Package 'ConsTree' reference manual

Title:	Fast Algorithms for Phylogenetic Consensus Trees
Description:	Efficient construction of phylogenetic consensus trees. Methods include strict, majority-rule, majority-rule (+), loose (combinable component / semi-strict), greedy, Adams, frequency difference, R*, and local consensus.
Authors:	Martin R. Smith [aut, cre, cph] (ORCID: <https://orcid.org/0000-0001-5660-1727>), Jesper Jansson [aut, cph] (ORCID: <https://orcid.org/0000-0001-6859-8932>, Consensus algorithms (FACT, FACT2, FDCT)), Zhaoxian Li [aut, cph] (Consensus algorithms (FACT)), Ramesh Rajaby [aut, cph] (ORCID: <https://orcid.org/0000-0001-9980-1913>, Consensus algorithms (FACT2, FDCT)), Chuanqi Shen [aut, cph] (Consensus algorithms (FACT)), Wing-Kin Sung [aut, cph] (ORCID: <https://orcid.org/0000-0001-7806-7086>, Consensus algorithms (FACT, FACT2, FDCT)), Yutong Yang [aut, cph] (Consensus algorithms (FDCT))
Maintainer:	Martin R. Smith <[email protected]>
License:	GPL (>= 3)
Version:	1.0.1
Built:	2026-10-16 18:05:26 UTC
Source:	https://github.com/ms609/constree

Adams consensus tree

Description

Adams() computes the Adams (1972) consensus tree.

Usage

Adams(trees)
Adams(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

The Adams consensus places each species in the smallest group to which it belongs on all input trees. Consequently, it may contain groupings that do not appear in any input tree. This implementation builds on the algorithm of (Jansson et al. 2017); please cite this paper where you use this method.

Value

Adams() returns an object of class phylo denoting the Adams consensus tree.

References

Adams EN (1972). “Consensus techniques and the comparison of taxonomic trees.” Systematic Zoology, 21(4), 390–397. doi:10.2307/2412432.

Jansson J, Li Z, Sung W (2017). “On finding the Adams consensus tree.” Information and Computation, 256, 334–347. doi:10.1016/j.ic.2017.08.002.

Examples

# Two rooted trees that disagree only on the position of one leaf
trees <- c(ape::read.tree(text = "(((a, b), c), d);"),
           ape::read.tree(text = "(((a, b), d), c);"))
# keeps the clade (a, b); leaves c, d unresolved at the root
ape::write.tree(Adams(trees))

# Two rooted trees that disagree only on the position of one leaf
trees <- c(ape::read.tree(text = "(((a, b), c), d);"),
           ape::read.tree(text = "(((a, b), d), c);"))
# keeps the clade (a, b); leaves c, d unresolved at the root
ape::write.tree(Adams(trees))

Average consensus tree

Description

Average() returns the average consensus (Lapointe and Cucumel 1997): the tree whose path-length (patristic) distances most closely match the average of the path-length distances of the input trees.

Usage

Average(
  trees,
  method = c("fastme.bal", "ls", "nj", "bionj", "fastme.ols"),
  weights = NULL,
  scale = c("none", "max"),
  edgeLengths = NA,
  outgroup = NULL,
  check.labels = TRUE,
  lsControl = list()
)
Average(
  trees,
  method = c("fastme.bal", "ls", "nj", "bionj", "fastme.ols"),
  weights = NULL,
  scale = c("none", "max"),
  edgeLengths = NA,
  outgroup = NULL,
  check.labels = TRUE,
  lsControl = list()
)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

method

Character specifying how to build the tree from the average distance matrix:

"fastme.bal" (the default) returns the balanced minimum-evolution tree (Desper and Gascuel 2002): a fast, accurate approximation of the least-squares tree;
"ls" searches for the least-squares tree using TreeSearch::LeastSquaresTree(), a non-negative least-squares NNI/SPR search;
"nj", "bionj" and "fastme.ols" return the corresponding distance tree (Saitou and Nei 1987; Gascuel 1997).

