# Source code for dendropy.calculate.treemeasure

```
#! /usr/bin/env python
# -*- coding: utf-8 -*-
##############################################################################
## DendroPy Phylogenetic Computing Library.
##
## Copyright 2010-2015 Jeet Sukumaran and Mark T. Holder.
## All rights reserved.
##
## See "LICENSE.rst" for terms and conditions of usage.
##
## If you use this work or any portion thereof in published work,
## please cite it as:
##
## Sukumaran, J. and M. T. Holder. 2010. DendroPy: a Python library
## for phylogenetic computing. Bioinformatics 26: 1569-1571.
##
##############################################################################
"""
Statistics, metrics, measurements, and values calculated on (single) trees.
"""
import math
from dendropy.calculate import phylogeneticdistance
EULERS_CONSTANT = 0.5772156649015328606065120900824024310421
## legacy: will soon be deprecated
[docs]class PatrisiticDistanceMatrix(phylogeneticdistance.PhylogeneticDistanceMatrix):
def __init__(self, tree):
phylogeneticdistance.PhylogeneticDistanceMatrix.__init__(self)
self.compile_from_tree(tree=tree)
[docs]def patristic_distance(tree, taxon1, taxon2, is_bipartitions_updated=False):
"""
Given a tree with bipartitions encoded, and two taxa on that tree, returns the
patristic distance between the two. Much more inefficient than constructing
a PhylogeneticDistanceMatrix object.
"""
mrca = tree.mrca(taxa=[taxon1, taxon2], is_bipartitions_updated=is_bipartitions_updated)
dist = 0
n = tree.find_node(lambda x: x.taxon == taxon1)
while n != mrca:
if n.edge.length is not None:
dist += n.edge.length
n = n.parent_node
n = tree.find_node(lambda x: x.taxon == taxon2)
while n != mrca:
if n.edge.length is not None:
dist += n.edge.length
n = n.parent_node
return dist
###########################################################################
### Metrics -- Unary
[docs]def B1(tree):
"""
Returns the B1 statistic: the reciprocal of the sum of the maximum
number of nodes between each interior node and tip over all internal
nodes excluding root.
"""
b1 = 0.0
nd_mi = {}
for nd in tree.postorder_node_iter():
if nd._parent_node is None:
continue
child_nodes = nd._child_nodes
if len(child_nodes) == 0:
nd_mi[nd] = 0.0
continue
mi = max(nd_mi[ch] for ch in child_nodes)
mi += 1
nd_mi[nd] = mi
b1 += 1.0/mi
return b1
[docs]def colless_tree_imbalance(tree, normalize="max"):
"""
Returns Colless' tree imbalance or I statistic: the sum of differences
of numbers of children in left and right subtrees over all internal
nodes. ``normalize`` specifies the normalization:
* "max" or True [DEFAULT]
normalized to maximum value for tree of
this size
* "yule"
normalized to the Yule model
* "pda"
normalized to the PDA (Proportional to Distinguishable
Arrangements) model
* None or False
no normalization
"""
colless = 0.0
num_leaves = 0
subtree_leaves = {}
for nd in tree.postorder_node_iter():
if nd.is_leaf():
subtree_leaves[nd] = 1
num_leaves += 1
else:
total_leaves = 0
if len(nd._child_nodes) > 2:
raise TypeError("Colless' tree imbalance statistic requires strictly bifurcating trees")
left = subtree_leaves[nd._child_nodes[0]]
right = subtree_leaves[nd._child_nodes[1]]
colless += abs(right-left)
subtree_leaves[nd] = right + left
if normalize == "yule":
colless = float(colless - (num_leaves * math.log(num_leaves)) - (num_leaves * (EULERS_CONSTANT - 1.0 - math.log(2))))/num_leaves
elif normalize == "pda":
colless = colless / pow(num_leaves, 3.0/2)
elif normalize is True or normalize == "max":
## note that Mooers 1995 (Evolution 49(2):379-384)
## remarks that the correct normalization factor is
## 2/((num_leaves - 1) * (num_leaves -2))
colless = colless * (2.0/(num_leaves * (num_leaves-3) + 2))
elif normalize is not None and normalize is not False:
raise TypeError("``normalization`` accepts only None, True, False, 'yule' or 'pda' as argument values")
return colless
[docs]def pybus_harvey_gamma(tree, prec=0.00001):
"""Returns the gamma statistic of Pybus and Harvey (2000). This statistic
is used to test for constancy of birth and death rates over the course of
a phylogeny. Under the pure-birth process, the statistic should follow
a standard Normal distibution: a Normal(mean=0, variance=1).
