def rogers_huff_r_between(gna, gnb, fill=np.nan):
"""Estimate the linkage disequilibrium parameter *r* for each pair of
variants between the two input arrays, using the method of Rogers and
Huff (2008).
Parameters
----------
gna, gnb : array_like, int8, shape (n_variants, n_samples)
Diploid genotypes at biallelic variants, coded as the number of
alternate alleles per call (i.e., 0 = hom ref, 1 = het, 2 = hom alt).
Returns
-------
r : ndarray, float, shape (m_variants, n_variants )
Matrix in rectangular form.
"""
# check inputs
gna = asarray_ndim(gna, 2, dtype='i1')
gnb = asarray_ndim(gnb, 2, dtype='i1')
# compute correlation coefficients
from allel.opt.stats import gn_pairwise2_corrcoef_int8
r = gn_pairwise2_corrcoef_int8(gna, gnb, fill)
# convenience for singletons
if r.size == 1:
r = r[0, 0]
return r
def joint_sfs(dac1, dac2):
"""Compute the joint site frequency spectrum between two populations.
Parameters
----------
dac1 : array_like, int, shape (n_variants,)
Derived allele counts for the first population.
dac2 : array_like, int, shape (n_variants,)
Derived allele counts for the second population.
Returns
-------
joint_sfs : ndarray, int, shape (m_chromosomes, n_chromosomes)
Array where the (i, j)th element is the number of variant sites with i
derived alleles in the first population and j derived alleles in the
second population.
"""
# check inputs
dac1 = asarray_ndim(dac1, 1)
dac2 = asarray_ndim(dac2, 1)
# compute site frequency spectrum
n = np.max(dac1) + 1
m = np.max(dac2) + 1
s = np.bincount(dac1 * m + dac2)
s.resize((n, m))
return s
def joint_sfs_folded(ac1, ac2):
"""Compute the joint folded site frequency spectrum between two
populations.
Parameters
----------
ac1 : array_like, int, shape (n_variants, 2)
Allele counts for the first population.
ac2 : array_like, int, shape (n_variants, 2)
Allele counts for the second population.
Returns
-------
joint_sfs_folded : ndarray, int, shape (m_chromosomes//2, n_chromosomes//2)
Array where the (i, j)th element is the number of variant sites with a
minor allele count of i in the first population and j in the second
population.
"""
# check inputs
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
assert ac1.shape[1] == ac2.shape[1] == 2, "only biallelic variants are supported"
# compute minor allele counts
mac1 = np.amin(ac1, axis=1)
mac2 = np.amin(ac2, axis=1)
# compute site frequency spectrum
m = np.max(mac1) + 1
n = np.max(mac2) + 1
s = np.bincount(mac1 * n + mac2)
s.resize((m, n))
return s
def plot_joint_sfs(s, ax=None, imshow_kwargs=None):
import matplotlib.pyplot as plt
import matplotlib as mpl
# check inputs
s = asarray_ndim(s, 2)
# setup axes
if ax is None:
w = plt.rcParams['figure.figsize'][0]
fig, ax = plt.subplots(figsize=(w, w))
# set plotting defaults
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('cmap', 'jet')
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('aspect', 'auto')
imshow_kwargs.setdefault('norm', mpl.colors.LogNorm())
# plot data
ax.imshow(s, **imshow_kwargs)
# tidy
ax.xaxis.tick_top()
ax.set_ylabel('derived allele count (population 1)')
ax.set_xlabel('derived allele count (population 2)')
ax.xaxis.set_label_position('top')
return ax
def plot_joint_sfs(s, ax=None, imshow_kwargs=None):
import matplotlib.pyplot as plt
import matplotlib as mpl
# check inputs
s = asarray_ndim(s, 2)
# setup axes
if ax is None:
w = plt.rcParams["figure.figsize"][0]
fig, ax = plt.subplots(figsize=(w, w))
# set plotting defaults
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault("cmap", "jet")
imshow_kwargs.setdefault("interpolation", "none")
imshow_kwargs.setdefault("aspect", "auto")
imshow_kwargs.setdefault("norm", mpl.colors.LogNorm())
# plot data
ax.imshow(s, **imshow_kwargs)
# tidy
ax.xaxis.tick_top()
ax.set_ylabel("derived allele count (population 1)")
ax.set_xlabel("derived allele count (population 2)")
ax.xaxis.set_label_position("top")
return ax
def sfs_folded(ac):
"""Compute the folded site frequency spectrum given reference and
alternate allele counts at a set of biallelic variants.
Parameters
----------
ac : array_like, int, shape (n_variants, 2)
Allele counts array.
Returns
-------
sfs_folded : ndarray, int, shape (n_chromosomes//2,)
Array where the kth element is the number of variant sites with a
minor allele count of k.
"""
# check input
ac = asarray_ndim(ac, 2)
assert ac.shape[1] == 2, 'only biallelic variants are supported'
# compute minor allele counts
mac = np.amin(ac, axis=1)
# compute folded site frequency spectrum
s = np.bincount(mac)
return s
def h_hat(ac):
"""Unbiased estimator for h, where 2*h is the heterozygosity
of the population.
Parameters
----------
ac : array_like, int, shape (n_variants, 2)
Allele counts array for a single population.
Returns
-------
h_hat : ndarray, float, shape (n_variants,)
Notes
-----
Used in Patterson (2012) for calculation of various statistics.
"""
# check inputs
ac = asarray_ndim(ac, 2)
assert ac.shape[1] == 2, 'only biallelic variants supported'
# compute allele number
an = ac.sum(axis=1)
# compute estimator
x = (ac[:, 0] * ac[:, 1]) / (an * (an - 1))
return x
def fold_sfs(s, n):
"""Fold a site frequency spectrum.
Parameters
----------
s : array_like, int, shape (n_chromosomes,)
Site frequency spectrum
n : int
Total number of chromosomes called.
Returns
-------
sfs_folded : ndarray, int
Folded site frequency spectrum
"""
# check inputs
s = asarray_ndim(s, 1)
assert s.shape[0] <= n + 1, 'invalid number of chromosomes'
# need to check s has all entries up to n
if s.shape[0] < n + 1:
sn = np.zeros(n + 1, dtype=s.dtype)
sn[:s.shape[0]] = s
s = sn
# fold
nf = (n + 1) // 2
n = nf * 2
o = s[:nf] + s[nf:n][::-1]
return o
def fit(self, gn):
# check input
gn = asarray_ndim(gn, 2)
# find mean
self.mean_ = np.mean(gn, axis=1, keepdims=True)
return self
def rogers_huff_r(gn, fill=np.nan):
"""Estimate the linkage disequilibrium parameter *r* for each pair of
variants using the method of Rogers and Huff (2008).
Parameters
----------
gn : array_like, int8, shape (n_variants, n_samples)
Diploid genotypes at biallelic variants, coded as the number of
alternate alleles per call (i.e., 0 = hom ref, 1 = het, 2 = hom alt).
