CollessLike (version 2.0)

colless.like.index: Computes the Colless-like balance index of a phylogenetic tree

Description

Given a phylogenetic tree, computes the Colless-like balance index of that phylogenetic tree.

Usage

colless.like.index(tree, f.size = "ln", diss = "MDM", norm = FALSE)

Arguments

tree

a single phylogenetic tree. It can be entered as a string in Newick format, as a 'phylo' object (ape package) or as an 'igraph' object (igraph package).

f.size

function to compute the f-size of the tree. See (Mir et al. , 2018) for details. Its default value is "ln" for f(n)=ln(n+e). Other value can be "exp" (f(n)=exp(n)). It can also be a user-defined function but in this case, the index cannot be normalized

diss

by default, the dissimilarity used to compute the balance index. See (Mir et al. , 2017) for details. Its default value is MDM (mean deviation from the median). Other values can be set as "sd" (sample standard deviation) or "var" (sample variance) . It can also be a user-defined function but in this case the index cannot be normalized.

norm

a logical object indicating if the indices should be normalized or not.

Value

A numeric value.

Details

The Colless-Like balance index is the generalization of the Colless balance index (see Colless,1982) for non-binary trees.

Given a function that computes the f-size of a tree and a dissimarity function that computes the difference of the f-sizes of the subtrees rooted at the children of every internal node of the tree, the Colless-Like index is defined as the sum of these dissimilarities for all internal nodes of the tree. (Mir et al. , 2017)

By default, the f-size function is f(n)=ln(n+e) and the dissimilarity is the mean deviation from the median (MDM). It is possible to change them by specifying it with the parameters f.size and diss, with "exp" the f-size would be f(n)=exp(n), and with "var" (or "sd") the dissimilarity would be the sample variance (or the sample standard deviation). It is also possible to set a new function for both parameters, see "References".

References

A. Mir, F. Rossello, L.Rotger, Sound Colless-like balance indices for multifurcating phylogenetic trees.PloS ONE 13 (2018), e0203401.

D. H. Colless, Review of "Phylogenetics: the theory and practice of phylogenetic systematics". Sys. Zool, 31 (1982), 100--104.

Examples

# NOT RUN {
# Computation of the Colless-Like balance index of trees 
# entered in newick format:
colless.like.index("(1,2,3,4,5);")
colless.like.index("(1,(2,(3,(4,5))));")

# Computation of the Colless-Like balance index of trees 
# entered as a phylo object:
require(ape)
random.tree = rtree(5,rooted=TRUE)
colless.like.index(random.tree)

# Computation of the Colless-Like balance index of a tree
# entered as a igraph object. The tree is randomly 
# generated from all trees with 5 leaves following
# the alpha-gamma model with alpha=0.5 and gamma=0.3.
a.g.tree = a.g.model(5,0.5,0.3)
colless.like.index(a.g.tree)

# All of them can be normalized (values between 0 and 1)
colless.like.index("(1,2,3,4,5);",norm=TRUE)
colless.like.index("(1,(2,(3,(4,5))));",norm=TRUE)
colless.like.index(random.tree,norm=TRUE)
colless.like.index(a.g.tree,norm=TRUE)

# Computation of the Colless-Like balance index of the
# previous generated tree with f-size function f(n)=exp(n):
colless.like.index(a.g.tree,f.size="exp")

# Computation of the Colless-Like balance index of the 
# previous generated tree that sets the sample variance 
# and the sample standard deviation as dissimilarity.
colless.like.index(a.g.tree,diss="var")
colless.like.index(a.g.tree,diss="sd")

# Computation of the Colless-Like balance index of the 
# previous generated tree with f-size function f(n)=exp(n)
# that sets the sample variance and the sample standard 
# deviation as dissimilarity.
colless.like.index(a.g.tree,f.size="exp",diss="var")
colless.like.index(a.g.tree,f.size="exp",diss="sd")

# }