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# Copyright (C) 2013 by Yanbo Ye ([email protected])
#
# This file is part of the Biopython distribution and governed by your
# choice of the "Biopython License Agreement" or the "BSD 3-Clause License".
# Please see the LICENSE file that should have been included as part of this
# package.
"""Classes and methods for tree construction."""
import itertools
import copy
import numbers
from Bio.Phylo import BaseTree
from Bio.Align import Alignment, MultipleSeqAlignment
from Bio.Align import substitution_matrices
# flake8: noqa
class _Matrix:
"""Base class for distance matrix or scoring matrix.
Accepts a list of names and a lower triangular matrix.::
matrix = [[0],
[1, 0],
[2, 3, 0],
[4, 5, 6, 0]]
represents the symmetric matrix of
[0,1,2,4]
[1,0,3,5]
[2,3,0,6]
[4,5,6,0]
:Parameters:
names : list
names of elements, used for indexing
matrix : list
nested list of numerical lists in lower triangular format
Examples
--------
>>> from Bio.Phylo.TreeConstruction import _Matrix
>>> names = ['Alpha', 'Beta', 'Gamma', 'Delta']
>>> matrix = [[0], [1, 0], [2, 3, 0], [4, 5, 6, 0]]
>>> m = _Matrix(names, matrix)
>>> m
_Matrix(names=['Alpha', 'Beta', 'Gamma', 'Delta'], matrix=[[0], [1, 0], [2, 3, 0], [4, 5, 6, 0]])
You can use two indices to get or assign an element in the matrix.
>>> m[1,2]
3
>>> m['Beta','Gamma']
3
>>> m['Beta','Gamma'] = 4
>>> m['Beta','Gamma']
4
Further more, you can use one index to get or assign a list of elements related to that index.
>>> m[0]
[0, 1, 2, 4]
>>> m['Alpha']
[0, 1, 2, 4]
>>> m['Alpha'] = [0, 7, 8, 9]
>>> m[0]
[0, 7, 8, 9]
>>> m[0,1]
7
Also you can delete or insert a column&row of elements by index.
>>> m
_Matrix(names=['Alpha', 'Beta', 'Gamma', 'Delta'], matrix=[[0], [7, 0], [8, 4, 0], [9, 5, 6, 0]])
>>> del m['Alpha']
>>> m
_Matrix(names=['Beta', 'Gamma', 'Delta'], matrix=[[0], [4, 0], [5, 6, 0]])
>>> m.insert('Alpha', [0, 7, 8, 9] , 0)
>>> m
_Matrix(names=['Alpha', 'Beta', 'Gamma', 'Delta'], matrix=[[0], [7, 0], [8, 4, 0], [9, 5, 6, 0]])
"""
def __init__(self, names, matrix=None):
"""Initialize matrix.
Arguments are a list of names, and optionally a list of lower
triangular matrix data (zero matrix used by default).
"""
# check names
if isinstance(names, list) and all(isinstance(s, str) for s in names):
if len(set(names)) == len(names):
self.names = names
else:
raise ValueError("Duplicate names found")
else:
raise TypeError("'names' should be a list of strings")
# check matrix
if matrix is None:
# create a new one with 0 if matrix is not assigned
matrix = [[0] * i for i in range(1, len(self) + 1)]
self.matrix = matrix
else:
# check if all elements are numbers
if (
isinstance(matrix, list)
and all(isinstance(row, list) for row in matrix)
and all(
isinstance(item, numbers.Number) for row in matrix for item in row
)
):
# check if the same length with names
if len(matrix) == len(names):
# check if is lower triangle format
if [len(row) for row in matrix] == list(range(1, len(self) + 1)):
self.matrix = matrix
else:
raise ValueError("'matrix' should be in lower triangle format")
else:
raise ValueError("'names' and 'matrix' should be the same size")
else:
raise TypeError("'matrix' should be a list of numerical lists")
def __getitem__(self, item):
"""Access value(s) by the index(s) or name(s).
For a _Matrix object 'dm'::
dm[i] get a value list from the given 'i' to others;
dm[i, j] get the value between 'i' and 'j';
dm['name'] map name to index first
dm['name1', 'name2'] map name to index first
"""
# Handle single indexing
if isinstance(item, (int, str)):
index = None
if isinstance(item, int):
index = item
elif isinstance(item, str):
if item in self.names:
index = self.names.index(item)
else:
raise ValueError("Item not found.")
else:
raise TypeError("Invalid index type.")
# check index
if index > len(self) - 1:
raise IndexError("Index out of range.")
return [self.matrix[index][i] for i in range(0, index)] + [
self.matrix[i][index] for i in range(index, len(self))
]
# Handle double indexing
elif len(item) == 2:
row_index = None
col_index = None
if all(isinstance(i, int) for i in item):
row_index, col_index = item
elif all(isinstance(i, str) for i in item):
row_name, col_name = item
if row_name in self.names and col_name in self.names:
row_index = self.names.index(row_name)
col_index = self.names.index(col_name)
else:
raise ValueError("Item not found.")
else:
raise TypeError("Invalid index type.")