weights

Numeric vector specifying the weight of each tree in the average (e.g. posterior probabilities), with one entry per tree. If NULL, each tree is weighted equally.

scale

Character specifying whether to rescale each tree's distance matrix before averaging. "none" leaves matrices unscaled; "max" divides each matrix by its largest entry, recommended when absolute distances are not comparable (Lapointe and Cucumel 1997).

edgeLengths

Logical specifying whether to use edge lengths when computing path-length distances. TRUE requires edge lengths; FALSE does not use edge lengths; NA uses edge lengths when all trees have them, and otherwise counts edges.

outgroup

Character vector specifying tip label(s) on which to root the result. NULL returns an unrooted tree.

check.labels

Logical specifying whether to confirm that every tree contains the same leaves.

lsControl

Named list of further arguments for the least-squares search (method = "ls"), passed to TreeSearch::LeastSquaresTree().

Details

Because the average of several path-length matrices is usually not itself realisable by any tree, Average() approximates it: by default, with the fast balanced minimum-evolution tree; or if method = "ls", by NP-hard least-squares search (Day 1987).

Value

Average() returns an object of class phylo with fitted branch lengths denoting the average consensus tree.

References

Day WHE (1987). “Computational complexity of inferring phylogenies from dissimilarity matrices.” Bulletin of Mathematical Biology, 49(4), 461–467. doi:10.1007/BF02458863.

Desper R, Gascuel O (2002). “Fast and accurate phylogeny reconstruction algorithms based on the minimum-evolution principle.” Journal of Computational Biology, 9(5), 687–705. doi:10.1089/106652702761034136.

Gascuel O (1997). “BIONJ: an improved version of the NJ algorithm based on a simple model of sequence data.” Molecular Biology and Evolution, 14(7), 685–695. doi:10.1093/oxfordjournals.molbev.a025808.

Lapointe F, Cucumel G (1997). “The average consensus procedure: combination of weighted trees containing identical or overlapping sets of taxa.” Systematic Biology, 46(2), 306–312. doi:10.1093/sysbio/46.2.306.

Saitou N, Nei M (1987). “The neighbor-joining method: a new method for reconstructing phylogenetic trees.” Molecular Biology and Evolution, 4(4), 406–425. doi:10.1093/oxfordjournals.molbev.a040454.

Examples

set.seed(5)
trees <- ape::rmtree(5, 8)    # five random eight-leaf trees
Average(trees)                # fast (balanced minimum evolution) default

if (requireNamespace("TreeSearch", quietly = TRUE) &&
    exists("LeastSquaresTree", where = asNamespace("TreeSearch"),
           mode = "function")) {
  Average(trees, method = "ls")    # faithful least-squares fit (slower)
  
  # use Fitch-Margoliash weighting:
  Average(trees, method = "ls",
    lsControl = list(spr = FALSE, maxHits = 5L, weight = "fm")
  )
}


set.seed(5)
trees <- ape::rmtree(5, 8)    # five random eight-leaf trees
Average(trees)                # fast (balanced minimum evolution) default

if (requireNamespace("TreeSearch", quietly = TRUE) &&
    exists("LeastSquaresTree", where = asNamespace("TreeSearch"),
           mode = "function")) {
  Average(trees, method = "ls")    # faithful least-squares fit (slower)
  
  # use Fitch-Margoliash weighting:
  Average(trees, method = "ls",
    lsControl = list(spr = FALSE, maxHits = 5L, weight = "fm")
  )
}

Geodesic (BHV) distance between trees

Description

BHVDistance() returns the geodesic distance between phylogenetic trees with edge lengths in the Billera-Holmes-Vogtmann (BHV) treespace (Billera et al. 2001), computed with the polynomial-time GTP algorithm of Owen and Provan (2011).

