FALSE)
```

##### Arguments

- n
- a positive numeric integer giving the number of tips.
- rooted
- a logical indicating whether the trees are rooted
(default is
`TRUE`

). - binary
- a logical indicating whether the trees are bifurcating
(default is
`TRUE`

). - labeled
- a logical indicating whether the trees have tips
labeled (default is
`TRUE`

). - detail
- a logical indicating whether the eventual intermediate
calculations should be returned (default is
`FALSE`

). This applies only for the multifurcating trees, and the bifurcating, rooted, unlabeled trees (aka tree shapes).

##### Details

In the cases of labeled binary trees, the calculation is done directly and a single numeric value is returned.

For multifurcating trees, and bifurcating, rooted, unlabeled trees,
the calculation is done iteratively for 1 to `n`

tips. Thus the
user can print all the intermediate values if `detail = TRUE`

, or
only a single value if `detail = FALSE`

(the default).

For multifurcating trees, if `detail = TRUE`

, a matrix is
returned with the number of tips as rows (named from `1`

to
`n`

), and the number of nodes as columns (named from `1`

to
`n - 1`

). For bifurcating, rooted, unlabeled trees, a vector is
returned with names equal to the number of tips (from `1`

to
`n`

).

The number of unlabeled trees (aka tree shapes) can be computed only for the rooted binary cases.

Note that if an infinite value (`Inf`

) is returned this does not
mean that there is an infinite number of trees (this cannot be if the
number of tips is finite), but that the calculation is beyond the
limits of the computer.

##### Value

- a single numeric value, or in the case where
`detail = TRUE`

is used, a named vector or matrix.

##### References

Felsenstein, J. (2004) *Inferring phylogenies*. Sunderland:
Sinauer Associates.

##### Examples

```
### Table 3.1 in Felsenstein 2004:
for (i in c(1:20, 30, 40, 50))
cat(paste(i, howmanytrees(i), sep = "t"), sep ="")
### Table 3.6:
howmanytrees(8, binary = FALSE, detail = TRUE)
```

*Documentation reproduced from package ape, version 2.6-3, License: GPL (>= 2)*