Functions for clanistics to compute clans, slices, clips for unrooted trees and functions to quantify the fragmentation of trees.
Usage
getClans(tree)
getSlices(tree)
getClips(tree, all = TRUE)
getDiversity(tree, x, norm = TRUE, var.names = NULL, labels = "new")
# S3 method for class 'clanistics'
summary(object, ...)
diversity(tree, X)Arguments
- tree
An object of class phylo or multiPhylo (getDiversity).
- all
A logical, return all or just the largest clip.
- x
An object of class phyDat.
- norm
A logical, return Equitability Index (default) or Shannon Diversity.
- var.names
A vector of variable names.
- labels
see details.
- object
an object for which a summary is desired.
- ...
Further arguments passed to or from other methods.
- X
a data.frame
Value
getClans, getSlices and getClips return a matrix of partitions, a
matrix of ones and zeros where rows correspond to a clan, slice or clip and
columns to tips. A one indicates that a tip belongs to a certain partition.
getDiversity returns a list with tree object, the first is a data.frame
of the equitability index or Shannon divergence and parsimony scores
(p-score) for all trees and variables. The data.frame has two attributes,
the first is a splits object to identify the taxa of each tree and the
second is a splits object containing all partitions that perfectly fit.
Details
Every split in an unrooted tree defines two complementary clans. Thus for an unrooted binary tree with \(n\) leaves there are \(2n - 3\) edges, and therefore \(4n - 6\) clans (including \(n\) trivial clans containing only one leave).
Slices are defined by a pair of splits or tripartitions, which are not clans. The number of distinguishable slices for a binary tree with \(n\) tips is \(2n^2 - 10n + 12\).
cophenetic distance and not by the topology. Namely clips are groups of leaves for which the maximum pairwise distance is smaller than threshold. distance within a clip is lower than the distance between any member of the clip and any other tip.
A clip is a different type of partition, defining groups of leaves that are related in terms of evolutionary distances and not only topology. Namely, clips are groups of leaves for which all pairwise path-length distances are smaller than a given threshold value (Lapointe et al. 2010). There exists different numbers of clips for different thresholds, the largest (and trivial) one being the whole tree. There is always a clip containing only the two leaves with the smallest pairwise distance.
Clans, slices and clips can be used to characterize how well a vector of categorial characters (natives/intruders) fit on a tree. We will follow the definitions of Lapointe et al.(2010). A complete clan is a clan that contains all leaves of a given state/color, but can also contain leaves of another state/color. A clan is homogeneous if it only contains leaves of one state/color.
getDiversity computes either the
Shannon Diversity: \(H =
-\sum_{i=1}^{k}(N_i/N) log(N_i/N), N=\sum_{i=1}^{k} N_i\)
or the
Equitability Index: \(E = H /
log(N)\)
where \(N_i\) are the sizes of the \(k\) largest homogeneous
clans of intruders. If the categories of the data can be separated by an
edge of the tree then the E-value will be zero, and maximum equitability
(E=1) is reached if all intruders are in separate clans. getDiversity
computes these Intruder indices for the whole tree, complete clans and
complete slices. Additionally the parsimony scores (p-scores) are reported.
The p-score indicates if the leaves contain only one color (p-score=0), if
the the leaves can be separated by a single split (perfect clan, p-score=1)
or by a pair of splits (perfect slice, p-score=2).
So far only 2 states are supported (native, intruder), however it is also possible to recode several states into the native or intruder state using contrasts, for details see section 2 in vignette("phangorn-specials"). Furthermore unknown character states are coded as ambiguous character, which can act either as native or intruder minimizing the number of clans or changes (in parsimony analysis) needed to describe a tree for given data.
Set attribute labels to "old" for analysis as in Schliep et al. (2010) or to "new" for names which are more intuitive.
diversity returns a data.frame with the parsimony score for each tree
and each levels of the variables in X. X has to be a
data.frame where each column is a factor and the rownames of X
correspond to the tips of the trees.
