Matching partitions

Calculates how many of the partitions present in tree 1 are also present in tree 2 (s), how many of the partitions in tree 1 are absent in tree 2 (d1), and how many of the partitions in tree 2 are absent in tree 1 (d2). The Robinson-Foulds (symmetric partition) distance is the sum of the latter two quantities, i.e. d1 + d2.

SplitStatus(trees, cf = trees[[1]])

SharedSplitStatus(trees, cf)

Arguments

trees

A list of trees of class phylo, with identically labelled tips.

cf

Comparison tree of class phylo. If unspecified, each tree is compared to the first tree in trees.

Value

Returns a two dimensional array. Rows correspond to the input trees, and are named if names were present. Columns report:

N: The total number of partitions present in the two trees, i.e. P1 + P2.

P1: The number of partitions present in tree 1.

P2: The number of partitions present in tree 2.

s: The number of partitions present in both trees.

d1: The number of partitions present in tree 1, but contradicted by tree 2.

d2: The number of partitions present in tree 2, but contradicted by tree 1.

r1: The number of partitions present in tree 1, and neither present nor contradicted in tree 2.

r2: The number of partitions present in tree 2, and neither present nor contradicted in tree 1.

Functions

• SharedSplitStatus(): Reports split statistics obtained after removing all tips that do not occur in both trees being compared.

References

• Robinson DF, Foulds LR (1981). “Comparison of phylogenetic trees.” Mathematical Biosciences, 53(1-2), 131--147. doi:10.1016/0025-5564(81)90043-2 .

• Penny D, Hendy MD (1985). “The use of tree comparison metrics.” Systematic Zoology, 34(1), 75--82. doi:10.2307/2413347 .

See also

Other element-by-element comparisons: CompareQuartets(), CompareQuartetsMulti(), CompareSplits(), PairSharedQuartetStatus(), QuartetState(), SharedQuartetStatus()

Author

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

Examples

data("sq_trees")

# Calculate the status of each quartet
splitStatuses <- SplitStatus(sq_trees)

# Calculate the raw symmetric difference (i.e. Robinson–Foulds distance)
RawSymmetricDifference(splitStatuses)
#>       ref_tree  move_one_near   move_one_mid   move_one_far  move_two_near 
#>              0              2              6              8              2 
#>   move_two_mid   move_two_far   collapse_one  collapse_some     m1mid_col1 
#>              4              6              1              5              7 
#>  m1mid_colsome     m2mid_col1  m2mid_colsome  opposite_tree    caterpillar 
#>              9              5              5             16              8 
#>   top_and_tail anti_pectinate    random_tree 
#>             16             16             16 

# Normalize the Robinson Foulds distance by dividing by the number of 
# splits present in the two trees:
RawSymmetricDifference(splitStatuses) / splitStatuses[, "N"]
#>       ref_tree  move_one_near   move_one_mid   move_one_far  move_two_near 
#>     0.00000000     0.12500000     0.37500000     0.50000000     0.12500000 
#>   move_two_mid   move_two_far   collapse_one  collapse_some     m1mid_col1 
#>     0.25000000     0.37500000     0.06666667     0.45454545     0.46666667 
#>  m1mid_colsome     m2mid_col1  m2mid_colsome  opposite_tree    caterpillar 
#>     0.69230769     0.33333333     0.45454545     1.00000000     0.50000000 
#>   top_and_tail anti_pectinate    random_tree 
#>     1.00000000     1.00000000     1.00000000 

# Normalize the Robinson Foulds distance by dividing by the total number of 
# splits that it is possible to resolve for `n` tips:
nTip <- length(sq_trees[[1]]$tip.label)
nPartitions <- 2 * (nTip - 3L) # Does not include the nTip partitions that 
                               # comprise but a single tip
RawSymmetricDifference(splitStatuses) / nPartitions
#>       ref_tree  move_one_near   move_one_mid   move_one_far  move_two_near 
#>         0.0000         0.1250         0.3750         0.5000         0.1250 
#>   move_two_mid   move_two_far   collapse_one  collapse_some     m1mid_col1 
#>         0.2500         0.3750         0.0625         0.3125         0.4375 
#>  m1mid_colsome     m2mid_col1  m2mid_colsome  opposite_tree    caterpillar 
#>         0.5625         0.3125         0.3125         1.0000         0.5000 
#>   top_and_tail anti_pectinate    random_tree 
#>         1.0000         1.0000         1.0000