Usage

BHVDistance(tree1, tree2 = NULL)

BHVDist(tree1, tree2 = NULL)

BHV(tree1, tree2 = NULL)
BHVDistance(tree1, tree2 = NULL)

BHVDist(tree1, tree2 = NULL)

BHV(tree1, tree2 = NULL)

Arguments

tree1, tree2

A phylo tree, a multiPhylo object, or a list of phylo trees, each carrying edge.length. All trees across both arguments must share the same leaf labels. tree2 may be omitted when tree1 is a collection, in which case all pairwise distances within tree1 are returned.

Value

BHVDistance() returns distances between the input trees:

If both inputs are single trees, the return value is a single non-negative number.
When comparing a tree to a collection of trees, the return value is a named numeric vector with one entry per tree in the collection.
If tree2 is omitted, or is identical to tree1, the return value is a stats::dist object of all pairwise distances.
If tree1 and tree2 are different collections, the return value comprises a numeric matrix with rows corresponding to tree1 and columns to tree2.

References

Billera LJ, Holmes SP, Vogtmann K (2001). “Geometry of the space of phylogenetic trees.” Advances in Applied Mathematics, 27(4), 733–767. doi:10.1006/aama.2001.0759.

Owen M, Provan JS (2011). “A fast algorithm for computing geodesic distances in tree space.” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8(1), 2–13. doi:10.1109/TCBB.2010.3.

Examples

set.seed(2)
trees <- lapply(1:4, function(i) 
  TreeTools::RandomTree(8, root = TRUE, lengths = runif)
)
t1 <- trees[[1]]
t2 <- trees[[2]]

BHVDistance(t1, t2)                  # scalar
BHVDistance(t1, trees)               # named vector
BHVDistance(trees)                   # dist (pairwise)
BHVDistance(trees[1:2], trees[3:4])  # matrix

set.seed(2)
trees <- lapply(1:4, function(i) 
  TreeTools::RandomTree(8, root = TRUE, lengths = runif)
)
t1 <- trees[[1]]
t2 <- trees[[2]]

BHVDistance(t1, t2)                  # scalar
BHVDistance(t1, trees)               # named vector
BHVDistance(trees)                   # dist (pairwise)
BHVDistance(trees[1:2], trees[3:4])  # matrix

Fréchet mean and variance in BHV treespace

Description

BHVMean() returns the Fréchet (Karcher) mean of a set of trees in BHV treespace: the tree that minimizes the sum of squared geodesic distances to the sample (Brown and Owen 2020). The mean is approximated by the iterative law-of-large-numbers algorithm of Sturm (2003) and Miller et al. (2015): starting from a sample tree, each step walks $\frac{1}{k+1}$ of the way along the geodesic towards a randomly chosen sample tree.

Usage

BHVMean(trees, tolerance = 1e-04, maxIter = 100000L, cauchyLength = 10L)

BHVVariance(trees, mean = NULL, type = c("average", "sum"))
BHVMean(trees, tolerance = 1e-04, maxIter = 100000L, cauchyLength = 10L)

BHVVariance(trees, mean = NULL, type = c("average", "sum"))

Arguments

trees

A list of trees, or a multiPhylo object; all entries must share the same leaf labels and carry edge.length.

tolerance

Numeric stating convergence threshold relative to the sample standard deviation. Iteration stops once cauchyLength consecutive steps each move the estimate less than tolerance times the sample standard deviation.

maxIter

Integer specifying the maximum number of iterations.

cauchyLength

Integer specifying the number of consecutive small steps required to declare convergence.

mean

Object of class phylo specifying a pre-computed mean tree; computed via BHVMean() if NULL.

type

Character specifying whether to return the mean squared distance ("average") or the total squared distance ("sum").

Details

BHVVariance() returns the Fréchet variance: by default the mean squared geodesic distance from the sample to its mean, $\frac{1}{r}\sum_i d(\bar T, T_i)^2$ ; with type = "sum", the total $\sum_i d(\bar T, T_i)^2$ .

The mean is "sticky": perturbing one sample tree need not move it, and it is pulled towards lower-dimensional (less resolved) orthants, so it may be unresolved even when the sample trees are binary (Brown and Owen 2020).