Returns
-------
r : ndarray, float, shape (n_variants * (n_variants - 1) // 2,)
Matrix in condensed form.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [1, 1], [0, 0]],
... [[0, 0], [1, 1], [0, 0]],
... [[1, 1], [0, 0], [1, 1]],
... [[0, 0], [0, 1], [-1, -1]]], dtype='i1')
>>> gn = g.to_n_alt(fill=-1)
>>> gn
array([[ 0, 2, 0],
[ 0, 2, 0],
[ 2, 0, 2],
[ 0, 1, -1]], dtype=int8)
>>> r = allel.stats.rogers_huff_r(gn)
>>> r
array([ 1. , -1.00000012, 1. , -1.00000012, 1. , -1. ], dtype=float32)
>>> r ** 2
array([ 1. , 1.00000024, 1. , 1.00000024, 1. , 1. ], dtype=float32)
>>> from scipy.spatial.distance import squareform
>>> squareform(r ** 2)
array([[ 0. , 1. , 1.00000024, 1. ],
[ 1. , 0. , 1.00000024, 1. ],
[ 1.00000024, 1.00000024, 0. , 1. ],
[ 1. , 1. , 1. , 0. ]])
""" # flake8: noqa
# check inputs
gn = asarray_ndim(gn, 2, dtype='i1')
# compute correlation coefficients
from allel.opt.stats import gn_pairwise_corrcoef_int8
r = gn_pairwise_corrcoef_int8(gn, fill)
# convenience for singletons
if r.size == 1:
r = r[0]
return r
def plot_sfs(s, yscale='log', bins=None, n=None,
clip_endpoints=True, label=None, plot_kwargs=None,
ax=None):
import matplotlib.pyplot as plt
import scipy
# check inputs
s = asarray_ndim(s, 1)
# setup axes
if ax is None:
fig, ax = plt.subplots()
# setup data
if bins is None:
if clip_endpoints:
x = np.arange(1, s.shape[0]-1)
y = s[1:-1]
else:
x = np.arange(s.shape[0])
y = s
else:
if clip_endpoints:
y, b, _ = scipy.stats.binned_statistic(
np.arange(1, s.shape[0]-1),
values=s[1:-1],
bins=bins,
statistic='sum')
else:
y, b, _ = scipy.stats.binned_statistic(
np.arange(s.shape[0]),
values=s,
bins=bins,
statistic='sum')
# use bin midpoints for plotting
x = (b[:-1] + b[1:]) / 2
if n:
# convert allele counts to allele frequencies
x = x / n
ax.set_xlabel('derived allele frequency')
else:
ax.set_xlabel('derived allele count')
# do plotting
if plot_kwargs is None:
plot_kwargs = dict()
ax.plot(x, y, label=label, **plot_kwargs)
# tidy
ax.set_yscale(yscale)
ax.set_ylabel('site frequency')
ax.autoscale(axis='x', tight=True)
return ax
def fit(self, gn):
# check input
gn = asarray_ndim(gn, 2)
# find mean
self.mean_ = np.mean(gn, axis=1, keepdims=True)
# find scaling factor
self.std_ = np.std(gn, axis=1, keepdims=True)
return self
def transform(self, gn, copy=None):
# check inputs
copy = copy if copy is not None else self.copy
gn = asarray_ndim(gn, 2, copy=copy)
if not gn.dtype.kind == 'f':
gn = gn.astype('f2')
# center
gn -= self.mean_
return gn
def fit(self, gn):
# check input
gn = asarray_ndim(gn, 2)
# find mean
self.mean_ = np.mean(gn, axis=1, keepdims=True)
# find scaling factor
p = self.mean_ / self.ploidy
self.std_ = np.sqrt(p * (1 - p))
return self
def pairwise_dxy(pos, gac, start=None, stop=None, is_accessible=None):
"""Convenience function to calculate a pairwise distance matrix using
nucleotide divergence (a.k.a. Dxy) as the distance metric.
Parameters
----------
pos : array_like, int, shape (n_variants,)
Variant positions.
gac : array_like, int, shape (n_variants, n_samples, n_alleles)
Per-genotype allele counts.
start : int, optional
Start position of region to use.
stop : int, optional
Stop position of region to use.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
dist : ndarray
Distance matrix in condensed form.
See Also
--------
allel.model.ndarray.GenotypeArray.to_allele_counts
"""
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
gac = asarray_ndim(gac, 3)
# compute this once here, to avoid repeated evaluation within the loop
gan = np.sum(gac, axis=2)
m = gac.shape[1]
dist = list()
for i, j in itertools.combinations(range(m), 2):
ac1 = gac[:, i, ...]
an1 = gan[:, i]
ac2 = gac[:, j, ...]
an2 = gan[:, j]
d = sequence_divergence(pos,
ac1,
ac2,
an1=an1,
an2=an2,
start=start,
stop=stop,
is_accessible=is_accessible)
dist.append(d)
return np.array(dist)
def fold_joint_sfs(s, m, n):
"""Fold a joint site frequency spectrum.
Parameters
----------
s : array_like, int, shape (m_chromosomes, n_chromosomes)
Joint site frequency spectrum.
m : int
Number of chromosomes called in the first population.
n : int
Number of chromosomes called in the second population.
Returns
-------
joint_sfs_folded : ndarray, int
Folded joint site frequency spectrum.
"""
# check inputs
s = asarray_ndim(s, 2)
assert s.shape[0] <= m + 1, "invalid number of chromosomes"
assert s.shape[1] <= n + 1, "invalid number of chromosomes"
# need to check s has all entries up to m
if s.shape[0] < m + 1:
sm = np.zeros((m + 1, s.shape[1]), dtype=s.dtype)
sm[: s.shape[0]] = s
s = sm
# need to check s has all entries up to n
if s.shape[1] < n + 1:
sn = np.zeros((s.shape[0], n + 1), dtype=s.dtype)
sn[:, : s.shape[1]] = s
s = sn
# fold
mf = (m + 1) // 2
nf = (n + 1) // 2
m = mf * 2
n = nf * 2
o = (
s[:mf, :nf]
+ s[mf:m, :nf][::-1] # top left
+ s[:mf, nf:n][:, ::-1] # top right
+ s[mf:m, nf:n][::-1, ::-1] # bottom left
) # bottom right
return o
def joint_sfs_folded(ac1, ac2):
"""Compute the joint folded site frequency spectrum between two
populations.
Parameters
----------
ac1 : array_like, int, shape (n_variants, 2)
Allele counts for the first population.
ac2 : array_like, int, shape (n_variants, 2)
Allele counts for the second population.
Returns
-------
joint_sfs_folded : ndarray, int, shape (m_chromosomes//2, n_chromosomes//2)
Array where the (i, j)th element is the number of variant sites with a
minor allele count of i in the first population and j in the second
population.
