A three-dimensional array listing the distances between
1 000
random pairs of trees drawn from the uniform distribution using
`RandomTree(nTip, root = TRUE)`

.

`randomTreeDistances`

An object of class `array`

of dimension 22 x 13 x 197.

Scripts used to generate data objects are housed in the
`data-raw`

directory.

Distances were calculated using `AllDists()`

; see the documentation at
there for details of methods and their normalization.

Rows are named with abbreviations of the tree comparison metrics tested (see 'Methods tested' below).

Columns list the summary statistics of calculated tree distances: the
minimum (`min`

),
1%, 5%, 10%, 25%, 50% (i.e. median), 75%, 90%, 95%, 99% percentiles,
maximum (`max`

), mean (`mean`

) and standard deviation (`sd`

).

The third dimension lists the number of leaves in the trees compared.

For analysis of this data, see the accompanying vignette.

`pid`

: Phylogenetic Information Distance (Smith 2020), normalized against the phylogenetic information content of the splits in the trees being compared.`msid`

: Matching Split Information Distance (Smith 2020), normalized against the phylogenetic information content of the splits in the trees being compared.`cid`

: Clustering Information Distance (Smith 2020), normalized against the entropy of the splits in the trees being compared.`qd`

: Quartet divergence (Smith 2019), normalized against its maximum possible value for*n*-leaf trees.`nye`

: Nye*et al.*tree distance (Nye*et al.*2006), normalized against the total number of splits in the trees being compared.`jnc2`

,`jnc4`

: Jaccard-Robinson-Foulds distances with*k*= 2, 4, conflicting pairings prohibited ('no-conflict'), normalized against the total number of splits in the trees being compared.`jco2`

,`jco4`

: Jaccard-Robinson-Foulds distances with*k*= 2, 4, conflicting pairings permitted ('conflict-ok'), normalized against the total number of splits in the trees being compared.`ms`

: Matching Split Distance (Bogdanowicz & Giaro 2012), unnormalized.`mast`

: Size of Maximum Agreement Subtree (Valiente 2009), unnormalized.`masti`

: Information content of Maximum Agreement Subtree, unnormalized.`nni_l`

,`nni_L`

,`nni_U`

,`nni_u`

: Lower, best lower, best upper, and upper bounds for nearest-neighbour interchange distance (Li*et al.*1996), unnormalized. 'Best' lower bounds jump sharply when mismatched regions of a tree become large enough that a tight upper bound cannot be exactly calculated, so are discontinuous and cannot readily be compared between trees.`spr`

: Approximate subtree prune and regraft SPR distance, unnormalized.`tbr_l`

,`tbr_u`

: Lower and upper bound for tree bisection and reconnection (TBR) distance, calculated using TBRDist; unnormalized.`rf`

: Robinson-Foulds distance (Robinson & Foulds 1981), unnormalized.`icrf`

: Robinson-Foulds distance, splits weighted by phylogenetic information content (Smith 2020), unnormalized.`path`

: Path distance (Steel & Penny 1993), unnormalized.

Bogdanowicz D, Giaro K (2012).
“Matching split distance for unrooted binary phylogenetic trees.”
*IEEE/ACM Transactions on Computational Biology and Bioinformatics*, **9**(1), 150--160.
doi: 10.1109/TCBB.2011.48
.

Li M, Tromp J, Zhang L (1996).
“Some notes on the nearest neighbour interchange distance.”
In Goos G, Hartmanis J, Leeuwen J, Cai J, Wong CK (eds.), *Computing and Combinatorics*, volume 1090, 343--351.
Springer, Berlin, Heidelberg.
ISBN 978-3-540-61332-9 978-3-540-68461-9, doi: 10.1007/3-540-61332-3_168
.

Kendall M, Colijn C (2016).
“Mapping phylogenetic trees to reveal distinct patterns of evolution.”
*Molecular Biology and Evolution*, **33**(10), 2735--2743.
doi: 10.1093/molbev/msw124
.

Nye TMW, Liò P, Gilks WR (2006).
“A novel algorithm and web-based tool for comparing two alternative phylogenetic trees.”
*Bioinformatics*, **22**(1), 117--119.
doi: 10.1093/bioinformatics/bti720
.

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

Smith MR (2019).
“Bayesian and parsimony approaches reconstruct informative trees from simulated morphological datasets.”
*Biology Letters*, **15**, 20180632.
doi: 10.1098/rsbl.2018.0632
.

Smith MR (2020).
“Information theoretic Generalized Robinson-Foulds metrics for comparing phylogenetic trees.”
*Bioinformatics*, online ahead of print.
doi: 10.1093/bioinformatics/btaa614
.

Steel MA, Penny D (1993).
“Distributions of tree comparison metrics---some new results.”
*Systematic Biology*, **42**(2), 126--141.
doi: 10.1093/sysbio/42.2.126
.

Valiente G (2009).
*Combinatorial Pattern Matching Algorithms in Computational Biology using Perl and R*, CRC Mathematical and Computing Biology Series.
CRC Press, Boca Raton.