# check index
if row_index > len(self) - 1 or col_index > len(self) - 1:
raise IndexError("Index out of range.")
if row_index > col_index:
return self.matrix[row_index][col_index]
else:
return self.matrix[col_index][row_index]
else:
raise TypeError("Invalid index type.")
def __setitem__(self, item, value):
"""Set value by the index(s) or name(s).
Similar to __getitem__::
dm[1] = [1, 0, 3, 4] set values from '1' to others;
dm[i, j] = 2 set the value from 'i' to 'j'
"""
# Handle single indexing
if isinstance(item, (int, str)):
index = None
if isinstance(item, int):
index = item
elif isinstance(item, str):
if item in self.names:
index = self.names.index(item)
else:
raise ValueError("Item not found.")
else:
raise TypeError("Invalid index type.")
# check index
if index > len(self) - 1:
raise IndexError("Index out of range.")
# check and assign value
if isinstance(value, list) and all(
isinstance(n, numbers.Number) for n in value
):
if len(value) == len(self):
for i in range(0, index):
self.matrix[index][i] = value[i]
for i in range(index, len(self)):
self.matrix[i][index] = value[i]
else:
raise ValueError("Value not the same size.")
else:
raise TypeError("Invalid value type.")
# Handle double indexing
elif len(item) == 2:
row_index = None
col_index = None
if all(isinstance(i, int) for i in item):
row_index, col_index = item
elif all(isinstance(i, str) for i in item):
row_name, col_name = item
if row_name in self.names and col_name in self.names:
row_index = self.names.index(row_name)
col_index = self.names.index(col_name)
else:
raise ValueError("Item not found.")
else:
raise TypeError("Invalid index type.")
# check index
if row_index > len(self) - 1 or col_index > len(self) - 1:
raise IndexError("Index out of range.")
# check and assign value
if isinstance(value, numbers.Number):
if row_index > col_index:
self.matrix[row_index][col_index] = value
else:
self.matrix[col_index][row_index] = value
else:
raise TypeError("Invalid value type.")
else:
raise TypeError("Invalid index type.")
def __delitem__(self, item):
"""Delete related distances by the index or name."""
index = None
if isinstance(item, int):
index = item
elif isinstance(item, str):
index = self.names.index(item)
else:
raise TypeError("Invalid index type.")
# remove distances related to index
for i in range(index + 1, len(self)):
del self.matrix[i][index]
del self.matrix[index]
# remove name
del self.names[index]
def insert(self, name, value, index=None):
"""Insert distances given the name and value.
:Parameters:
name : str
name of a row/col to be inserted
value : list
a row/col of values to be inserted
"""
if isinstance(name, str):
# insert at the given index or at the end
if index is None:
index = len(self)
if not isinstance(index, int):
raise TypeError("Invalid index type.")
# insert name
self.names.insert(index, name)
# insert elements of 0, to be assigned
self.matrix.insert(index, [0] * index)
for i in range(index, len(self)):
self.matrix[i].insert(index, 0)
# assign value
self[index] = value
else:
raise TypeError("Invalid name type.")
def __len__(self):
"""Matrix length."""
return len(self.names)
def __repr__(self):
"""Return Matrix as a string."""
return self.__class__.__name__ + "(names=%s, matrix=%s)" % tuple(
map(repr, (self.names, self.matrix))
)
def __str__(self):
"""Get a lower triangular matrix string."""
matrix_string = "\n".join(
[
self.names[i]
+ "\t"
+ "\t".join([format(n, "f") for n in self.matrix[i]])
for i in range(0, len(self))
]
)
matrix_string = matrix_string + "\n\t" + "\t".join(self.names)
return matrix_string.expandtabs(tabsize=4)
class DistanceMatrix(_Matrix):
"""Distance matrix class that can be used for distance based tree algorithms.
All diagonal elements will be zero no matter what the users provide.
"""
def __init__(self, names, matrix=None):
"""Initialize the class."""
_Matrix.__init__(self, names, matrix)
self._set_zero_diagonal()
def __setitem__(self, item, value):
"""Set Matrix's items to values."""
_Matrix.__setitem__(self, item, value)
self._set_zero_diagonal()
def _set_zero_diagonal(self):
"""Set all diagonal elements to zero (PRIVATE)."""
for i in range(0, len(self)):
self.matrix[i][i] = 0
def format_phylip(self, handle):
"""Write data in Phylip format to a given file-like object or handle.
The output stream is the input distance matrix format used with Phylip
programs (e.g. 'neighbor'). See:
http://evolution.genetics.washington.edu/phylip/doc/neighbor.html
:Parameters:
handle : file or file-like object
A writeable text mode file handle or other object supporting
the 'write' method, such as StringIO or sys.stdout.