"""
# check inputs
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
assert ac1.shape[1] == ac2.shape[1] == 2, \
'only biallelic variants are supported'
# compute minor allele counts
mac1 = np.amin(ac1, axis=1)
mac2 = np.amin(ac2, axis=1)
# compute site frequency spectrum
m = np.max(mac1) + 1
n = np.max(mac2) + 1
s = np.bincount(mac1 * n + mac2)
s.resize((m, n))
return s
def transform(self, gn, copy=None):
# check inputs
copy = copy if copy is not None else self.copy
gn = asarray_ndim(gn, 2, copy=copy)
if not gn.dtype.kind == 'f':
gn = gn.astype('f2')
# center
gn -= self.mean_
# scale
gn /= self.std_
return gn
def maxFDA(pos, ac, start=None, stop=None, is_accessible=None):
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac = asarray_ndim(ac, 2)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate values of the stat
dafs = []
for i in range(len(ac)):
p1 = ac[i, 1]
n = p1+ac[i, 0]
dafs.append(p1/float(n))
return max(dafs)
def fold_joint_sfs(s, m, n):
"""Fold a joint site frequency spectrum.
Parameters
----------
s : array_like, int, shape (m_chromosomes, n_chromosomes)
Joint site frequency spectrum.
m : int
Number of chromosomes called in the first population.
n : int
Number of chromosomes called in the second population.
Returns
-------
joint_sfs_folded : ndarray, int
Folded joint site frequency spectrum.
"""
# check inputs
s = asarray_ndim(s, 2)
assert s.shape[0] <= m + 1, 'invalid number of chromosomes'
assert s.shape[1] <= n + 1, 'invalid number of chromosomes'
# need to check s has all entries up to m
if s.shape[0] < m + 1:
sm = np.zeros((m + 1, s.shape[1]), dtype=s.dtype)
sm[:s.shape[0]] = s
s = sm
# need to check s has all entries up to n
if s.shape[1] < n + 1:
sn = np.zeros((s.shape[0], n + 1), dtype=s.dtype)
sn[:, :s.shape[1]] = s
s = sn
# fold
mf = (m + 1) // 2
nf = (n + 1) // 2
m = mf * 2
n = nf * 2
o = (
s[:mf, :nf] + # top left
s[mf:m, :nf][::-1] + # top right
s[:mf, nf:n][:, ::-1] + # bottom left
s[mf:m, nf:n][::-1, ::-1]) # bottom right
return o
def plot_joint_sfs(s, ax=None, imshow_kwargs=None):
"""Plot a joint site frequency spectrum.
Parameters
----------
s : array_like, int, shape (n_chromosomes_pop1, n_chromosomes_pop2)
Joint site frequency spectrum.
ax : axes, optional
Axes on which to draw. If not provided, a new figure will be created.
imshow_kwargs : dict-like
Additional keyword arguments, passed through to ax.imshow().
Returns
-------
ax : axes
The axes on which the plot was drawn.
"""
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
# check inputs
s = asarray_ndim(s, 2)
# setup axes
if ax is None:
w = plt.rcParams['figure.figsize'][0]
fig, ax = plt.subplots(figsize=(w, w))
# set plotting defaults
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('cmap', 'jet')
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('aspect', 'auto')
imshow_kwargs.setdefault('norm', LogNorm())
# plot data
ax.imshow(s.T, **imshow_kwargs)
# tidy
ax.invert_yaxis()
ax.set_xlabel('derived allele count (population 1)')
ax.set_ylabel('derived allele count (population 2)')
return ax
def plot_joint_sfs(s, ax=None, imshow_kwargs=None):
"""Plot a joint site frequency spectrum.
Parameters
----------
s : array_like, int, shape (n_chromosomes_pop1, n_chromosomes_pop2)
Joint site frequency spectrum.
ax : axes, optional
Axes on which to draw. If not provided, a new figure will be created.
imshow_kwargs : dict-like
Additional keyword arguments, passed through to ax.imshow().
Returns
-------
ax : axes
The axes on which the plot was drawn.
"""
import matplotlib.pyplot as plt
from matplotlib.colors import LogNorm
# check inputs
s = asarray_ndim(s, 2)
# setup axes
if ax is None:
w = plt.rcParams['figure.figsize'][0]
fig, ax = plt.subplots(figsize=(w, w))
# set plotting defaults
if imshow_kwargs is None:
imshow_kwargs = dict()
imshow_kwargs.setdefault('cmap', 'jet')
imshow_kwargs.setdefault('interpolation', 'none')
imshow_kwargs.setdefault('aspect', 'auto')
imshow_kwargs.setdefault('norm', LogNorm())
# plot data
ax.imshow(s.T, **imshow_kwargs)
# tidy
ax.invert_yaxis()
ax.set_xlabel('derived allele count (population 1)')
ax.set_ylabel('derived allele count (population 2)')
return ax
def pairwise_dxy(pos, gac, start=None, stop=None, is_accessible=None):
"""Convenience function to calculate a pairwise distance matrix using
nucleotide divergence (a.k.a. Dxy) as the distance metric.
Parameters
----------
pos : array_like, int, shape (n_variants,)
Variant positions.
gac : array_like, int, shape (n_variants, n_samples, n_alleles)
Per-genotype allele counts.
start : int, optional
Start position of region to use.
stop : int, optional
Stop position of region to use.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
dist : ndarray
Distance matrix in condensed form.
See Also
--------
allel.model.ndarray.GenotypeArray.to_allele_counts
"""
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
gac = asarray_ndim(gac, 3)
# compute this once here, to avoid repeated evaluation within the loop
gan = np.sum(gac, axis=2)
m = gac.shape[1]
dist = list()
for i, j in itertools.combinations(range(m), 2):
ac1 = gac[:, i, ...]
an1 = gan[:, i]
ac2 = gac[:, j, ...]
an2 = gan[:, j]
d = sequence_divergence(pos, ac1, ac2, an1=an1, an2=an2,
start=start, stop=stop,
is_accessible=is_accessible)
dist.append(d)
return np.array(dist)
def heterozygosity_expected(af, ploidy, fill=np.nan):
"""Calculate the expected rate of heterozygosity for each variant
under Hardy-Weinberg equilibrium.
Parameters
----------
af : array_like, float, shape (n_variants, n_alleles)
Allele frequencies array.
ploidy : int
Sample ploidy.
fill : float, optional
Use this value for variants where allele frequencies do not sum to 1.
Returns
-------
he : ndarray, float, shape (n_variants,)
Expected heterozygosity
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0], [0, 0]],
... [[0, 0], [0, 1], [1, 1]],
... [[0, 0], [1, 1], [2, 2]],
... [[1, 1], [1, 2], [-1, -1]]])
>>> af = g.count_alleles().to_frequencies()
>>> allel.stats.heterozygosity_expected(af, ploidy=2)
array([ 0. , 0.5 , 0.66666667, 0.375 ])
"""
# check inputs
af = asarray_ndim(af, 2)
# calculate expected heterozygosity
out = 1 - np.sum(np.power(af, ploidy), axis=1)
# fill values where allele frequencies could not be calculated
af_sum = np.sum(af, axis=1)
with ignore_invalid():
out[(af_sum < 1) | np.isnan(af_sum)] = fill
return out
def fold_joint_sfs(s, n1, n2):
"""Fold a joint site frequency spectrum.
