Calculate the phylogenetic information shared, or not shared, between two splits. See the accompanying vignette for definitions.

SplitSharedInformation(n, A1, A2 = A1)

SplitDifferentInformation(n, A1, A2 = A1)

TreesConsistentWithTwoSplits(n, A1, A2 = A1)

LnTreesConsistentWithTwoSplits(n, A1, A2 = A1)

Log2TreesConsistentWithTwoSplits(n, A1, A2 = A1)

Log2TreesConsistentWithTwoSplits(n, A1, A2 = A1)

## Arguments

n

Integer specifying the number of leaves

A1, A2

Integers specifying the number of taxa in A1 and A2, once the splits have been arranged such that A1 fully overlaps with A2.

## Value

TreesConsistentWithTwoSplits() returns the number of unrooted bifurcating trees consistent with two splits.

SplitSharedInformation() returns the phylogenetic information that two splits have in common (Meila 2007) , in bits.

SplitDifferentInformation() returns the amount of phylogenetic information distinct to one of the two splits, in bits.

## Details

Split S1 divides n leaves into two splits, A1 and B1. Split S2 divides the same leaves into the splits A2 and B2.

Splits must be named such that A1 fully overlaps with A2: that is to say, all taxa in A1 are also in A2, or vice versa. Thus, all taxa in the smaller of A1 and A2 also occur in the larger.

## Functions

• SplitDifferentInformation(): Different information between two splits.

• TreesConsistentWithTwoSplits(): Number of trees consistent with two splits.

• LnTreesConsistentWithTwoSplits(): Natural logarithm of TreesConsistentWithTwoSplits().

• Log2TreesConsistentWithTwoSplits(): Base two logarithm of TreesConsistentWithTwoSplits().

• Log2TreesConsistentWithTwoSplits(): Base 2 logarithm of TreesConsistentWithTwoSplits().

## References

Meila M (2007). “Comparing clusterings---an information based distance.” Journal of Multivariate Analysis, 98(5), 873--895. doi:10.1016/j.jmva.2006.11.013 .

Other information functions: SplitEntropy(), TreeInfo

## Examples

  # Eight leaves, labelled A to H.
# Split 1: ABCD|EFGH
# Split 2: ABC|DEFGH
# Let A1 = ABCD (four taxa), and A2 = ABC (three taxa).
# A1 and A2 overlap (both contain ABC).

TreesConsistentWithTwoSplits(n = 8, A1 = 4, A2 = 3)
#> [1] 45
SplitSharedInformation(n = 8, A1 = 4, A2 = 3)
#> [1] 2.722466
SplitDifferentInformation(n = 8, A1 = 4, A2 = 3)
#> [1] 5.129283

# If splits are identical, then their shared information is the same
# as the information of either split:
SplitSharedInformation(n = 8, A1 = 3, A2 = 3)
#> [1] 5.044394
TreeTools::SplitInformation(3, 5)
#> [1] 5.044394