Value

BHVMean() returns an object of class phylo denoting the mean tree, with attributes iterations (integer; number of steps taken) and converged (logical). Because the step length shrinks as $1/(k+1)$ , converged = TRUE indicates that successive estimates have stopped moving appreciably (the stopping rule was met before maxIter), not a guaranteed bound on the distance to the exact mean; tighten tolerance for greater precision.

BHVVariance() returns a single non-negative number.

References

Brown DG, Owen M (2020). “Mean and variance of phylogenetic trees.” Systematic Biology, 69(1), 139–154. doi:10.1093/sysbio/syz041.

Miller E, Owen M, Provan JS (2015). “Polyhedral computational geometry for averaging metric phylogenetic trees.” Advances in Applied Mathematics, 68, 51–91. doi:10.1016/j.aam.2015.04.002.

Sturm K (2003). “Probability measures on metric spaces of nonpositive curvature.” In Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces, volume 338 of Contemporary Mathematics, 357–390. doi:10.1090/conm/338/06080.

Examples

set.seed(0)
trees <- lapply(1:25, function(i) {
  tree <- TreeTools::RandomTree(6, root = FALSE)
  tree$edge.length <- runif(nrow(tree$edge))
  tree
})
meanTree <- BHVMean(trees)
BHVVariance(trees, mean = meanTree)

set.seed(0)
trees <- lapply(1:25, function(i) {
  tree <- TreeTools::RandomTree(6, root = FALSE)
  tree$edge.length <- runif(nrow(tree$edge))
  tree
})
meanTree <- BHVMean(trees)
BHVVariance(trees, mean = meanTree)

Frequency-difference consensus tree

Description

Frequency() computes the frequency-difference consensus, which retains each split that occurs more often than every split that conflicts with it (Goloboff et al. 2003).

Usage

Frequency(trees)
Frequency(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

The frequency-difference consensus is at least as resolved as the majority-rule consensus (Majority()), and is contained within the greedy consensus (Greedy()).

This implementation builds on the FDCT algorithm of Jansson et al. (2026); please cite that paper when using this method.

Value

Frequency() returns an object of class phylo denoting the frequency consensus, rooted as in the first entry of trees.

References

Goloboff PA, Farris JS, Källersjö M, Oxelman B, Ramírez MJ, Szumik CA (2003). “Improvements to resampling measures of group support.” Cladistics, 19(4), 324–332. doi:10.1111/j.1096-0031.2003.tb00376.x.

Jansson J, Sung W, Tabatabaee SA, Yang Y (2026). “A faster algorithm for constructing the frequency difference consensus tree.” Journal of Computer and System Sciences, 161, 103831. doi:10.1016/j.jcss.2026.103831.

Examples

trees <- ape::as.phylo(0:5, 8)
Frequency(trees)

trees <- ape::as.phylo(0:5, 8)
Frequency(trees)

Greedy (extended majority-rule) consensus tree

Description

Greedy() computes the greedy consensus (Felsenstein 1993), also termed the extended majority-rule consensus (Bryant 2003). Distinct splits are considered in decreasing order of their frequency across the input trees, breaking ties arbitrarily; each is added to the growing consensus if it is compatible with every split already accepted.

Usage

Greedy(trees)
Greedy(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

The implementation builds upon the greedyConsensusFast algorithm of (Jansson et al. 2016); please cite that paper when using this method.

Value

Greedy() returns an object of class phylo denoting the consensus, rooted as in the first entry of trees.

References

Examples

trees <- ape::as.phylo(0:5, 8)
Greedy(trees)

trees <- ape::as.phylo(0:5, 8)
Greedy(trees)

Local consensus tree

Description

Local() returns the local consensus (Kannan et al. 1998) of a set of rooted trees. The local consensus is the most conservative tree consistent with the rooted triplets shared by every input tree. The minimum rooted local consensus (MinRLC, type = "rooted") and the minimum induced local consensus (MinILC, type = "induced") differ in how the resolution of the result is scored.