If the lengths of different paths to the node differ by more than ``prec``,
then a ValueError exception will be raised indicating deviation from
ultrametricty.
Raises a Value Error if the tree is not ultrametric, is non-binary, or has
only 2 leaves.
As a side effect a ``age`` attribute is added to the nodes of the tree.
Pybus and Harvey. 2000. "Testing macro-evolutionary models using incomplete
molecular phylogenies." Proc. Royal Society Series B: Biological Sciences.
(267). 2267-2272
"""
# the equation is given by:
# T = \sum_{j=2}^n (jg_j)
# C = T \sqrt{\frac{1}{12(n-2)}}
# C gamma = \frac{1}{n-2}\sum_{i=2}^{n-1} (\sum_{k=2}^i kg_k) - \frac{T}{2}
# where n is the number of taxa, and g_2 ... g_n is the vector of waiting
# times between consecutive (in time, not along a branch) speciation times.
node = None
speciation_ages = []
n = 0
if tree.seed_node.age is None:
tree.calc_node_ages(ultrametricity_precision=prec)
for node in tree.postorder_node_iter():
if len(node.child_nodes()) == 2:
speciation_ages.append(node.age)
else:
n += 1
if node is None:
raise ValueError("Empty tree encountered")
speciation_ages.sort(reverse=True)
g = []
older = speciation_ages[0]
for age in speciation_ages[1:]:
g.append(older - age)
older = age
g.append(older)
if not g:
raise ValueError("No internal nodes found (other than the root)")
assert(len(g) == (n - 1))
T = 0.0
accum = 0.0
for i in range(2, n):
list_index = i - 2
T += i * float(g[list_index])
accum += T
list_index = n - 2
T += (n) * g[list_index]
nmt = n - 2.0
numerator = accum/nmt - T/2.0
C = T*pow(1/(12*nmt), 0.5)
return numerator/C
[docs]def N_bar(tree):
"""
Returns the $\bar{N}$ statistic: the average number of nodes above a
terminal node.
"""
leaf_count = 0
nbar = 0
for leaf_node in tree.leaf_node_iter():
leaf_count += 1
for parent in leaf_node.ancestor_iter(inclusive=False):
nbar += 1
return float(nbar) / leaf_count
[docs]def sackin_index(tree, normalize=True):
"""
Returns the Sackin's index: the sum of the number of ancestors for each
tip of the tree. The larger the Sackin's index, the less balanced the
tree. ``normalize`` specifies the normalization:
* True [DEFAULT]
normalized to number of leaves; this results in a value
equivalent to that given by Tree.N_bar()
* "yule"
normalized to the Yule model
* "pda"
normalized to the PDA (Proportional to Distinguishable
Arrangements) model
* None or False
no normalization
"""
leaf_count = 0
num_anc = 0
for leaf_node in tree.leaf_node_iter():
leaf_count += 1
for parent in leaf_node.ancestor_iter(inclusive=False):
num_anc += 1
if normalize == "yule":
x = sum(1.0/j for j in range(2, leaf_count+1))
s = float(num_anc - (2 * leaf_count * x))/leaf_count
elif normalize == "pda":
s = float(num_anc)/(pow(leaf_count, 3.0/2))
elif normalize is True:
s = float(num_anc)/leaf_count
elif normalize is None or normalize is False:
s = float(num_anc)
elif normalize is not None and normalize is not False:
raise TypeError("``normalization`` accepts only None, True, False, 'yule' or 'pda' as argument values")
return s
[docs]def treeness(tree):
"""
Returns the proportion of total tree length that is taken up by
internal branches.
"""
internal = 0.0
external = 0.0
for nd in tree.postorder_node_iter():
if not nd._parent_node:
continue
if nd.is_leaf():
external += nd.edge.length
else:
internal += nd.edge.length
return internal/(external + internal)
```