"""
handle.write(f" {len(self.names)}\n")
# Phylip needs space-separated, vertically aligned columns
name_width = max(12, max(map(len, self.names)) + 1)
value_fmts = ("{" + str(x) + ":.4f}" for x in range(1, len(self.matrix) + 1))
row_fmt = "{0:" + str(name_width) + "s}" + " ".join(value_fmts) + "\n"
for i, (name, values) in enumerate(zip(self.names, self.matrix)):
# Mirror the matrix values across the diagonal
mirror_values = (self.matrix[j][i] for j in range(i + 1, len(self.matrix)))
fields = itertools.chain([name], values, mirror_values)
handle.write(row_fmt.format(*fields))
# Shim for compatibility with Biopython<1.70 (#1304)
_DistanceMatrix = DistanceMatrix
class DistanceCalculator:
"""Calculates the distance matrix from a DNA or protein sequence alignment.
This class calculates the distance matrix from a multiple sequence alignment
of DNA or protein sequences, and the given name of the substitution model.
Currently only scoring matrices are used.
:Parameters:
model : str
Name of the model matrix to be used to calculate distance.
The attribute ``dna_models`` contains the available model
names for DNA sequences and ``protein_models`` for protein
sequences.
Examples
--------
Loading a small PHYLIP alignment from which to compute distances::
>>> from Bio.Phylo.TreeConstruction import DistanceCalculator
>>> from Bio import AlignIO
>>> aln = AlignIO.read(open('TreeConstruction/msa.phy'), 'phylip')
>>> print(aln) # doctest:+NORMALIZE_WHITESPACE
Alignment with 5 rows and 13 columns
AACGTGGCCACAT Alpha
AAGGTCGCCACAC Beta
CAGTTCGCCACAA Gamma
GAGATTTCCGCCT Delta
GAGATCTCCGCCC Epsilon
DNA calculator with 'identity' model::
>>> calculator = DistanceCalculator('identity')
>>> dm = calculator.get_distance(aln)
>>> print(dm) # doctest:+NORMALIZE_WHITESPACE
Alpha 0.000000
Beta 0.230769 0.000000
Gamma 0.384615 0.230769 0.000000
Delta 0.538462 0.538462 0.538462 0.000000
Epsilon 0.615385 0.384615 0.461538 0.153846 0.000000
Alpha Beta Gamma Delta Epsilon
Protein calculator with 'blosum62' model::
>>> calculator = DistanceCalculator('blosum62')
>>> dm = calculator.get_distance(aln)
>>> print(dm) # doctest:+NORMALIZE_WHITESPACE
Alpha 0.000000
Beta 0.369048 0.000000
Gamma 0.493976 0.250000 0.000000
Delta 0.585366 0.547619 0.566265 0.000000
Epsilon 0.700000 0.355556 0.488889 0.222222 0.000000
Alpha Beta Gamma Delta Epsilon
Same calculation, using the new Alignment object::
>>> from Bio.Phylo.TreeConstruction import DistanceCalculator
>>> from Bio import Align
>>> aln = Align.read('TreeConstruction/msa.phy', 'phylip')
>>> print(aln) # doctest:+NORMALIZE_WHITESPACE
Alpha 0 AACGTGGCCACAT 13
Beta 0 AAGGTCGCCACAC 13
Gamma 0 CAGTTCGCCACAA 13
Delta 0 GAGATTTCCGCCT 13
Epsilon 0 GAGATCTCCGCCC 13
<BLANKLINE>
DNA calculator with 'identity' model::
>>> calculator = DistanceCalculator('identity')
>>> dm = calculator.get_distance(aln)
>>> print(dm) # doctest:+NORMALIZE_WHITESPACE
Alpha 0.000000
Beta 0.230769 0.000000
Gamma 0.384615 0.230769 0.000000
Delta 0.538462 0.538462 0.538462 0.000000
Epsilon 0.615385 0.384615 0.461538 0.153846 0.000000
Alpha Beta Gamma Delta Epsilon
Protein calculator with 'blosum62' model::
>>> calculator = DistanceCalculator('blosum62')
>>> dm = calculator.get_distance(aln)
>>> print(dm) # doctest:+NORMALIZE_WHITESPACE
Alpha 0.000000
Beta 0.369048 0.000000
Gamma 0.493976 0.250000 0.000000
Delta 0.585366 0.547619 0.566265 0.000000
Epsilon 0.700000 0.355556 0.488889 0.222222 0.000000
Alpha Beta Gamma Delta Epsilon
"""
protein_alphabet = set("ABCDEFGHIKLMNPQRSTVWXYZ")
dna_models = []
protein_models = []
# matrices available
names = substitution_matrices.load()
for name in names:
matrix = substitution_matrices.load(name)
if name == "NUC.4.4":
# BLAST nucleic acid scoring matrix
name = "blastn"
else:
name = name.lower()
if protein_alphabet.issubset(set(matrix.alphabet)):
protein_models.append(name)
else:
dna_models.append(name)
del protein_alphabet
del name
del names
del matrix
models = ["identity"] + dna_models + protein_models
def __init__(self, model="identity", skip_letters=None):
"""Initialize with a distance model."""
# Shim for backward compatibility (#491)
if skip_letters:
self.skip_letters = skip_letters
elif model == "identity":
self.skip_letters = ()
else:
self.skip_letters = ("-", "*")
if model == "identity":
self.scoring_matrix = None
elif model in self.models:
if model == "blastn":
name = "NUC.4.4"
else:
name = model.upper()
self.scoring_matrix = substitution_matrices.load(name)
else:
raise ValueError(
"Model not supported. Available models: " + ", ".join(self.models)
)
def _pairwise(self, seq1, seq2):
"""Calculate pairwise distance from two sequences (PRIVATE).