Usage

Local(trees, type = c("rooted", "induced"))
Local(trees, type = c("rooted", "induced"))

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

type

Character specifying whether to compute the minimum rooted local consensus ("rooted", the default; MinRLC) or the minimum induced local consensus ("induced"; MinILC).

Details

The implementation builds on the algorithms of Jansson et al. (2018), which generalize the RV-II type consensus of Kannan et al. (1998); please cite both papers when using this method.

Because the algorithm is exponential, Local() is limited to n <= 20 leaves. Running time is faster when input trees are more congruent.

Value

Local() returns an object of class phylo denoting the local consensus tree. When there is no valid consensus (as no common triplets separate any pair of trees), a star tree is returned.

References

Jansson J, Rajaby R, Sung W (2018). “Minimal phylogenetic supertrees and local consensus trees.” AIMS Medical Science, 5(2), 181–203. doi:10.3934/medsci.2018.2.181.

Kannan S, Warnow T, Yooseph S (1998). “Computing the local consensus of trees.” SIAM Journal on Computing, 27(6), 1695–1724. doi:10.1137/S0097539795287642.

Examples

# Two trees that agree on one cherry but disagree on overall topology
t1 <- ape::read.tree(text = "(1,((2,3),4));")
t2 <- ape::read.tree(text = "(1,((2,4),3));")
Local(list(t1, t2), "rooted")  # keeps clade {2,3,4} only

# Two trees that agree on one cherry but disagree on overall topology
t1 <- ape::read.tree(text = "(1,((2,3),4));")
t2 <- ape::read.tree(text = "(1,((2,4),3));")
Local(list(t1, t2), "rooted")  # keeps clade {2,3,4} only

Loose consensus tree

Description

Loose() computes the loose consensus, also known as the semi-strict or combinable-component consensus (Bremer 1990). It contains every split that is not contradicted by any input tree.

Usage

Loose(trees)
Loose(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

The loose consensus refines the strict consensus (Strict()). In contrast to the majority-rule consensus (Majority()), a split present in most trees may still be contradicted by a minority, and so be excluded from the loose consensus; yet a split that occurs in just one tree is retained if no other tree contradicts it.

This implementation builds on the looseConsensusFast algorithm of Jansson et al. (2016); please cite that paper when using this method.

Value

Loose() returns the consensus tree, an object of class phylo, rooted as in the first entry of trees.

References

Bremer K (1990). “Combinable component consensus.” Cladistics, 6(4), 369–372. doi:10.1111/j.1096-0031.1990.tb00551.x.

Jansson J, Shen C, Sung W (2016). “Improved algorithms for constructing consensus trees.” Journal of the ACM, 63(3), 1–24. doi:10.1145/2925985.

Examples

trees <- ape::as.phylo(0:5, 8)
Loose(trees)

trees <- ape::as.phylo(0:5, 8)
Loose(trees)

Majority-rule consensus tree

Description

Majority() is a simple alias of TreeTools::Consensus(), which computes the majority-rule consensus: the tree that contains each split that occurs in more than p of the input trees (Margush and McMorris 1981).

Usage

Majority(trees, p = 0.5)

MajorityRule(trees, p = 0.5)

MR(trees, p = 0.5)
Majority(trees, p = 0.5)

MajorityRule(trees, p = 0.5)

MR(trees, p = 0.5)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

p

Numeric between 0.5 and 1: the minimum proportion of trees that must contain a split for it to be retained.

Value

Majority() returns an object of class phylo denoting the majority rule consensus, rooted as in the first entry of trees.

References

Margush T, McMorris FR (1981). “Consensus n-trees.” Bulletin of Mathematical Biology, 43(2), 239–244. doi:10.1007/BF02459446.

