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`

.

## 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()`

## 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
```