Returns a value between 0 (identical sequences) and 1 (completely
different, or seq1 is an empty string.)
"""
score = 0
max_score = 0
if self.scoring_matrix is None:
# Score by character identity, not skipping any special letters
score = sum(
l1 == l2
for l1, l2 in zip(seq1, seq2)
if l1 not in self.skip_letters and l2 not in self.skip_letters
)
max_score = len(seq1)
else:
max_score1 = 0
max_score2 = 0
for i in range(0, len(seq1)):
l1 = seq1[i]
l2 = seq2[i]
if l1 in self.skip_letters or l2 in self.skip_letters:
continue
try:
max_score1 += self.scoring_matrix[l1, l1]
except IndexError:
raise ValueError(
f"Bad letter '{l1}' in sequence '{seq1.id}' at position '{i}'"
) from None
try:
max_score2 += self.scoring_matrix[l2, l2]
except IndexError:
raise ValueError(
f"Bad letter '{l2}' in sequence '{seq2.id}' at position '{i}'"
) from None
score += self.scoring_matrix[l1, l2]
# Take the higher score if the matrix is asymmetrical
max_score = max(max_score1, max_score2)
if max_score == 0:
return 1 # max possible scaled distance
return 1 - (score / max_score)
def get_distance(self, msa):
"""Return a DistanceMatrix for an Alignment or MultipleSeqAlignment object.
:Parameters:
msa : Alignment or MultipleSeqAlignment object representing a
DNA or protein multiple sequence alignment.
"""
if isinstance(msa, Alignment):
names = [s.id for s in msa.sequences]
dm = DistanceMatrix(names)
n = len(names)
for i1 in range(n):
for i2 in range(i1):
dm[names[i1], names[i2]] = self._pairwise(msa[i1], msa[i2])
elif isinstance(msa, MultipleSeqAlignment):
names = [s.id for s in msa]
dm = DistanceMatrix(names)
for seq1, seq2 in itertools.combinations(msa, 2):
dm[seq1.id, seq2.id] = self._pairwise(seq1, seq2)
else:
raise TypeError(
"Must provide an Alignment object or a MultipleSeqAlignment object."
)
return dm
class TreeConstructor:
"""Base class for all tree constructor."""
def build_tree(self, msa):
"""Caller to build the tree from an Alignment or MultipleSeqAlignment object.
This should be implemented in subclass.
"""
raise NotImplementedError("Method not implemented!")
class DistanceTreeConstructor(TreeConstructor):
"""Distance based tree constructor.
:Parameters:
method : str
Distance tree construction method, 'nj'(default) or 'upgma'.
distance_calculator : DistanceCalculator
The distance matrix calculator for multiple sequence alignment.
It must be provided if ``build_tree`` will be called.
Examples
--------
Loading a small PHYLIP alignment from which to compute distances, and then
build a upgma Tree::
>>> from Bio.Phylo.TreeConstruction import DistanceTreeConstructor
>>> from Bio.Phylo.TreeConstruction import DistanceCalculator
>>> from Bio import AlignIO
>>> aln = AlignIO.read(open('TreeConstruction/msa.phy'), 'phylip')
>>> constructor = DistanceTreeConstructor()
>>> calculator = DistanceCalculator('identity')
>>> dm = calculator.get_distance(aln)
>>> upgmatree = constructor.upgma(dm)
>>> print(upgmatree)
Tree(rooted=True)
Clade(branch_length=0, name='Inner4')
Clade(branch_length=0.18749999999999994, name='Inner1')
Clade(branch_length=0.07692307692307693, name='Epsilon')
Clade(branch_length=0.07692307692307693, name='Delta')
Clade(branch_length=0.11057692307692304, name='Inner3')
Clade(branch_length=0.038461538461538464, name='Inner2')
Clade(branch_length=0.11538461538461536, name='Gamma')
Clade(branch_length=0.11538461538461536, name='Beta')
Clade(branch_length=0.15384615384615383, name='Alpha')
Build a NJ Tree::
>>> njtree = constructor.nj(dm)
>>> print(njtree)
Tree(rooted=False)
Clade(branch_length=0, name='Inner3')
Clade(branch_length=0.18269230769230765, name='Alpha')
Clade(branch_length=0.04807692307692307, name='Beta')
Clade(branch_length=0.04807692307692307, name='Inner2')
Clade(branch_length=0.27884615384615385, name='Inner1')
Clade(branch_length=0.051282051282051266, name='Epsilon')
Clade(branch_length=0.10256410256410259, name='Delta')
Clade(branch_length=0.14423076923076922, name='Gamma')
Same example, using the new Alignment class::
>>> from Bio.Phylo.TreeConstruction import DistanceTreeConstructor