Examples

trees <- ape::as.phylo(0:5, 8)
Majority(trees, p = 0.6)

trees <- ape::as.phylo(0:5, 8)
Majority(trees, p = 0.6)

Majority-rule (+) consensus tree

Description

MajorityPlus() computes the majority-rule (+) consensus, which displays each clade that occurs in more input trees than contradict it (Dong et al. 2010).

Usage

MajorityPlus(trees)
MajorityPlus(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

This implementation uses the algorithm of Jansson et al. (2018); please cite both this and Dong et al. (2010) when using this method.

Value

MajorityPlus() returns an object of class phylo denoting the majority-plus consensus tree, rooted as in the first entry of trees.

References

Dong J, Fernández-Baca D, McMorris FR, Powers RC (2010). “Majority-rule (+) consensus trees.” Mathematical Biosciences, 228(1), 10–15. doi:10.1016/j.mbs.2010.08.002.

Jansson J, Rajaby R, Shen C, Sung W (2018). “Algorithms for the majority rule (+) consensus tree and the frequency difference consensus tree.” IEEE/ACM Transactions on Computational Biology and Bioinformatics, 15(1), 15–26. doi:10.1109/TCBB.2016.2609923.

Examples

trees <- ape::as.phylo(0:5, 8)
MajorityPlus(trees)

trees <- ape::as.phylo(0:5, 8)
MajorityPlus(trees)

Consensus tree that minimizes quartet distance

Description

Quartet() constructs a consensus tree that minimizes the sum of symmetric quartet distances to a set of input trees, using a greedy add-and-prune heuristic.

Usage

Quartet(
  trees,
  init = c("majority", "star", "extended"),
  greedy = c("best", "first")
)
Quartet(
  trees,
  init = c("majority", "star", "extended"),
  greedy = c("best", "first")
)

Arguments

trees

Object of class multiPhylo specifying the input trees. All trees must share the same tip labels.

init

Character string specifying the initial tree:

"majority": the majority-rule consensus.
"star": a fully unresolved star tree.
"extended": the extended (greedy) majority-rule consensus.

greedy

Character string specifying the greedy strategy:

"best": evaluate all candidates and pick the best action at each step.
"first": pick the first improving action encountered (faster; may give a slightly worse result).

Details

Where the majority-rule consensus minimizes the sum of Robinson-Foulds distances to the input trees (Barthélemy and McMorris 1986), Quartet() finds an approximate median tree under the symmetric quartet distance (Estabrook et al. 1985; Takazawa et al. 2026), which counts both false-positive and false-negative resolved quartets equally.

Because the quartet distance gives greater weight to deep branches (which resolve more quartets), quartet consensus trees tend to be more resolved than majority-rule trees, especially when phylogenetic signal is low.

The function supports trees with up to 100 tips.

Value

Quartet() returns a consensus tree, an object of class phylo, unrooted.

References

Barthélemy J, McMorris FR (1986). “The median procedure for n-trees.” Journal of Classification, 3(2), 329–334. doi:10.1007/BF01894194.

Estabrook GF, McMorris FR, Meacham CA (1985). “Comparison of undirected phylogenetic trees based on subtrees of four evolutionary units.” Systematic Zoology, 34(2), 193–200. doi:10.2307/2413326.

Takazawa Y, Takeda A, Hayamizu M, Gascuel O (2026). “Outperforming the majority-rule consensus tree using fine-grained dissimilarity measures.” bioRxiv. doi:10.64898/2026.03.16.712085.

Examples

library("TreeTools", quietly = TRUE)

# Generate bootstrap-like trees
trees <- as.phylo(1:30, nTip = 8)

# Quartet consensus
qc <- Quartet(trees)
plot(qc)

# Compare resolution with majority-rule
mr <- UnrootTree(Consensus(trees, p = 0.5))
cat("Majority-rule splits:", NSplits(mr), "\n")
cat("Quartet consensus splits:", NSplits(qc), "\n")

library("TreeTools", quietly = TRUE)

# Generate bootstrap-like trees
trees <- as.phylo(1:30, nTip = 8)

# Quartet consensus
qc <- Quartet(trees)
plot(qc)

# Compare resolution with majority-rule
mr <- UnrootTree(Consensus(trees, p = 0.5))
cat("Majority-rule splits:", NSplits(mr), "\n")
cat("Quartet consensus splits:", NSplits(qc), "\n")

R* consensus tree

Description

RStar() returns the R* consensus (Degnan et al. 2009) of a set of rooted trees.

