R: Number of trees

NRooted {TreeTools} | R Documentation

## Number of trees

### Description

These functions return the number of rooted or unrooted binary trees consistent with a given pattern of splits.

### Usage

    NRooted(tips)

    NUnrooted(tips)

    NRooted64(tips)

    NUnrooted64(tips)

    LnUnrooted(tips)

    LnUnrooted.int(tips)

    Log2Unrooted(tips)

    Log2Unrooted.int(tips)

    LnRooted(tips)

    LnRooted.int(tips)

    Log2Rooted(tips)

    Log2Rooted.int(tips)

    LnUnrootedSplits(...)

    Log2UnrootedSplits(...)

    NUnrootedSplits(...)

    LnUnrootedMult(...)

    Log2UnrootedMult(...)

    NUnrootedMult(...)

### Arguments

`tips` | Integer specifying the number of leaves.
`...` | Integer vector, or series of integers, listing the number of leaves in each split.

### Details

Functions starting `N` return the number of rooted or unrooted trees. Replace this initial `N` with `Ln` for the natural logarithm of this number; or `Log2` for its base 2 logarithm.

Calculations follow Cavalli-Sforza & Edwards (1967) and Carter et al. 1990, Theorem 2.

### Functions

- `NUnrooted`: Number of unrooted trees

- `NRooted64`: Exact number of rooted trees as 64-bit integer (13 < `nTip` < 19)

- `NUnrooted64`: Exact number of unrooted trees as 64-bit integer (14 < `nTip` < 20)

- `LnUnrooted`: Log Number of unrooted trees

- `LnUnrooted.int`: Log Number of unrooted trees (as integer)

- `LnRooted`: Log Number of rooted trees

- `LnRooted.int`: Log Number of rooted trees (as integer)

- `NUnrootedSplits`: Number of unrooted trees consistent with a bipartition split.

- `NUnrootedMult`: Number of unrooted trees consistent with a multi-partition split.

### Author(s)

Martin R. Smith (martin.smith@durham.ac.uk)

### References

Carter M, Hendy M, Penny D, Székely LA, Wormald NC (1990). “On the distribution of lengths of evolutionary trees.” SIAM Journal on Discrete Mathematics, 3(1), 38–47. doi: 10.1137/0403005.

Cavalli-Sforza LL, Edwards AWF (1967). “Phylogenetic analysis: models and estimation procedures.” Evolution, 21(3), 550–570. ISSN 00143820, doi: 10.1111/j.1558-5646.1967.tb03411.x.

### See Also

Other tree information functions: `CladisticInfo()`, `TreesMatchingTree()`

### Examples

    NRooted(10)
    NUnrooted(10)
    LnRooted(10)
    LnUnrooted(10)
    Log2Unrooted(10)
    # Number of trees consistent with a character whose states are
    # 00000 11111 222
    NUnrootedMult(c(5,5,3))

    NUnrooted64(18)
    LnUnrootedSplits(c(2,4))
    LnUnrootedSplits(3, 3)
    Log2UnrootedSplits(c(2,4))
    Log2UnrootedSplits(3, 3)
    NUnrootedSplits(c(2,4))
    NUnrootedSplits(3, 3)

[Package TreeTools version 1.5.1 Index]