Parameters
----------
s : array_like, int, shape (m_chromosomes, n_chromosomes)
Joint site frequency spectrum.
n1, n2 : int, optional
The total number of chromosomes called in each population.
Returns
-------
joint_sfs_folded : ndarray, int
Folded joint site frequency spectrum.
"""
# check inputs
s = asarray_ndim(s, 2)
assert s.shape[0] <= n1 + 1, 'invalid number of chromosomes'
assert s.shape[1] <= n2 + 1, 'invalid number of chromosomes'
# need to check s has all entries up to m
if s.shape[0] < n1 + 1:
sm = np.zeros((n1 + 1, s.shape[1]), dtype=s.dtype)
sm[:s.shape[0]] = s
s = sm
# need to check s has all entries up to n
if s.shape[1] < n2 + 1:
sn = np.zeros((s.shape[0], n2 + 1), dtype=s.dtype)
sn[:, :s.shape[1]] = s
s = sn
# fold
mf = (n1 + 1) // 2
nf = (n2 + 1) // 2
n1 = mf * 2
n2 = nf * 2
o = (
s[:mf, :nf] + # top left
s[mf:n1, :nf][::-1] + # top right
s[:mf, nf:n2][:, ::-1] + # bottom left
s[mf:n1, nf:n2][::-1, ::-1]) # bottom right
return o
def heterozygosity_expected(af, ploidy, fill=np.nan):
"""Calculate the expected rate of heterozygosity for each variant
under Hardy-Weinberg equilibrium.
Parameters
----------
af : array_like, float, shape (n_variants, n_alleles)
Allele frequencies array.
fill : float, optional
Use this value for variants where allele frequencies do not sum to 1.
Returns
-------
he : ndarray, float, shape (n_variants,)
Expected heterozygosity
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0], [0, 0]],
... [[0, 0], [0, 1], [1, 1]],
... [[0, 0], [1, 1], [2, 2]],
... [[1, 1], [1, 2], [-1, -1]]])
>>> af = g.count_alleles().to_frequencies()
>>> allel.stats.heterozygosity_expected(af, ploidy=2)
array([ 0. , 0.5 , 0.66666667, 0.375 ])
"""
# check inputs
af = asarray_ndim(af, 2)
# calculate expected heterozygosity
out = 1 - np.sum(np.power(af, ploidy), axis=1)
# fill values where allele frequencies could not be calculated
af_sum = np.sum(af, axis=1)
with ignore_invalid():
out[(af_sum < 1) | np.isnan(af_sum)] = fill
return out
def count_alleles(self, max_allele=None, subpop=None):
# if max_allele not specified, count all alleles
if max_allele is None:
max_allele = self.max().compute()[()]
# deal with subpop
subpop = asarray_ndim(subpop, 1, allow_none=True, dtype=np.int64)
if subpop is not None:
gd = self.take(subpop, axis=1).values
else:
gd = self.values
# determine output chunks - preserve axis0; change axis1, axis2
chunks = (gd.chunks[0], (1, ) * len(gd.chunks[1]), (max_allele + 1, ))
if self.mask is None:
# simple case, no mask
def f(block):
gb = GenotypeArray(block)
return gb.count_alleles(max_allele=max_allele)[:, None, :]
# map blocks and reduce
out = da.map_blocks(f, gd, chunks=chunks).sum(axis=1, dtype='i4')
else:
# map with mask
def f(block, bmask):
g = GenotypeArray(block)
g.mask = bmask[:, :, 0]
return g.count_alleles(max_allele=max_allele)[:, None, :]
md = self.mask[:, :, None]
out = da.map_blocks(f, gd, md, chunks=chunks).sum(axis=1,
dtype='i4')
return AlleleCountsDaskArray(out)
def sfs(dac):
"""Compute the site frequency spectrum given derived allele counts at
a set of biallelic variants.
Parameters
----------
dac : array_like, int, shape (n_variants,)
Array of derived allele counts.
Returns
-------
sfs : ndarray, int, shape (n_chromosomes,)
Array where the kth element is the number of variant sites with k
derived alleles.
"""
# check input
dac = asarray_ndim(dac, 1)
# compute site frequency spectrum
s = np.bincount(dac)
return s
def sfs(dac):
"""Compute the site frequency spectrum given derived allele counts at
a set of biallelic variants.
Parameters
----------
dac : array_like, int, shape (n_variants,)
Array of derived allele counts.
Returns
-------
sfs : ndarray, int, shape (n_chromosomes,)
Array where the kth element is the number of variant sites with k
derived alleles.
"""
# check input
dac = asarray_ndim(dac, 1)
# compute site frequency spectrum
s = np.bincount(dac)
return s
def windowed_df(pos,
ac1,
ac2,
size=None,
start=None,
stop=None,
step=None,
windows=None,
is_accessible=None,
fill=np.nan):
"""Calculate the density of fixed differences between two populations in
windows over a single chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
df : ndarray, float, shape (n_windows,)
Per-base density of fixed differences in each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
See Also
--------
allel.model.locate_fixed_differences
"""
# check inputs
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# locate fixed differences
loc_df = locate_fixed_differences(ac1, ac2)
# count number of fixed differences in windows
n_df, windows, counts = windowed_statistic(pos,
values=loc_df,
statistic=np.count_nonzero,
size=size,
start=start,
stop=stop,
step=step,
windows=windows,
fill=0)
# calculate value per base
df, n_bases = per_base(n_df,
windows,
is_accessible=is_accessible,
fill=fill)
return df, windows, n_bases, counts
def hudson_fst(ac1, ac2, fill=np.nan):
"""Calculate the numerator and denominator for Fst estimation using the
method of Hudson (1992) elaborated by Bhatia et al. (2013).
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
fill : float
Use this value where there are no pairs to compare (e.g.,
all allele calls are missing).
Returns
-------
num : ndarray, float, shape (n_variants,)
Divergence between the two populations minus average
of diversity within each population.
den : ndarray, float, shape (n_variants,)
Divergence between the two populations.