References
Lapointe, F.-J., Lopez, P., Boucher, Y., Koenig, J., Bapteste, E. (2010) Clanistics: a multi-level perspective for harvesting unrooted gene trees. Trends in Microbiology 18: 341-347
Wilkinson, M., McInerney, J.O., Hirt, R.P., Foster, P.G., Embley, T.M. (2007) Of clades and clans: terms for phylogenetic relationships in unrooted trees. Trends in Ecology and Evolution 22: 114-115
Schliep, K., Lopez, P., Lapointe F.-J., Bapteste E. (2011) Harvesting Evolutionary Signals in a Forest of Prokaryotic Gene Trees, Molecular Biology and Evolution 28(4): 1393-1405
Author
Klaus Schliep klaus.schliep@snv.jussieu.fr
Francois-Joseph Lapointe francois-joseph.lapointe@umontreal.ca
Examples
set.seed(111)
tree <- rtree(10)
getClans(tree)
#> t3 t8 t2 t1 t5 t6 t9 t10 t4 t7
#> [1,] 1 0 0 0 0 0 0 0 0 0
#> [2,] 0 1 0 0 0 0 0 0 0 0
#> [3,] 0 0 1 0 0 0 0 0 0 0
#> [4,] 0 0 0 1 0 0 0 0 0 0
#> [5,] 0 0 0 0 1 0 0 0 0 0
#> [6,] 0 0 0 0 0 1 0 0 0 0
#> [7,] 0 0 0 0 0 0 1 0 0 0
#> [8,] 0 0 0 0 0 0 0 1 0 0
#> [9,] 0 0 0 0 0 0 0 0 1 0
#> [10,] 0 0 0 0 0 0 0 0 0 1
#> [11,] 0 1 1 1 1 1 1 1 1 1
#> [12,] 1 0 1 1 1 1 1 1 1 1
#> [13,] 1 1 0 1 1 1 1 1 1 1
#> [14,] 1 1 1 0 1 1 1 1 1 1
#> [15,] 1 1 1 1 0 1 1 1 1 1
#> [16,] 1 1 1 1 1 0 1 1 1 1
#> [17,] 1 1 1 1 1 1 0 1 1 1
#> [18,] 1 1 1 1 1 1 1 0 1 1
#> [19,] 1 1 1 1 1 1 1 1 0 1
#> [20,] 1 1 1 1 1 1 1 1 1 0
#> [21,] 1 1 1 0 0 0 0 0 0 0
#> [22,] 0 1 1 0 0 0 0 0 0 0
#> [23,] 0 0 0 0 1 1 1 1 1 1
#> [24,] 0 0 0 0 0 1 1 1 1 1
#> [25,] 0 0 0 0 0 1 1 1 0 0
#> [26,] 0 0 0 0 0 0 1 1 0 0
#> [27,] 0 0 0 0 0 0 0 0 1 1
#> [28,] 0 0 0 1 1 1 1 1 1 1
#> [29,] 1 0 0 1 1 1 1 1 1 1
#> [30,] 1 1 1 1 0 0 0 0 0 0
#> [31,] 1 1 1 1 1 0 0 0 0 0
#> [32,] 1 1 1 1 1 0 0 0 1 1
#> [33,] 1 1 1 1 1 1 0 0 1 1
#> [34,] 1 1 1 1 1 1 1 1 0 0
getClips(tree, all=TRUE)
#> t3 t8 t2 t1 t5 t6 t9 t10 t4 t7
#> [1,] 1 0 1 0 0 0 0 0 0 0
#> [2,] 0 0 0 0 0 0 1 1 0 0
#> [3,] 0 0 0 0 0 0 0 0 1 1
getSlices(tree)