Usage

RStar(trees)
RStar(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

The R* consensus is a rooted-triplet method. For every set of three leaves it tallies, across the input trees, the three possible resolved rooted triplets (ab|c, ac|b, bc|a) and keeps whichever appears most frequently. Ties are not kept. The kept triplets form the set of majority resolved triplets, $R_{maj}$ . Then $R^*$ is the most resolved tree that displays no resolved triplet outside $R_{maj}$ .

$R^*$ is always a refinement of the majority-rule consensus: every majority clade also appears in RStar().

RStar() finds the strong clusters of $R_{maj}$ among candidate clusters built from triplet similarities (Jansson and Sung 2013; Jansson et al. 2016). For two trees it takes $O(n^2)$ time (Jansson et al. 2016), testing each candidate with the criterion of Jansson and Sung (2013). For more trees it tallies every triplet directly (Bryant 2003), in $O(kn^3)$ time; this outpaces the $O(n^2 \log^{k+2} n)$ algorithm of Jansson et al. (2016) unless $k$ is very small. Set options(mc.cores = ) to count triplets on several threads.

Value

RStar() returns the consensus tree, an object of class phylo. It is rooted by construction, but when the resolved triplets leave the deepest divergence unresolved the root is a polytomy.

References

Bryant D (2003). “A classification of consensus methods for phylogenetics.” In Janowitz MF, Lapointe F, McMorris FR, Mirkin B, Roberts FS (eds.), Bioconsensus, volume 61 of DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 163–184. American Mathematical Society. doi:10.1090/dimacs/061/11.

Degnan JH, DeGiorgio M, Bryant D, Rosenberg NA (2009). “Properties of consensus methods for inferring species trees from gene trees.” Systematic Biology, 58(1), 35–54. doi:10.1093/sysbio/syp008.

Jansson J, Sung W (2013). “Constructing the R* consensus tree of two trees in subcubic time.” Algorithmica, 66(2), 329–345. doi:10.1007/s00453-012-9639-1.

Jansson J, Sung W, Vu H, Yiu S (2016). “Faster algorithms for computing the R* consensus tree.” Algorithmica, 76(4), 1224–1244. doi:10.1007/s00453-016-0122-2.

Examples

# Five trees whose majority signal recovers the species tree (((a,b),c),d):
trees <- c(
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, c), b), d);"),
  ape::read.tree(text = "(((b, c), a), d);")
)

# (a, b) wins {a,b,c} by plurality (3 vs 1 vs 1)
ape::write.tree(RStar(trees))

# Five trees whose majority signal recovers the species tree (((a,b),c),d):
trees <- c(
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, b), c), d);"),
  ape::read.tree(text = "(((a, c), b), d);"),
  ape::read.tree(text = "(((b, c), a), d);")
)

# (a, b) wins {a,b,c} by plurality (3 vs 1 vs 1)
ape::write.tree(RStar(trees))

Strict consensus tree

Description

Strict() returns the strict consensus of a set of trees: the tree that contains exactly those splits (clades) present in every input tree (Day 1985; Sokal and Rohlf 1981).

Usage

Strict(trees)
Strict(trees)

Arguments

trees

A list of trees, or a multiPhylo object. All entries must share the same leaf labels.

Details

This is an alias of TreeTools::Consensus() with p = 1.

Value

Strict() returns the consensus tree, an object of class phylo, rooted as in the first entry of trees.

References

Day WHE (1985). “Optimal algorithms for comparing trees with labeled leaves.” Journal of Classification, 2(1), 7–28. doi:10.1007/BF01908061.

