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)
Integer specifying the number of leaves
Integers specifying the number of taxa in A1 and A2, once the splits have been arranged such that A1 fully overlaps with A2.
TreesConsistentWithTwoSplits() returns the number of unrooted bifurcating
trees consistent with two splits.
SplitSharedInformation() returns the phylogenetic information that two splits
have in common, in bits.
SplitDifferentInformation() returns the amount of phylogenetic information
distinct to one of the two splits, in bits.
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.
SplitDifferentInformation: Different information between two splits.
TreesConsistentWithTwoSplits: Number of trees consistent with two
LnTreesConsistentWithTwoSplits: Natural logarithm of
Log2TreesConsistentWithTwoSplits: Base two logarithm of
Log2TreesConsistentWithTwoSplits: Base 2 logarithm of
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 .
# 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) #>  45 SplitSharedInformation(n = 8, A1 = 4, A2 = 3) #>  2.722466 SplitDifferentInformation(n = 8, A1 = 4, A2 = 3) #>  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) #>  5.044394 TreeTools::SplitInformation(3, 5) #>  5.044394