#> t3 t8 t2 t1 t5 t6 t9 t10 t4 t7
#> [1,] 0 0 1 1 1 1 1 1 1 1
#> [2,] 0 1 0 1 1 1 1 1 1 1
#> [3,] 0 1 1 0 1 1 1 1 1 1
#> [4,] 0 1 1 1 0 1 1 1 1 1
#> [5,] 0 1 1 1 1 0 1 1 1 1
#> [6,] 0 1 1 1 1 1 0 1 1 1
#> [7,] 0 1 1 1 1 1 1 0 1 1
#> [8,] 0 1 1 1 1 1 1 1 0 1
#> [9,] 0 1 1 1 1 1 1 1 1 0
#> [10,] 0 1 1 1 0 0 0 0 0 0
#> [11,] 0 1 1 1 1 0 0 0 0 0
#> [12,] 0 1 1 1 1 0 0 0 1 1
#> [13,] 0 1 1 1 1 1 0 0 1 1
#> [14,] 0 1 1 1 1 1 1 1 0 0
#> [15,] 1 0 1 0 1 1 1 1 1 1
#> [16,] 1 0 1 1 0 1 1 1 1 1
#> [17,] 1 0 1 1 1 0 1 1 1 1
#> [18,] 1 0 1 1 1 1 0 1 1 1
#> [19,] 1 0 1 1 1 1 1 0 1 1
#> [20,] 1 0 1 1 1 1 1 1 0 1
#> [21,] 1 0 1 1 1 1 1 1 1 0
#> [22,] 1 0 1 0 0 0 0 0 0 0
#> [23,] 1 0 1 1 0 0 0 0 0 0
#> [24,] 1 0 1 1 1 0 0 0 0 0
#> [25,] 1 0 1 1 1 0 0 0 1 1
#> [26,] 1 0 1 1 1 1 0 0 1 1
#> [27,] 1 0 1 1 1 1 1 1 0 0
#> [28,] 1 1 0 0 1 1 1 1 1 1
#> [29,] 1 1 0 1 0 1 1 1 1 1
#> [30,] 1 1 0 1 1 0 1 1 1 1
#> [31,] 1 1 0 1 1 1 0 1 1 1
#> [32,] 1 1 0 1 1 1 1 0 1 1
#> [33,] 1 1 0 1 1 1 1 1 0 1
#> [34,] 1 1 0 1 1 1 1 1 1 0
#> [35,] 1 1 0 0 0 0 0 0 0 0
#> [36,] 1 1 0 1 0 0 0 0 0 0
#> [37,] 1 1 0 1 1 0 0 0 0 0
#> [38,] 1 1 0 1 1 0 0 0 1 1
#> [39,] 1 1 0 1 1 1 0 0 1 1
#> [40,] 1 1 0 1 1 1 1 1 0 0
#> [41,] 1 1 1 0 0 1 1 1 1 1
#> [42,] 1 1 1 0 1 0 1 1 1 1
#> [43,] 1 1 1 0 1 1 0 1 1 1
#> [44,] 1 1 1 0 1 1 1 0 1 1
#> [45,] 1 1 1 0 1 1 1 1 0 1
#> [46,] 1 1 1 0 1 1 1 1 1 0
#> [47,] 1 0 0 0 1 1 1 1 1 1
#> [48,] 1 1 1 0 1 0 0 0 0 0
#> [49,] 1 1 1 0 1 0 0 0 1 1
#> [50,] 1 1 1 0 1 1 0 0 1 1
#> [51,] 1 1 1 0 1 1 1 1 0 0
#> [52,] 1 1 1 1 0 0 1 1 1 1
#> [53,] 1 1 1 1 0 1 0 1 1 1
#> [54,] 1 1 1 1 0 1 1 0 1 1
#> [55,] 1 1 1 1 0 1 1 1 0 1
#> [56,] 1 1 1 1 0 1 1 1 1 0
#> [57,] 0 0 0 1 0 1 1 1 1 1
#> [58,] 1 0 0 1 0 1 1 1 1 1
#> [59,] 1 1 1 1 0 0 0 0 1 1
#> [60,] 1 1 1 1 0 1 0 0 1 1
#> [61,] 1 1 1 1 0 1 1 1 0 0
#> [62,] 1 1 1 1 1 0 0 1 1 1
#> [63,] 1 1 1 1 1 0 1 0 1 1
#> [64,] 1 1 1 1 1 0 1 1 0 1
#> [65,] 1 1 1 1 1 0 1 1 1 0
#> [66,] 0 0 0 0 1 0 1 1 1 1