>>> from Bio.Phylo.TreeConstruction import DistanceCalculator
>>> from Bio import Align
>>> aln = Align.read(open('TreeConstruction/msa.phy'), 'phylip')
>>> constructor = DistanceTreeConstructor()
>>> calculator = DistanceCalculator('identity')
>>> dm = calculator.get_distance(aln)
>>> upgmatree = constructor.upgma(dm)
>>> print(upgmatree)
Tree(rooted=True)
Clade(branch_length=0, name='Inner4')
Clade(branch_length=0.18749999999999994, name='Inner1')
Clade(branch_length=0.07692307692307693, name='Epsilon')
Clade(branch_length=0.07692307692307693, name='Delta')
Clade(branch_length=0.11057692307692304, name='Inner3')
Clade(branch_length=0.038461538461538464, name='Inner2')
Clade(branch_length=0.11538461538461536, name='Gamma')
Clade(branch_length=0.11538461538461536, name='Beta')
Clade(branch_length=0.15384615384615383, name='Alpha')
Build a NJ Tree::
>>> njtree = constructor.nj(dm)
>>> print(njtree)
Tree(rooted=False)
Clade(branch_length=0, name='Inner3')
Clade(branch_length=0.18269230769230765, name='Alpha')
Clade(branch_length=0.04807692307692307, name='Beta')
Clade(branch_length=0.04807692307692307, name='Inner2')
Clade(branch_length=0.27884615384615385, name='Inner1')
Clade(branch_length=0.051282051282051266, name='Epsilon')
Clade(branch_length=0.10256410256410259, name='Delta')
Clade(branch_length=0.14423076923076922, name='Gamma')
"""
methods = ["nj", "upgma"]
def __init__(self, distance_calculator=None, method="nj"):
"""Initialize the class."""
if distance_calculator is None or isinstance(
distance_calculator, DistanceCalculator
):
self.distance_calculator = distance_calculator
else:
raise TypeError("Must provide a DistanceCalculator object.")
if method in self.methods:
self.method = method
else:
raise TypeError(
"Bad method: "
+ method
+ ". Available methods: "
+ ", ".join(self.methods)
)
def build_tree(self, msa):
"""Construct and return a Tree, Neighbor Joining or UPGMA."""
if self.distance_calculator:
dm = self.distance_calculator.get_distance(msa)
tree = None
if self.method == "upgma":
tree = self.upgma(dm)
else:
tree = self.nj(dm)
return tree
else:
raise TypeError("Must provide a DistanceCalculator object.")
def upgma(self, distance_matrix):
"""Construct and return an UPGMA tree.
Constructs and returns an Unweighted Pair Group Method
with Arithmetic mean (UPGMA) tree.
:Parameters:
distance_matrix : DistanceMatrix
The distance matrix for tree construction.
"""
if not isinstance(distance_matrix, DistanceMatrix):
raise TypeError("Must provide a DistanceMatrix object.")
# make a copy of the distance matrix to be used
dm = copy.deepcopy(distance_matrix)
# init terminal clades
clades = [BaseTree.Clade(None, name) for name in dm.names]
# init minimum index
min_i = 0
min_j = 0
inner_count = 0
while len(dm) > 1:
min_dist = dm[1, 0]
# find minimum index
for i in range(1, len(dm)):
for j in range(0, i):
if min_dist >= dm[i, j]:
min_dist = dm[i, j]
min_i = i
min_j = j
# create clade
clade1 = clades[min_i]
clade2 = clades[min_j]
inner_count += 1
inner_clade = BaseTree.Clade(None, "Inner" + str(inner_count))
inner_clade.clades.append(clade1)
inner_clade.clades.append(clade2)
# assign branch length
if clade1.is_terminal():
clade1.branch_length = min_dist / 2
else:
clade1.branch_length = min_dist / 2 - self._height_of(clade1)
if clade2.is_terminal():
clade2.branch_length = min_dist / 2
else:
clade2.branch_length = min_dist / 2 - self._height_of(clade2)
# update node list
clades[min_j] = inner_clade
del clades[min_i]
# rebuild distance matrix,
# set the distances of new node at the index of min_j
for k in range(0, len(dm)):
if k != min_i and k != min_j:
dm[min_j, k] = (dm[min_i, k] + dm[min_j, k]) / 2
dm.names[min_j] = "Inner" + str(inner_count)
del dm[min_i]
inner_clade.branch_length = 0
return BaseTree.Tree(inner_clade)
def nj(self, distance_matrix):
"""Construct and return a Neighbor Joining tree.
:Parameters:
distance_matrix : DistanceMatrix
The distance matrix for tree construction.
"""
if not isinstance(distance_matrix, DistanceMatrix):
raise TypeError("Must provide a DistanceMatrix object.")
