Phylogenetic Trees

Introduction

Phylogenetic trees represent the evolutionary history of some species of consideration. Here we consider phylogenetic trees with branch lengths as defined in [SS03].

Construction

phylogenetic_tree — Function

phylogenetic_tree(T::Type{<:Union{Float64, QQFieldElem}}, newick::String)

Constructs a rooted phylogenetic tree with Newick representation newick. T indicates the numerical type of the edge lengths.

Examples

Make a phylogenetic tree with 4 leaves from its Newick representation and print its taxa and cophenetic matrix.

julia> phylo_t = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);");

julia> taxa(phylo_t)
4-element Vector{String}:
 "B"
 "C"
 "G"
 "H"

julia> cophenetic_matrix(phylo_t)
4×4 Matrix{Float64}:
 0.0  2.0  8.0  6.0
 2.0  0.0  8.0  6.0
 8.0  8.0  0.0  8.0
 6.0  6.0  8.0  0.0

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phylogenetic_tree(M::Matrix{T}, taxa::Vector{String}) where T <: Union{Float64, QQFieldElem}

Constructs a phylogenetic tree with cophenetic matrix M and taxa taxa. The matrix M must be ultrametric, otherwise an error will be thrown.

Examples

Make a phylogenetic tree on 4 taxa with given cophenetic matrix and print one Newick representation.

julia> mat = [0. 2 8 6; 2 0 8 6; 8 8 0 8; 6 6 8 0]
4×4 Matrix{Float64}:
 0.0  2.0  8.0  6.0
 2.0  0.0  8.0  6.0
 8.0  8.0  0.0  8.0
 6.0  6.0  8.0  0.0

julia> tax = ["Bonobo", "Chimpanzee", "Gorilla", "Human"]
4-element Vector{String}:
 "Bonobo"
 "Chimpanzee"
 "Gorilla"
 "Human"

julia> tree_mat = phylogenetic_tree(mat, tax);

julia> newick(tree_mat)
"Gorilla:4,(Human:3,(Bonobo:1,Chimpanzee:1):2):1;"

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Some Helpful Functions

adjacency_tree — Function

adjacency_tree(ptree::PhylogeneticTree)

Returns the underlying graph of the phylogenetic tree ptree.

Examples

Make a phylogenetic tree with given Newick format and print its underlying graph.

julia> ptree = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);");

julia> adjacency_tree(ptree)
Directed graph with 7 nodes and the following edges:
(1, 2)(1, 7)(2, 3)(2, 4)(4, 5)(4, 6)

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is_equidistant — Function

is_equidistant(ptree::PhylogeneticTree)

Checks if the phylogenetic tree ptree is equidistant.

Examples

Make a phylogenetic tree with given Newick format and check if it is equidistant.

julia> ptree = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);");

julia> is_equidistant(ptree)
true

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cophenetic_matrix — Function

cophenetic_matrix(ptree::PhylogeneticTree)

Returns the cophenetic matrix of the phylogenetic tree ptree.

Examples

Make a phylogenetic tree with given Newick format and print its cophenetic matrix.

julia> ptree = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);");

julia> cophenetic_matrix(ptree)
4×4 Matrix{Float64}:
 0.0  2.0  8.0  6.0
 2.0  0.0  8.0  6.0
 8.0  8.0  0.0  8.0
 6.0  6.0  8.0  0.0

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taxa — Function

taxa(ptree::PhylogeneticTree)

Returns the taxa of the phylogenetic tree ptree.

Examples

Make a phylogenetic tree with given Newick format and print its taxa.

julia> ptree = phylogenetic_tree(Float64, "((H:3,(C:1,B:1):2):1,G:4);");

julia> taxa(ptree)
4-element Vector{String}:
 "B"
 "C"
 "G"
 "H"

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newick — Function

newick(ptree::PhylogeneticTree)

Returns a Newick representation of the phylogenetic tree ptree.

Examples

Make a phylogenetic tree from a matrix and print a Newick representation of it.

julia> mat = [0. 2 8 6; 2 0 8 6; 8 8 0 8; 6 6 8 0]
4×4 Matrix{Float64}:
 0.0  2.0  8.0  6.0
 2.0  0.0  8.0  6.0
 8.0  8.0  0.0  8.0
 6.0  6.0  8.0  0.0

julia> tax = ["Bonobo", "Chimpanzee", "Gorilla", "Human"]
4-element Vector{String}:
 "Bonobo"
 "Chimpanzee"
 "Gorilla"
 "Human"

julia> tree_mat = phylogenetic_tree(mat, tax);

julia> newick(tree_mat)
"Gorilla:4,(Human:3,(Bonobo:1,Chimpanzee:1):2):1;"

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tropical_median_consensus — Function

tropical_median_consensus(arr::Vector{PhylogeneticTree{T}})

Computes the tropical median consensus tree of the phylogenetic trees from the vector arr.

Examples

Compute the tropical median consensus of three trees and print one of its Newick representations.

julia> t1 = phylogenetic_tree(Float64, "((H:30,(C:10,B:10):20):10,G:40);");

julia> t2 = phylogenetic_tree(Float64, "(((H:10,C:10):20,B:30):10,G:40);");

julia> t3 = phylogenetic_tree(Float64, "((H:25,C:25):15,(B:15,G:15):25);");

julia> arr = [t1, t2, t3];

julia> tc = tropical_median_consensus(arr);

julia> newick(tc)
"G:40,(B:35,(C:30,H:30):5):5;"

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tropical_median_consensus(trees::Vararg{PhylogeneticTree, N}) where {N}

Computes the tropical median consensus tree of any number of phylogenetic trees given as parameters.

Examples

Compute the tropical median consensus of three trees and print one of its Newick representations.

julia> t1 = phylogenetic_tree(Float64, "((H:30,(C:10,B:10):20):10,G:40);");

julia> t2 = phylogenetic_tree(Float64, "(((H:10,C:10):20,B:30):10,G:40);");

julia> t3 = phylogenetic_tree(Float64, "((H:25,C:25):15,(B:15,G:15):25);");

julia> tc = tropical_median_consensus(t1, t2, t3);

julia> newick(tc)
"G:40,(B:35,(C:30,H:30):5):5;"

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