#> [67,] 0 0 0 0 0 0 1 1 1 1
#> [68,] 0 0 0 1 1 0 1 1 1 1
#> [69,] 1 0 0 1 1 0 1 1 1 1
#> [70,] 1 1 1 1 1 0 1 1 0 0
#> [71,] 1 1 1 1 1 1 0 1 0 1
#> [72,] 1 1 1 1 1 1 0 1 1 0
#> [73,] 0 0 0 0 1 1 0 1 1 1
#> [74,] 0 0 0 0 0 1 0 1 1 1
#> [75,] 0 0 0 0 0 1 0 1 0 0
#> [76,] 0 0 0 1 1 1 0 1 1 1
#> [77,] 1 0 0 1 1 1 0 1 1 1
#> [78,] 1 1 1 1 1 1 0 1 0 0
#> [79,] 1 1 1 1 1 1 1 0 0 1
#> [80,] 1 1 1 1 1 1 1 0 1 0
#> [81,] 0 0 0 0 1 1 1 0 1 1
#> [82,] 0 0 0 0 0 1 1 0 1 1
#> [83,] 0 0 0 0 0 1 1 0 0 0
#> [84,] 0 0 0 1 1 1 1 0 1 1
#> [85,] 1 0 0 1 1 1 1 0 1 1
#> [86,] 1 1 1 1 1 1 1 0 0 0
#> [87,] 0 0 0 0 1 1 1 1 0 1
#> [88,] 0 0 0 0 0 1 1 1 0 1
#> [89,] 0 0 0 1 1 1 1 1 0 1
#> [90,] 1 0 0 1 1 1 1 1 0 1
#> [91,] 1 1 1 1 1 0 0 0 0 1
#> [92,] 1 1 1 1 1 1 0 0 0 1
#> [93,] 0 0 0 0 1 1 1 1 1 0
#> [94,] 0 0 0 0 0 1 1 1 1 0
#> [95,] 0 0 0 1 1 1 1 1 1 0
#> [96,] 1 0 0 1 1 1 1 1 1 0
#> [97,] 1 1 1 1 1 0 0 0 1 0
#> [98,] 1 1 1 1 1 1 0 0 1 0
#> [99,] 0 0 0 0 1 0 0 0 1 1
#> [100,] 0 0 0 0 1 1 0 0 1 1
#> [101,] 0 0 0 0 1 1 1 1 0 0
#> [102,] 0 0 0 0 0 1 0 0 1 1
#> [103,] 0 0 0 1 1 0 0 0 0 0
#> [104,] 0 0 0 1 1 0 0 0 1 1
#> [105,] 0 0 0 1 1 1 0 0 1 1
#> [106,] 0 0 0 1 1 1 1 1 0 0
#> [107,] 1 0 0 1 0 0 0 0 0 0
#> [108,] 1 0 0 1 1 0 0 0 0 0
#> [109,] 1 0 0 1 1 0 0 0 1 1
#> [110,] 1 0 0 1 1 1 0 0 1 1
#> [111,] 1 0 0 1 1 1 1 1 0 0
#> [112,] 1 1 1 1 1 1 0 0 0 0
set.seed(123)
trees <- rmtree(10, 20)
X <- matrix(sample(c("red", "blue", "violet"), 100, TRUE, c(.5,.4, .1)),
ncol=5, dimnames=list(paste('t',1:20, sep=""), paste('Var',1:5, sep="_")))
x <- phyDat(X, type = "USER", levels = c("red", "blue"), ambiguity="violet")
plot(trees[[1]], "u", tip.color = X[trees[[1]]$tip,1]) # intruders are blue
(divTab <- getDiversity(trees, x, var.names=colnames(X)))
#> Warning: The variable names have changed
#> tree variable E clan # natives # intruder # unknown E slice # intruder
#> 1 1 Var_1 0.8568636 9 10 1 1.0000000 7
