Number of trees
These functions return the number of rooted or unrooted binary trees consistent with a given pattern of splits.
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(...)
tips |
Integer specifying the number of leaves. |
... |
Integer vector, or series of integers, listing the number of leaves in each split. |
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.
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.
Martin R. Smith (martin.smith@durham.ac.uk)
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, https://doi.org/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, https://doi.org/10.1111/j.1558-5646.1967.tb03411.x.
Other tree information functions:
CladisticInfo(),
TreesMatchingTree()
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)
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