# make a copy of the distance matrix to be used
dm = copy.deepcopy(distance_matrix)
# init terminal clades
clades = [BaseTree.Clade(None, name) for name in dm.names]
# init node distance
node_dist = [0] * len(dm)
# init minimum index
min_i = 0
min_j = 0
inner_count = 0
# special cases for Minimum Alignment Matrices
if len(dm) == 1:
root = clades[0]
return BaseTree.Tree(root, rooted=False)
elif len(dm) == 2:
# minimum distance will always be [1,0]
min_i = 1
min_j = 0
clade1 = clades[min_i]
clade2 = clades[min_j]
clade1.branch_length = dm[min_i, min_j] / 2.0
clade2.branch_length = dm[min_i, min_j] - clade1.branch_length
inner_clade = BaseTree.Clade(None, "Inner")
inner_clade.clades.append(clade1)
inner_clade.clades.append(clade2)
clades[0] = inner_clade
root = clades[0]
return BaseTree.Tree(root, rooted=False)
while len(dm) > 2:
# calculate nodeDist
for i in range(0, len(dm)):
node_dist[i] = 0
for j in range(0, len(dm)):
node_dist[i] += dm[i, j]
node_dist[i] = node_dist[i] / (len(dm) - 2)
# find minimum distance pair
min_dist = dm[1, 0] - node_dist[1] - node_dist[0]
min_i = 0
min_j = 1
for i in range(1, len(dm)):
for j in range(0, i):
temp = dm[i, j] - node_dist[i] - node_dist[j]
if min_dist > temp:
min_dist = temp
min_i = i
min_j = j
# create clade
clade1 = clades[min_i]
clade2 = clades[min_j]
inner_count += 1
inner_clade = BaseTree.Clade(None, "Inner" + str(inner_count))
inner_clade.clades.append(clade1)
inner_clade.clades.append(clade2)
# assign branch length
clade1.branch_length = (
dm[min_i, min_j] + node_dist[min_i] - node_dist[min_j]
) / 2.0
clade2.branch_length = dm[min_i, min_j] - clade1.branch_length
# update node list
clades[min_j] = inner_clade
del clades[min_i]
# rebuild distance matrix,
# set the distances of new node at the index of min_j
for k in range(0, len(dm)):
if k != min_i and k != min_j:
dm[min_j, k] = (
dm[min_i, k] + dm[min_j, k] - dm[min_i, min_j]
) / 2.0
dm.names[min_j] = "Inner" + str(inner_count)
del dm[min_i]
# set the last clade as one of the child of the inner_clade
root = None
if clades[0] == inner_clade:
clades[0].branch_length = 0
clades[1].branch_length = dm[1, 0]
clades[0].clades.append(clades[1])
root = clades[0]
else:
clades[0].branch_length = dm[1, 0]
clades[1].branch_length = 0
clades[1].clades.append(clades[0])
root = clades[1]
return BaseTree.Tree(root, rooted=False)
def _height_of(self, clade):
"""Calculate clade height -- the longest path to any terminal (PRIVATE)."""
height = 0
if clade.is_terminal():
height = clade.branch_length
else:
height = height + max(self._height_of(c) for c in clade.clades)
return height
# #################### Tree Scoring and Searching Classes #####################
class Scorer:
"""Base class for all tree scoring methods."""
def get_score(self, tree, alignment):
"""Caller to get the score of a tree for the given alignment.
This should be implemented in subclass.
"""
raise NotImplementedError("Method not implemented!")
class TreeSearcher:
"""Base class for all tree searching methods."""
def search(self, starting_tree, alignment):
"""Caller to search the best tree with a starting tree.
This should be implemented in subclass.
"""
raise NotImplementedError("Method not implemented!")
class NNITreeSearcher(TreeSearcher):
"""Tree searching with Nearest Neighbor Interchanges (NNI) algorithm.
:Parameters:
scorer : ParsimonyScorer
parsimony scorer to calculate the parsimony score of
different trees during NNI algorithm.
"""
def __init__(self, scorer):
"""Initialize the class."""
if isinstance(scorer, Scorer):
self.scorer = scorer
else:
raise TypeError("Must provide a Scorer object.")
def search(self, starting_tree, alignment):
"""Implement the TreeSearcher.search method.
:Parameters:
starting_tree : Tree
starting tree of NNI method.
alignment : Alignment or MultipleSeqAlignment object
multiple sequence alignment used to calculate parsimony
score of different NNI trees.
"""
return self._nni(starting_tree, alignment)
def _nni(self, starting_tree, alignment):
"""Search for the best parsimony tree using the NNI algorithm (PRIVATE)."""
best_tree = starting_tree
while True:
best_score = self.scorer.get_score(best_tree, alignment)
temp = best_score
for t in self._get_neighbors(best_tree):
score = self.scorer.get_score(t, alignment)
if score < best_score:
best_score = score
best_tree = t
# stop if no smaller score exist
if best_score >= temp:
break
return best_tree
def _get_neighbors(self, tree):
"""Get all neighbor trees of the given tree (PRIVATE).
Currently only for binary rooted trees.