Examples
--------
Calculate numerator and denominator for Fst estimation::
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0], [1, 1], [1, 1]],
... [[0, 1], [0, 1], [0, 1], [0, 1]],
... [[0, 0], [0, 0], [0, 0], [0, 0]],
... [[0, 1], [1, 2], [1, 1], [2, 2]],
... [[0, 0], [1, 1], [0, 1], [-1, -1]]])
>>> subpops = [[0, 1], [2, 3]]
>>> ac1 = g.count_alleles(subpop=subpops[0])
>>> ac2 = g.count_alleles(subpop=subpops[1])
>>> num, den = allel.hudson_fst(ac1, ac2)
>>> num
array([ 1. , -0.16666667, 0. , -0.125 , -0.33333333])
>>> den
array([1. , 0.5 , 0. , 0.625, 0.5 ])
Estimate Fst for each variant individually::
>>> fst = num / den
>>> fst
array([ 1. , -0.33333333, nan, -0.2 , -0.66666667])
Estimate Fst averaging over variants::
>>> fst = np.sum(num) / np.sum(den)
>>> fst
0.1428571428571429
""" # flake8: noqa
# check inputs
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
check_dim0_aligned(ac1, ac2)
ac1, ac2 = ensure_dim1_aligned(ac1, ac2)
# calculate these once only
an1 = np.sum(ac1, axis=1)
an2 = np.sum(ac2, axis=1)
# calculate average diversity (a.k.a. heterozygosity) within each
# population
within = (mean_pairwise_difference(ac1, an1, fill=fill) +
mean_pairwise_difference(ac2, an2, fill=fill)) / 2
# calculate divergence (a.k.a. heterozygosity) between each population
between = mean_pairwise_difference_between(ac1, ac2, an1, an2, fill=fill)
# define numerator and denominator for Fst calculations
num = between - within
den = between
return num, den
def windowed_watterson_theta(pos,
ac,
size=None,
start=None,
stop=None,
step=None,
windows=None,
is_accessible=None,
fill=np.nan):
"""Calculate the value of Watterson's estimator in windows over a single
chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
theta_hat_w : ndarray, float, shape (n_windows,)
Watterson's estimator (theta hat per base).
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w, windows, n_bases, counts = allel.windowed_watterson_theta(
... pos, ac, size=10, start=1, stop=31
... )
>>> theta_hat_w
array([0.10909091, 0.16363636, 0.04958678])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 31]])
>>> n_bases
array([10, 10, 11])
>>> counts
array([3, 4, 2])
""" # flake8: noqa
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# locate segregating variants
is_seg = ac.is_segregating()
# count segregating variants in windows
S, windows, counts = windowed_statistic(pos,
is_seg,
statistic=np.count_nonzero,
size=size,
start=start,
stop=stop,
step=step,
windows=windows,
fill=0)
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# absolute value of Watterson's theta
theta_hat_w_abs = S / a1
# theta per base
theta_hat_w, n_bases = per_base(theta_hat_w_abs,
windows=windows,
is_accessible=is_accessible,
fill=fill)
return theta_hat_w, windows, n_bases, counts
def watterson_theta(pos, ac, start=None, stop=None, is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, 'count_segregating'):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
def xpnsl(h1, h2, use_threads=True):
"""Cross-population version of the NSL statistic.
Parameters
----------
h1 : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array for the first population.
h2 : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array for the second population.
use_threads : bool, optional
If True use multiple threads to compute.
Returns
-------
score : ndarray, float, shape (n_variants,)
Unstandardized XPNSL scores.
"""
# check inputs
h1 = asarray_ndim(h1, 2)
check_integer_dtype(h1)
h2 = asarray_ndim(h2, 2)
check_integer_dtype(h2)
check_dim0_aligned(h1, h2)
if use_threads and multiprocessing.cpu_count() > 1:
# use multiple threads
# setup threadpool
pool = ThreadPool(min(4, multiprocessing.cpu_count()))
# scan forward
res1_fwd = pool.apply_async(nsl_scan, args=(h1, ))
res2_fwd = pool.apply_async(nsl_scan, args=(h2, ))
# scan backward
res1_rev = pool.apply_async(nsl_scan, args=(h1[::-1], ))
res2_rev = pool.apply_async(nsl_scan, args=(h2[::-1], ))
# wait for both to finish
pool.close()
pool.join()
# obtain results
nsl1_fwd = res1_fwd.get()
nsl2_fwd = res2_fwd.get()
nsl1_rev = res1_rev.get()
nsl2_rev = res2_rev.get()
# cleanup
pool.terminate()
else:
# compute without threads
# scan forward
nsl1_fwd = nsl_scan(h1)
nsl2_fwd = nsl_scan(h2)
# scan backward
nsl1_rev = nsl_scan(h1[::-1])
nsl2_rev = nsl_scan(h2[::-1])
# handle reverse scans
nsl1_rev = nsl1_rev[::-1]
nsl2_rev = nsl2_rev[::-1]
# compute unstandardized score
nsl1 = nsl1_fwd + nsl1_rev
nsl2 = nsl2_fwd + nsl2_rev
score = np.log(nsl1 / nsl2)
return score
def tabulate_state_blocks(x, states, pos=None):
"""Construct a dataframe where each row provides information about continuous state blocks.
Parameters
----------
x : array_like, int
1-dimensional array of state values.
states : set
Set of states of interest. Any state value not in this set will be ignored.
pos : array_like, int, optional
Array of positions corresponding to values in `x`.
Returns
-------
df : DataFrame
Examples
--------
>>> import allel
>>> x = [1, 1, 0, 1, 1, 2, 2, 0, 2, 1, 1]
>>> df = allel.tabulate_state_blocks(x, states={1, 2})
>>> df
state support start_lidx ... size_min size_max is_marginal
0 1 4 -1 ... 5 -1 True
1 2 3 4 ... 4 4 False
2 1 2 8 ... 2 -1 True
[3 rows x 9 columns]
>>> pos = [2, 4, 7, 8, 10, 14, 19, 23, 28, 30, 31]
>>> df = allel.tabulate_state_blocks(x, states={1, 2}, pos=pos)
>>> df
state support start_lidx ... stop_rpos length_min length_max
0 1 4 -1 ... 14 9 -1
1 2 3 4 ... 30 15 19
2 1 2 8 ... -1 2 -1
[3 rows x 15 columns]
"""
# check inputs
x = asarray_ndim(x, 1)
check_integer_dtype(x)
x = memoryview_safe(x)
# find state transitions
switch_points, transitions, observations = state_transitions(x, states)
# setup some helpers
t = transitions[1:, 0]
o = observations[1:]
s1 = switch_points[:-1]
s2 = switch_points[1:]
is_marginal = (s1[:, 0] < 0) | (s2[:, 1] < 0)
size_min = s2[:, 0] - s1[:, 1] + 1
size_max = s2[:, 1] - s1[:, 0] - 1
size_max[is_marginal] = -1
# start to build a dataframe
items = [
('state', t),
('support', o),
('start_lidx', s1[:, 0]),
('start_ridx', s1[:, 1]),
('stop_lidx', s2[:, 0]),
('stop_ridx', s2[:, 1]),
('size_min', size_min),
('size_max', size_max),
('is_marginal', is_marginal)
]
# deal with optional positions
if pos is not None:
pos = asarray_ndim(pos, 1)
check_dim0_aligned(x, pos)
check_integer_dtype(pos)
# obtain switch positions
switch_positions = np.take(pos, switch_points)
# deal with boundary transitions
switch_positions[0, 0] = -1
switch_positions[-1, 1] = -1
# setup helpers
p1 = switch_positions[:-1]
p2 = switch_positions[1:]
length_min = p2[:, 0] - p1[:, 1] + 1
length_max = p2[:, 1] - p1[:, 0] - 1
length_max[is_marginal] = -1
items += [
('start_lpos', p1[:, 0]),
('start_rpos', p1[:, 1]),
('stop_lpos', p2[:, 0]),
('stop_rpos', p2[:, 1]),
('length_min', length_min),
('length_max', length_max),
]
import pandas
return pandas.DataFrame.from_dict(OrderedDict(items))
def windowed_statistic(pos, values, statistic, size=None, start=None,
stop=None, step=None, windows=None, fill=np.nan):
"""Calculate a statistic from items in windows over a single
chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
The item positions in ascending order, using 1-based coordinates..
values : array_like, int, shape (n_items,)
The values to summarise. May also be a tuple of values arrays,
in which case each array will be sliced and passed through to the
statistic function as separate arguments.
statistic : function
The statistic to compute.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
fill : object, optional
The value to use where a window is empty, i.e., contains no items.