#> 2 1 Var_2 0.6562658 11 7 2 0.7500000 4
#> 3 1 Var_3 0.7500962 8 11 1 0.8018797 8
#> 4 1 Var_4 0.9474428 7 11 2 1.0000000 9
#> 5 1 Var_5 1.0000000 8 10 2 1.0000000 9
#> 6 2 Var_1 0.8568636 9 10 1 1.0000000 7
#> 7 2 Var_2 0.7964530 11 7 2 0.8277294 5
#> 8 2 Var_3 0.9474428 8 11 1 1.0000000 9
#> 9 2 Var_4 0.8224909 7 11 2 0.9166667 8
#> 10 2 Var_5 0.6387640 8 10 2 0.7420981 6
#> 11 3 Var_1 0.8795880 9 10 1 0.9166667 8
#> 12 3 Var_2 0.8982265 11 7 2 1.0000000 5
#> 13 3 Var_3 0.7372138 8 11 1 0.8982265 7
#> 14 3 Var_4 0.8948855 7 11 2 0.9298967 9
#> 15 3 Var_5 1.0000000 8 10 2 1.0000000 9
#> 16 4 Var_1 0.8795880 9 10 1 0.9166667 8
#> 17 4 Var_2 0.8982265 11 7 2 1.0000000 5
#> 18 4 Var_3 0.7372138 8 11 1 0.8982265 7
#> 19 4 Var_4 0.8948855 7 11 2 0.9298967 9
#> 20 4 Var_5 1.0000000 8 10 2 1.0000000 9
#> 21 5 Var_1 0.7966576 9 10 1 0.8982265 7
#> 22 5 Var_2 0.8982265 11 7 2 1.0000000 5
#> 23 5 Var_3 0.8224909 8 11 1 0.9166667 8
#> 24 5 Var_4 0.5699628 7 11 2 0.6934264 6
#> 25 5 Var_5 0.4729033 8 10 2 0.7500000 4
#> 26 6 Var_1 0.7966576 9 10 1 0.8982265 7
#> 27 6 Var_2 0.8982265 11 7 2 1.0000000 5
#> 28 6 Var_3 0.8224909 8 11 1 0.9166667 8
#> 29 6 Var_4 1.0000000 7 11 2 1.0000000 10
#> 30 6 Var_5 0.9397940 8 10 2 1.0000000 8
#> 31 7 Var_1 0.8795880 9 10 1 0.9166667 8
#> 32 7 Var_2 1.0000000 11 7 2 1.0000000 6
#> 33 7 Var_3 0.9474428 8 11 1 1.0000000 9
#> 34 7 Var_4 0.7500962 7 11 2 0.8018797 8
#> 35 7 Var_5 0.9397940 8 10 2 1.0000000 8
#> 36 8 Var_1 0.8795880 9 10 1 0.9166667 8
#> 37 8 Var_2 0.8982265 11 7 2 1.0000000 5
#> 38 8 Var_3 0.8224909 8 11 1 0.9166667 8
#> 39 8 Var_4 0.6846566 7 11 2 0.7964530 7
#> 40 8 Var_5 0.8568636 8 10 2 1.0000000 7
#> 41 9 Var_1 0.7364516 9 10 1 0.7964530 7
#> 42 9 Var_2 0.7964530 11 7 2 0.8277294 5
#> 43 9 Var_3 0.8948855 8 11 1 0.9298967 9
#> 44 9 Var_4 0.7897710 7 11 2 0.7896901 9
#> 45 9 Var_5 0.7591760 8 10 2 1.0000000 6
#> 46 10 Var_1 0.5903090 9 10 1 0.8277294 5