"""
# make child to parent dict
parents = {}
for clade in tree.find_clades():
if clade != tree.root:
node_path = tree.get_path(clade)
# cannot get the parent if the parent is root. Bug?
if len(node_path) == 1:
parents[clade] = tree.root
else:
parents[clade] = node_path[-2]
neighbors = []
root_childs = []
for clade in tree.get_nonterminals(order="level"):
if clade == tree.root:
left = clade.clades[0]
right = clade.clades[1]
root_childs.append(left)
root_childs.append(right)
if not left.is_terminal() and not right.is_terminal():
# make changes around the left_left clade
# left_left = left.clades[0]
left_right = left.clades[1]
right_left = right.clades[0]
right_right = right.clades[1]
# neighbor 1 (left_left + right_right)
del left.clades[1]
del right.clades[1]
left.clades.append(right_right)
right.clades.append(left_right)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# neighbor 2 (left_left + right_left)
del left.clades[1]
del right.clades[0]
left.clades.append(right_left)
right.clades.append(right_right)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# change back (left_left + left_right)
del left.clades[1]
del right.clades[0]
left.clades.append(left_right)
right.clades.insert(0, right_left)
elif clade in root_childs:
# skip root child
continue
else:
# method for other clades
# make changes around the parent clade
left = clade.clades[0]
right = clade.clades[1]
parent = parents[clade]
if clade == parent.clades[0]:
sister = parent.clades[1]
# neighbor 1 (parent + right)
del parent.clades[1]
del clade.clades[1]
parent.clades.append(right)
clade.clades.append(sister)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# neighbor 2 (parent + left)
del parent.clades[1]
del clade.clades[0]
parent.clades.append(left)
clade.clades.append(right)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# change back (parent + sister)
del parent.clades[1]
del clade.clades[0]
parent.clades.append(sister)
clade.clades.insert(0, left)
else:
sister = parent.clades[0]
# neighbor 1 (parent + right)
del parent.clades[0]
del clade.clades[1]
parent.clades.insert(0, right)
clade.clades.append(sister)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# neighbor 2 (parent + left)
del parent.clades[0]
del clade.clades[0]
parent.clades.insert(0, left)
clade.clades.append(right)
temp_tree = copy.deepcopy(tree)
neighbors.append(temp_tree)
# change back (parent + sister)
del parent.clades[0]
del clade.clades[0]
parent.clades.insert(0, sister)
clade.clades.insert(0, left)
return neighbors
# ######################## Parsimony Classes ##########################
class ParsimonyScorer(Scorer):
"""Parsimony scorer with a scoring matrix.
This is a combination of Fitch algorithm and Sankoff algorithm.
See ParsimonyTreeConstructor for usage.
:Parameters:
matrix : _Matrix
scoring matrix used in parsimony score calculation.
"""
def __init__(self, matrix=None):
"""Initialize the class."""
if not matrix or isinstance(matrix, _Matrix):
self.matrix = matrix
else:
raise TypeError("Must provide a _Matrix object.")
def get_score(self, tree, alignment):
"""Calculate parsimony score using the Fitch algorithm.
Calculate and return the parsimony score given a tree and the
MSA using either the Fitch algorithm (without a penalty matrix)
or the Sankoff algorithm (with a matrix).
"""
# make sure the tree is rooted and bifurcating
if not tree.is_bifurcating():
raise ValueError("The tree provided should be bifurcating.")
if not tree.rooted:
tree.root_at_midpoint()
# sort tree terminals and alignment
terms = tree.get_terminals()
terms.sort(key=lambda term: term.name)
alignment.sort()
if isinstance(alignment, MultipleSeqAlignment):
if not all(t.name == a.id for t, a in zip(terms, alignment)):
raise ValueError(
"Taxon names of the input tree should be the same with the alignment."
)
else: # Alignment object
if not all(t.name == s.id for t, s in zip(terms, alignment.sequences)):
raise ValueError(
"Taxon names of the input tree should be the same with the alignment."
)
# term_align = dict(zip(terms, alignment))
score = 0
for i in range(len(alignment[0])):
# parsimony score for column_i
score_i = 0
# get column
column_i = alignment[:, i]
# skip non-informative column
if column_i == len(column_i) * column_i[0]:
continue
# start calculating score_i using the tree and column_i
# Fitch algorithm without the penalty matrix
if not self.matrix:
# init by mapping terminal clades and states in column_i
clade_states = dict(zip(terms, [{c} for c in column_i]))
for clade in tree.get_nonterminals(order="postorder"):
clade_childs = clade.clades
left_state = clade_states[clade_childs[0]]
right_state = clade_states[clade_childs[1]]
state = left_state & right_state
if not state:
state = left_state | right_state
score_i += 1
clade_states[clade] = state
# Sankoff algorithm with the penalty matrix
else:
inf = float("inf")
# init score arrays for terminal clades
alphabet = self.matrix.names
length = len(alphabet)
clade_scores = {}
for j in range(len(column_i)):
array = [inf] * length
index = alphabet.index(column_i[j])
array[index] = 0
clade_scores[terms[j]] = array
# bottom up calculation
for clade in tree.get_nonterminals(order="postorder"):
clade_childs = clade.clades
left_score = clade_scores[clade_childs[0]]
right_score = clade_scores[clade_childs[1]]
array = []
for m in range(length):
min_l = inf
min_r = inf
for n in range(length):
sl = self.matrix[alphabet[m], alphabet[n]] + left_score[n]
sr = self.matrix[alphabet[m], alphabet[n]] + right_score[n]
if min_l > sl:
min_l = sl
if min_r > sr:
min_r = sr
array.append(min_l + min_r)
clade_scores[clade] = array
# minimum from root score
score_i = min(array)
# TODO: resolve internal states
score += score_i
return score
class ParsimonyTreeConstructor(TreeConstructor):
"""Parsimony tree constructor.