Returns
-------
out : ndarray, shape (n_windows,)
The value of the statistic for each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
counts : ndarray, int, shape (n_windows,)
The number of items in each window.
Notes
-----
The window stop positions are included within a window.
The final window will be truncated to the specified stop position,
and so may be smaller than the other windows.
Examples
--------
Count non-zero (i.e., True) items in non-overlapping windows::
>>> import allel
>>> pos = [1, 7, 12, 15, 28]
>>> values = [True, False, True, False, False]
>>> nnz, windows, counts = allel.stats.windowed_statistic(
... pos, values, statistic=np.count_nonzero, size=10
... )
>>> nnz
array([1, 1, 0])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 28]])
>>> counts
array([2, 2, 1])
Compute a sum over items in half-overlapping windows::
>>> values = [3, 4, 2, 6, 9]
>>> x, windows, counts = allel.stats.windowed_statistic(
... pos, values, statistic=np.sum, size=10, step=5, fill=0
... )
>>> x
array([ 7, 12, 8, 0, 9])
>>> windows
array([[ 1, 10],
[ 6, 15],
[11, 20],
[16, 25],
[21, 28]])
>>> counts
array([2, 3, 2, 0, 1])
"""
# assume sorted positions
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
# check lengths are equal
if isinstance(values, tuple):
# assume multiple values arrays
check_equal_length(pos, *values)
else:
# assume a single values array
check_equal_length(pos, values)
# setup windows
if windows is None:
windows = position_windows(pos, size, start, stop, step)
else:
windows = asarray_ndim(windows, 2)
# find window locations
locs = window_locations(pos, windows)
# setup outputs
out = []
counts = []
# iterate over windows
for start_idx, stop_idx in locs:
# calculate number of values in window
n = stop_idx - start_idx
if n == 0:
# window is empty
s = fill
else:
if isinstance(values, tuple):
# assume multiple values arrays
wv = [v[start_idx:stop_idx] for v in values]
s = statistic(*wv)
else:
# assume a single values array
wv = values[start_idx:stop_idx]
s = statistic(wv)
# store outputs
out.append(s)
counts.append(n)
# convert to arrays for output
return np.asarray(out), windows, np.asarray(counts)
def mean_pairwise_difference(ac, an=None, fill=np.nan):
"""Calculate for each variant the mean number of pairwise differences
between chromosomes sampled from within a single population.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
an : array_like, int, shape (n_variants,), optional
Allele numbers. If not provided, will be calculated from `ac`.
fill : float
Use this value where there are no pairs to compare (e.g.,
all allele calls are missing).
Returns
-------
mpd : ndarray, float, shape (n_variants,)
Notes
-----
The values returned by this function can be summed over a genome
region and divided by the number of accessible bases to estimate
nucleotide diversity, a.k.a. *pi*.
Examples
--------
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1]])
>>> ac = h.count_alleles()
>>> allel.mean_pairwise_difference(ac)
array([0. , 0.5 , 0.66666667, 0.5 , 0. ,
0.83333333, 0.83333333, 1. ])
See Also
--------
sequence_diversity, windowed_diversity
"""
# This function calculates the mean number of pairwise differences
# between haplotypes within a single population, generalising to any number
# of alleles.
# check inputs
ac = asarray_ndim(ac, 2)
# total number of haplotypes
if an is None:
an = np.sum(ac, axis=1)
else:
an = asarray_ndim(an, 1)
check_dim0_aligned(ac, an)
# total number of pairwise comparisons for each variant:
# (an choose 2)
n_pairs = an * (an - 1) / 2
# number of pairwise comparisons where there is no difference:
# sum of (ac choose 2) for each allele (i.e., number of ways to
# choose the same allele twice)
n_same = np.sum(ac * (ac - 1) / 2, axis=1)
# number of pairwise differences
n_diff = n_pairs - n_same
# mean number of pairwise differences, accounting for cases where
# there are no pairs
with ignore_invalid():
mpd = np.where(n_pairs > 0, n_diff / n_pairs, fill)
return mpd
def roh_mhmm(gv,
pos,
phet_roh=0.001,
phet_nonroh=(0.0025, 0.01),
transition=1e-6,
min_roh=0,
is_accessible=None,
contig_size=None):
"""Call ROH (runs of homozygosity) in a single individual given a genotype vector.
This function computes the likely ROH using a Multinomial HMM model. There are 3
observable states at each position in a chromosome/contig: 0 = Hom, 1 = Het,
2 = inaccessible (i.e., unobserved).
The model is provided with a probability of observing a het in a ROH (`phet_roh`) and one
or more probabilities of observing a het in a non-ROH, as this probability may not be
constant across the genome (`phet_nonroh`).
Parameters
----------
gv : array_like, int, shape (n_variants, ploidy)
Genotype vector.
pos: array_like, int, shape (n_variants,)
Positions of variants, same 0th dimension as `gv`.
phet_roh: float, optional
Probability of observing a heterozygote in a ROH. Appropriate values
will depend on de novo mutation rate and genotype error rate.
phet_nonroh: tuple of floats, optional
One or more probabilites of observing a heterozygote outside of ROH.
Appropriate values will depend primarily on nucleotide diversity within
the population, but also on mutation rate and genotype error rate.
transition: float, optional
Probability of moving between states.
min_roh: integer, optional
Minimum size (bp) to condsider as a ROH. Will depend on contig size
and recombination rate.
is_accessible: array_like, bool, shape (`contig_size`,), optional
Boolean array for each position in contig describing whether accessible
or not.
contig_size: int, optional
If is_accessible not known/not provided, allows specification of
total length of contig.
Returns
-------
df_roh: DataFrame
Data frame where each row describes a run of homozygosity. Columns are 'start',
'stop', 'length' and 'is_marginal'. Start and stop are 1-based, stop-inclusive.
froh: float
Proportion of genome in a ROH.
Notes
-----
This function requires `hmmlearn <http://hmmlearn.readthedocs.io/en/latest/>`_ to be
installed.
This function currently requires around 4GB memory for a contig size of ~50Mbp.