Sokal RR, Rohlf FJ (1981). “Taxonomic congruence in the Leptopodomorpha re-examined.” Systematic Zoology, 30(3), 309–325. doi:10.2307/2413252.

Examples

trees <- ape::as.phylo(0:5, 8)
Strict(trees)

trees <- ape::as.phylo(0:5, 8)
Strict(trees)

Consensus tree minimizing transfer distance

Description

Construct a consensus tree that minimizes the sum of transfer distances to a set of input trees, using a greedy add-and-prune heuristic.

Usage

Transfer(
  trees,
  scale = TRUE,
  greedy = c("best", "first"),
  init = c("empty", "majority")
)
Transfer(
  trees,
  scale = TRUE,
  greedy = c("best", "first"),
  init = c("empty", "majority")
)

Arguments

trees

An object of class multiPhylo: the input trees. All trees must share the same tip labels.

scale

Logical; if TRUE (default), use the scaled transfer distance (normalized by light-side size minus one). If FALSE, use the unscaled (raw Hamming) transfer distance.

greedy

Character string specifying the greedy strategy: "best" (default) picks the single highest-benefit action at each step; "first" picks the first improving action encountered (faster but potentially lower quality).

init

Character string specifying the initial consensus: "empty" (default) starts with no splits (purely additive); "majority" starts with the majority-rule consensus and refines.

Details

Unlike the majority-rule consensus, which minimizes Robinson-Foulds distance (Barthélemy and McMorris 1986) and can be highly unresolved when phylogenetic signal is low, Transfer() uses the finer-grained transfer distance (Lemoine et al. 2018) to construct a more resolved consensus tree.

The algorithm pools all splits observed across input trees, computes pairwise transfer distances between them, and greedily adds or removes splits to minimize total transfer dissimilarity cost. The approach follows Takazawa et al. (2026), reimplemented for 'ConsTree' infrastructure. Set options(mc.cores = ) to use several threads.

Value

A tree of class phylo.

References

Barthélemy J, McMorris FR (1986). “The median procedure for n-trees.” Journal of Classification, 3(2), 329–334. doi:10.1007/BF01894194.

Lemoine F, Domelevo Entfellner J, Wilkinson E, Correia D, Dávila Felipe M, De Oliveira T, Gascuel O (2018). “Renewing Felsenstein's phylogenetic bootstrap in the era of big data.” Nature, 556(7702), 452–456. doi:10.1038/s41586-018-0043-0.

Takazawa Y, Takeda A, Hayamizu M, Gascuel O (2026). “Outperforming the majority-rule consensus tree using fine-grained dissimilarity measures.” bioRxiv. doi:10.64898/2026.03.16.712085.

Examples

library(TreeTools)
trees <- as.phylo(50:69, nTip = 12)

tc <- Transfer(trees)
mr <- Majority(trees)

plot(tc, main = "Transfer consensus")
plot(mr, main = "Majority rule", direction = "left")
# Compare resolution
cat("Majority-rule splits:", NSplits(mr), "\n")
cat("Transfer consensus splits:", NSplits(tc), "\n")

library(TreeTools)
trees <- as.phylo(50:69, nTip = 12)

tc <- Transfer(trees)
mr <- Majority(trees)

plot(tc, main = "Transfer consensus")
plot(mr, main = "Majority rule", direction = "left")
# Compare resolution
cat("Majority-rule splits:", NSplits(mr), "\n")
cat("Transfer consensus splits:", NSplits(tc), "\n")

Package 'ConsTree'

Help Index

Adams consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Average consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Geodesic (BHV) distance between trees

Description

Usage

Arguments

Value

References

See Also

Examples

Fréchet mean and variance in BHV treespace

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Frequency-difference consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Greedy (extended majority-rule) consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Local consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Loose consensus tree

Description

Usage

Arguments

Details

Value

References

See Also

Examples

Majority-rule consensus tree

Description

Usage

Arguments

Value

References

See Also