:Parameters:
searcher : TreeSearcher
tree searcher to search the best parsimony tree.
starting_tree : Tree
starting tree provided to the searcher.
Examples
--------
We will load an alignment, and then load various trees which have already been computed from it::
>>> from Bio import AlignIO, Phylo
>>> aln = AlignIO.read(open('TreeConstruction/msa.phy'), 'phylip')
>>> print(aln)
Alignment with 5 rows and 13 columns
AACGTGGCCACAT Alpha
AAGGTCGCCACAC Beta
CAGTTCGCCACAA Gamma
GAGATTTCCGCCT Delta
GAGATCTCCGCCC Epsilon
Load a starting tree::
>>> starting_tree = Phylo.read('TreeConstruction/nj.tre', 'newick')
>>> print(starting_tree)
Tree(rooted=False, weight=1.0)
Clade(branch_length=0.0, name='Inner3')
Clade(branch_length=0.01421, name='Inner2')
Clade(branch_length=0.23927, name='Inner1')
Clade(branch_length=0.08531, name='Epsilon')
Clade(branch_length=0.13691, name='Delta')
Clade(branch_length=0.2923, name='Alpha')
Clade(branch_length=0.07477, name='Beta')
Clade(branch_length=0.17523, name='Gamma')
Build the Parsimony tree from the starting tree::
>>> scorer = Phylo.TreeConstruction.ParsimonyScorer()
>>> searcher = Phylo.TreeConstruction.NNITreeSearcher(scorer)
>>> constructor = Phylo.TreeConstruction.ParsimonyTreeConstructor(searcher, starting_tree)
>>> pars_tree = constructor.build_tree(aln)
>>> print(pars_tree)
Tree(rooted=True, weight=1.0)
Clade(branch_length=0.0)
Clade(branch_length=0.19732999999999998, name='Inner1')
Clade(branch_length=0.13691, name='Delta')
Clade(branch_length=0.08531, name='Epsilon')
Clade(branch_length=0.04194000000000003, name='Inner2')
Clade(branch_length=0.01421, name='Inner3')
Clade(branch_length=0.17523, name='Gamma')
Clade(branch_length=0.07477, name='Beta')
Clade(branch_length=0.2923, name='Alpha')
Same example, using the new Alignment class::
>>> from Bio import Align, Phylo
>>> alignment = Align.read(open('TreeConstruction/msa.phy'), 'phylip')
>>> print(alignment)
Alpha 0 AACGTGGCCACAT 13
Beta 0 AAGGTCGCCACAC 13
Gamma 0 CAGTTCGCCACAA 13
Delta 0 GAGATTTCCGCCT 13
Epsilon 0 GAGATCTCCGCCC 13
<BLANKLINE>
Load a starting tree::
>>> starting_tree = Phylo.read('TreeConstruction/nj.tre', 'newick')
>>> print(starting_tree)
Tree(rooted=False, weight=1.0)
Clade(branch_length=0.0, name='Inner3')
Clade(branch_length=0.01421, name='Inner2')
Clade(branch_length=0.23927, name='Inner1')
Clade(branch_length=0.08531, name='Epsilon')
Clade(branch_length=0.13691, name='Delta')
Clade(branch_length=0.2923, name='Alpha')
Clade(branch_length=0.07477, name='Beta')
Clade(branch_length=0.17523, name='Gamma')
Build the Parsimony tree from the starting tree::
>>> scorer = Phylo.TreeConstruction.ParsimonyScorer()
>>> searcher = Phylo.TreeConstruction.NNITreeSearcher(scorer)
>>> constructor = Phylo.TreeConstruction.ParsimonyTreeConstructor(searcher, starting_tree)
>>> pars_tree = constructor.build_tree(alignment)
>>> print(pars_tree)
Tree(rooted=True, weight=1.0)
Clade(branch_length=0.0)
Clade(branch_length=0.19732999999999998, name='Inner1')
Clade(branch_length=0.13691, name='Delta')
Clade(branch_length=0.08531, name='Epsilon')
Clade(branch_length=0.04194000000000003, name='Inner2')
Clade(branch_length=0.01421, name='Inner3')
Clade(branch_length=0.17523, name='Gamma')
Clade(branch_length=0.07477, name='Beta')
Clade(branch_length=0.2923, name='Alpha')
"""
def __init__(self, searcher, starting_tree=None):
"""Initialize the class."""
self.searcher = searcher
self.starting_tree = starting_tree
def build_tree(self, alignment):
"""Build the tree.
:Parameters:
alignment : MultipleSeqAlignment
multiple sequence alignment to calculate parsimony tree.
"""
# if starting_tree is none,
# create a upgma tree with 'identity' scoring matrix
if self.starting_tree is None:
dtc = DistanceTreeConstructor(DistanceCalculator("identity"), "upgma")
self.starting_tree = dtc.build_tree(alignment)
return self.searcher.search(self.starting_tree, alignment)
if __name__ == "__main__":
from Bio._utils import run_doctest
run_doctest()
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