"""
from hmmlearn import hmm
# setup inputs
if isinstance(phet_nonroh, float):
phet_nonroh = phet_nonroh,
gv = GenotypeVector(gv)
pos = asarray_ndim(pos, 1)
check_dim0_aligned(gv, pos)
is_accessible = asarray_ndim(is_accessible, 1, dtype=bool)
# heterozygote probabilities
het_px = np.concatenate([(phet_roh, ), phet_nonroh])
# start probabilities (all equal)
start_prob = np.repeat(1 / het_px.size, het_px.size)
# transition between underlying states
transition_mx = _hmm_derive_transition_matrix(transition, het_px.size)
# probability of inaccessible
if is_accessible is None:
if contig_size is None:
raise ValueError(
"If is_accessibile argument is not provided, you must provide contig_size"
)
p_accessible = 1.0
else:
p_accessible = is_accessible.mean()
contig_size = is_accessible.size
emission_mx = _mhmm_derive_emission_matrix(het_px, p_accessible)
# initialize HMM
roh_hmm = hmm.MultinomialHMM(n_components=het_px.size)
roh_hmm.n_symbols_ = 3
roh_hmm.startprob_ = start_prob
roh_hmm.transmat_ = transition_mx
roh_hmm.emissionprob_ = emission_mx
# locate heterozygous calls
is_het = gv.is_het()
# predict ROH state
pred, obs = _mhmm_predict_roh_state(roh_hmm, is_het, pos, is_accessible,
contig_size)
# find ROH windows
df_blocks = tabulate_state_blocks(pred, states=list(range(len(het_px))))
df_roh = df_blocks[(df_blocks.state == 0)].reset_index(drop=True)
# adapt the dataframe for ROH
for col in 'state', 'support', 'start_lidx', 'stop_ridx', 'size_max':
del df_roh[col]
df_roh.rename(columns={
'start_ridx': 'start',
'stop_lidx': 'stop',
'size_min': 'length'
},
inplace=True)
# make coordinates 1-based
df_roh['start'] = df_roh['start'] + 1
df_roh['stop'] = df_roh['stop'] + 1
# filter by ROH size
if min_roh > 0:
df_roh = df_roh[df_roh.length >= min_roh]
# compute FROH
froh = df_roh.length.sum() / contig_size
return df_roh, froh
def windowed_count(pos, size=None, start=None, stop=None, step=None,
windows=None):
"""Count the number of items in windows over a single chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
The item positions in ascending order, using 1-based coordinates..
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
Returns
-------
counts : ndarray, int, shape (n_windows,)
The number of items in each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
Notes
-----
The window stop positions are included within a window.
The final window will be truncated to the specified stop position,
and so may be smaller than the other windows.
Examples
--------
Non-overlapping windows::
>>> import allel
>>> pos = [1, 7, 12, 15, 28]
>>> counts, windows = allel.stats.windowed_count(pos, size=10)
>>> counts
array([2, 2, 1])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 28]])
Half-overlapping windows::
>>> counts, windows = allel.stats.windowed_count(pos, size=10, step=5)
>>> counts
array([2, 3, 2, 0, 1])
>>> windows
array([[ 1, 10],
[ 6, 15],
[11, 20],
[16, 25],
[21, 28]])
"""
# assume sorted positions
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
# setup windows
if windows is None:
windows = position_windows(pos, size, start, stop, step)
else:
windows = asarray_ndim(windows, 2)
# find window locations
locs = window_locations(pos, windows)
# count number of items in each window
counts = np.diff(locs, axis=1).reshape(-1)
return counts, windows
def standardize_by_allele_count(score,
aac,
bins=None,
n_bins=None,
diagnostics=True):
"""Standardize `score` within allele frequency bins.
Parameters
----------
score : array_like, float
The score to be standardized, e.g., IHS or NSL.
aac : array_like, int
An array of alternate allele counts.
bins : array_like, int, optional
Allele count bins, overrides `n_bins`.
n_bins : int, optional
Number of allele count bins to use.
diagnostics : bool, optional
If True, plot some diagnostic information about the standardization.
Returns
-------
score_standardized : ndarray, float
Standardized scores.
bins : ndarray, int
Allele count bins used for standardization.
"""
from scipy.stats import binned_statistic
# check inputs
score = asarray_ndim(score, 1)
aac = asarray_ndim(aac, 1)
check_dim0_aligned(score, aac)
# remove nans
nonan = ~np.isnan(score)
score_nonan = score[nonan]
aac_nonan = aac[nonan]
if bins is None:
# make our own similar sized bins
# how many bins to make?
if n_bins is None:
# something vaguely reasonable
n_bins = np.max(aac) // 2
# make bins
bins = make_similar_sized_bins(aac_nonan, n_bins)
else:
# user-provided bins
bins = asarray_ndim(bins, 1)
mean_score, _, _ = binned_statistic(aac_nonan,
score_nonan,
statistic=np.mean,
bins=bins)
std_score, _, _ = binned_statistic(aac_nonan,
score_nonan,
statistic=np.std,
bins=bins)
if diagnostics:
import matplotlib.pyplot as plt
x = (bins[:-1] + bins[1:]) / 2
plt.figure()
plt.fill_between(x,
mean_score - std_score,
mean_score + std_score,
alpha=.5,
label='std')
plt.plot(x, mean_score, marker='o', label='mean')
plt.grid(axis='y')
plt.xlabel('Alternate allele count')
plt.ylabel('Unstandardized score')
plt.title('Standardization diagnostics')
plt.legend()
# apply standardization
score_standardized = np.empty_like(score)
for i in range(len(bins) - 1):
x1 = bins[i]
x2 = bins[i + 1]
if i == 0:
# first bin
loc = (aac < x2)
elif i == len(bins) - 2:
# last bin
loc = (aac >= x1)
else:
# middle bins
loc = (aac >= x1) & (aac < x2)
m = mean_score[i]
s = std_score[i]
score_standardized[loc] = (score[loc] - m) / s
return score_standardized, bins
def sequence_divergence(pos,
ac1,
ac2,
an1=None,
an2=None,
start=None,
stop=None,
is_accessible=None):
"""Estimate nucleotide divergence between two populations within a
given region, which is the average proportion of sites (including
monomorphic sites not present in the data) that differ between randomly
chosen pairs of chromosomes, one from each population.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
an1 : array_like, int, shape (n_variants,), optional
Allele numbers for the first population. If not provided, will be
calculated from `ac1`.
an2 : array_like, int, shape (n_variants,), optional
Allele numbers for the second population. If not provided, will be
calculated from `ac2`.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy = sequence_divergence(pos, ac1, ac2, start=1, stop=31)
>>> dxy
0.12096774193548387
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
if an1 is not None:
an1 = asarray_ndim(an1, 1)
if an2 is not None:
an2 = asarray_ndim(an2, 1)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# handle start/stop
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac1 = ac1[loc]
ac2 = ac2[loc]
if an1 is not None:
an1 = an1[loc]
if an2 is not None:
an2 = an2[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference between the two populations
mpd = mean_pairwise_difference_between(ac1, ac2, an1=an1, an2=an2, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base, N.B., expect pos is 1-based
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
dxy = mpd_sum / n_bases
return dxy
def compute_ihh_gaps(pos, map_pos, gap_scale, max_gap, is_accessible):
"""Compute spacing between variants for integrating haplotype
homozygosity.
