# Using TBRDist

#### Martin R. Smith

#### 2020-09-17

‘TBRDist’ is an R package to compare unrooted phylogenetic trees using the SPR, TBR and Replug distances.

## Loading trees

This document assumes familiarity with the process of loading trees into R.

We’ll work with some simple trees generated using the ‘TreeTools’ package.

    library('TreeTools', quietly = TRUE, warn.conflicts = FALSE)

    tree1 <- BalancedTree(10)
    tree2 <- PectinateTree(10)

    origPar <- par(mfrow = 1:2, mar = rep(0.2, 4)) # Set up plotting area
    plot(tree1)
    plot(tree2)

## Calculating distances

After installing TBRDist (`install.packages('TBRDist')`), load the package into R with

    library('TBRDist')

To generate an approximate SPR distance between two unrooted trees, use:

    USPRDist(tree1, tree2)

    ## [1] 2

For Replug distances, it’s:

    ReplugDist(tree1, tree2)

    ## [1] 2

For TBR distances, use:

    TBRDist(tree1, tree2, exact = TRUE)

    ## [1] 1

When calculating an exact TBR distance, we receive information on the maximum agreement forest for free (i.e. with no extra processing cost):

    TBRDist(tree1, tree2, exact = TRUE, maf = TRUE)

    ## $tbr_exact
    ## [1] 1
    ##
    ## $maf_1
    ## [1] "(t4,t5,((t1,t2),t3)); ((t9,t10),t8,(t7,t6));"
    ##
    ## $maf_2
    ## [1] "(((t1,t2),t3),t4,t5); ((t6,t7),(t9,t10),t8);"

Once trees have more than about a dozen tips, it becomes slow to calculate the exact distance. In the interests of speed, we may wish to approximate the value of the TBR distance:

    TBRDist(tree1, tree2, exact = FALSE)

    ## $tbr_min
    ## [1] 1
    ##
    ## $tbr_max
    ## [1] 3

## Comparing multiple trees

To avoid multiple calls, each function can also be used to compare lists of trees (or `multiPhylo` objects) against a single tree:

    TBRDist(tree1, list(tree1, tree2), exact = TRUE, maf = TRUE)

    ## $tbr_exact
    ## [1] 0 1
    ##
    ## $maf_1
    ## [1] "((((t1,t2),t3),(t4,t5)),(t9,t10),((t6,t7),t8));"
    ## [2] "(t4,t5,((t1,t2),t3)); ((t9,t10),t8,(t7,t6));"
    ##
    ## $maf_2
    ## [1] "((((t1,t2),t3),(t4,t5)),(t9,t10),((t6,t7),t8));"
    ## [2] "(((t1,t2),t3),t4,t5); ((t6,t7),(t9,t10),t8);"

Or against each corresponding entry in a second list:

    USPRDist(list(tree1, tree2, tree2), list(tree2, tree1, tree2))

    ## [1] 2 2 0

## Citation

If you use ‘TBRDist’ in your research, please cite:

- Chris Whidden and Frederick A. Matsen IV (2017). Calculating the Unrooted Subtree-Prune-and-Regraft Distance. eprint arXiv:1511.07529.

Optionally, a citation to the ‘TBRDist’ R package would be welcome:

- Smith (2019). TBRDist: Calculate SPR and TBR distance between unrooted phylogenetic trees. doi:10.5281/zenodo.3548333