#> 47 10 Var_2 0.8982265 11 7 2 1.0000000 5
#> 48 10 Var_3 0.8224909 8 11 1 0.9166667 8
#> 49 10 Var_4 0.8750481 7 11 2 1.0000000 8
#> 50 10 Var_5 0.9397940 8 10 2 1.0000000 8
#> # unknown E melange # intruder # unknown bs 1 bs 2 p-score
#> 1 1 1.0000000 6 1 NA NA 8
#> 2 2 1.0000000 2 2 NA NA 4
#> 3 1 1.0000000 5 1 NA NA 6
#> 4 2 1.0000000 8 2 NA NA 7
#> 5 2 1.0000000 8 2 NA NA 7
#> 6 1 1.0000000 6 1 NA NA 7
#> 7 2 1.0000000 3 1 NA NA 5
#> 8 1 1.0000000 8 1 NA NA 7
#> 9 2 1.0000000 6 2 NA NA 5
#> 10 1 0.7500000 4 1 NA NA 5
#> 11 1 1.0000000 6 1 NA NA 7
#> 12 2 1.0000000 4 2 NA NA 6
#> 13 1 1.0000000 5 1 NA NA 7
#> 14 2 1.0000000 7 1 NA NA 5
#> 15 2 1.0000000 8 2 NA NA 8
#> 16 1 1.0000000 6 1 NA NA 4
#> 17 2 1.0000000 4 2 NA NA 5
#> 18 1 1.0000000 5 1 NA NA 6
#> 19 2 1.0000000 7 2 NA NA 6
#> 20 2 1.0000000 8 2 NA NA 8
#> 21 1 1.0000000 5 1 NA NA 7
#> 22 2 1.0000000 4 2 NA NA 6
#> 23 1 1.0000000 6 1 NA NA 7
#> 24 0 1.0000000 3 0 NA NA 5
#> 25 2 1.0000000 2 2 NA NA 4
#> 26 1 1.0000000 5 1 NA NA 6
#> 27 1 1.0000000 4 1 NA NA 6
#> 28 1 1.0000000 6 1 NA NA 6
#> 29 2 1.0000000 9 2 NA NA 7
#> 30 2 1.0000000 7 2 NA NA 7
#> 31 1 1.0000000 6 0 NA NA 6
#> 32 2 1.0000000 5 2 NA NA 6
#> 33 1 1.0000000 8 1 NA NA 7
#> 34 1 1.0000000 5 1 NA NA 5
#> 35 2 1.0000000 7 2 NA NA 7
#> 36 1 1.0000000 6 0 NA NA 8
#> 37 2 1.0000000 4 2 NA NA 6
#> 38 1 1.0000000 6 1 NA NA 7
#> 39 2 0.8277294 5 2 NA NA 6
#> 40 2 1.0000000 6 2 NA NA 4
#> 41 1 0.8277294 5 1 NA NA 6
#> 42 2 1.0000000 3 1 NA NA 4
#> 43 1 1.0000000 7 1 NA NA 7
#> 44 2 0.7964530 7 2 NA NA 5
#> 45 2 1.0000000 5 2 NA NA 6
#> 46 1 1.0000000 3 1 NA NA 5
#> 47 2 1.0000000 4 2 NA NA 6
#> 48 1 1.0000000 6 1 NA NA 5
#> 49 2 1.0000000 7 2 NA NA 6
#> 50 1 1.0000000 7 1 NA NA 7
summary(divTab)
#> Variable Natives_only Intruder_only Clan Slice Melange
#> 1 Var_1 0 0 0 0 10
#> 2 Var_2 0 0 0 0 10
#> 3 Var_3 0 0 0 0 10
#> 4 Var_4 0 0 0 0 10
#> 5 Var_5 0 0 0 0 10