Parameters
----------
pos : array_like, int, shape (n_variants,)
Variant positions (physical distance).
map_pos : array_like, float, shape (n_variants,)
Variant positions (genetic map distance).
gap_scale : int, optional
Rescale distance between variants if gap is larger than this value.
max_gap : int, optional
Do not report scores if EHH spans a gap larger than this number of
base pairs.
is_accessible : array_like, bool, optional
Genome accessibility array. If provided, distance between variants
will be computed as the number of accessible bases between them.
Returns
-------
gaps : ndarray, float, shape (n_variants - 1,)
"""
# check inputs
if map_pos is None:
# integrate over physical distance
map_pos = pos
else:
map_pos = asarray_ndim(map_pos, 1)
check_dim0_aligned(pos, map_pos)
# compute physical gaps
physical_gaps = np.diff(pos)
# compute genetic gaps
gaps = np.diff(map_pos).astype('f8')
if is_accessible is not None:
# compute accessible gaps
is_accessible = asarray_ndim(is_accessible, 1)
assert is_accessible.shape[0] > pos[-1], \
'accessibility array too short'
accessible_gaps = np.zeros_like(physical_gaps)
for i in range(1, len(pos)):
# N.B., expect pos is 1-based
n_access = np.count_nonzero(is_accessible[pos[i - 1] - 1:pos[i] -
1])
accessible_gaps[i - 1] = n_access
# adjust using accessibility
scaling = accessible_gaps / physical_gaps
gaps = gaps * scaling
elif gap_scale is not None and gap_scale > 0:
scaling = np.ones(gaps.shape, dtype='f8')
loc_scale = physical_gaps > gap_scale
scaling[loc_scale] = gap_scale / physical_gaps[loc_scale]
gaps = gaps * scaling
if max_gap is not None and max_gap > 0:
# deal with very large gaps
gaps[physical_gaps > max_gap] = -1
return gaps
def windowed_divergence(pos,
ac1,
ac2,
size=None,
start=None,
stop=None,
step=None,
windows=None,
is_accessible=None,
fill=np.nan):
"""Estimate nucleotide divergence between two populations in windows
over a single chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence in each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy, windows, n_bases, counts = windowed_divergence(
... pos, ac1, ac2, size=10, start=1, stop=31
... )
>>> dxy
array([0.15 , 0.225, 0. ])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 31]])
>>> n_bases
array([10, 10, 11])
>>> counts
array([3, 4, 2])
"""
# check inputs
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# calculate mean pairwise divergence
mpd = mean_pairwise_difference_between(ac1, ac2, fill=0)
# sum in windows
mpd_sum, windows, counts = windowed_statistic(pos,
values=mpd,
statistic=np.sum,
size=size,
start=start,
stop=stop,
step=step,
windows=windows,
fill=0)
# calculate value per base
dxy, n_bases = per_base(mpd_sum,
windows,
is_accessible=is_accessible,
fill=fill)
return dxy, windows, n_bases, counts
def tabulate_state_transitions(x, states, pos=None):
"""Construct a dataframe where each row provides information about a state transition.
Parameters
----------
x : array_like, int
1-dimensional array of state values.
states : set
Set of states of interest. Any state value not in this set will be ignored.
pos : array_like, int, optional
Array of positions corresponding to values in `x`.
Returns
-------
df : DataFrame
Notes
-----
The resulting dataframe includes one row at the start representing the first state
observation and one row at the end representing the last state observation.
Examples
--------
>>> import allel
>>> x = [1, 1, 0, 1, 1, 2, 2, 0, 2, 1, 1]
>>> df = allel.tabulate_state_transitions(x, states={1, 2})
>>> df
lstate rstate lidx ridx
0 -1 1 -1 0
1 1 2 4 5
2 2 1 8 9
3 1 -1 10 -1
>>> pos = [2, 4, 7, 8, 10, 14, 19, 23, 28, 30, 31]
>>> df = allel.tabulate_state_transitions(x, states={1, 2}, pos=pos)
>>> df
lstate rstate lidx ridx lpos rpos
0 -1 1 -1 0 -1 2
1 1 2 4 5 10 14
2 2 1 8 9 28 30
3 1 -1 10 -1 31 -1
"""
# check inputs
x = asarray_ndim(x, 1)
check_integer_dtype(x)
x = memoryview_safe(x)
# find state transitions
switch_points, transitions, _ = state_transitions(x, states)
# start to build a dataframe
items = [('lstate', transitions[:, 0]),
('rstate', transitions[:, 1]),
('lidx', switch_points[:, 0]),
('ridx', switch_points[:, 1])]
# deal with optional positions
if pos is not None:
pos = asarray_ndim(pos, 1)
check_dim0_aligned(x, pos)
check_integer_dtype(pos)
# find switch positions
switch_positions = np.take(pos, switch_points)
# deal with boundary transitions
switch_positions[0, 0] = -1
switch_positions[-1, 1] = -1
# add columns into dataframe
items += [('lpos', switch_positions[:, 0]),
('rpos', switch_positions[:, 1])]
import pandas
return pandas.DataFrame.from_dict(OrderedDict(items))
def windowed_watterson_theta(
pos, ac, size=None, start=None, stop=None, step=None, windows=None, is_accessible=None, fill=np.nan
):
"""Calculate the value of Watterson's estimator in windows over a single
chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
theta_hat_w : ndarray, float, shape (n_windows,)
Watterson's estimator (theta hat per base).
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w, windows, n_bases, counts = allel.stats.windowed_watterson_theta(
... pos, ac, size=10, start=1, stop=31
... )
>>> theta_hat_w
array([ 0.10909091, 0.16363636, 0.04958678])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 31]])
>>> n_bases
array([10, 10, 11])
>>> counts
array([3, 4, 2])
""" # flake8: noqa
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# locate segregating variants
is_seg = ac.is_segregating()
# count segregating variants in windows
S, windows, counts = windowed_statistic(
pos, is_seg, statistic=np.count_nonzero, size=size, start=start, stop=stop, step=step, windows=windows, fill=0
)
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# absolute value of Watterson's theta
theta_hat_w_abs = S / a1
# theta per base
theta_hat_w, n_bases = per_base(theta_hat_w_abs, windows=windows, is_accessible=is_accessible, fill=fill)
return theta_hat_w, windows, n_bases, counts
def xpehh(h1,
h2,
pos,
map_pos=None,
min_ehh=0.05,
include_edges=False,
gap_scale=20000,
max_gap=200000,
is_accessible=None,
use_threads=True):
"""Compute the unstandardized cross-population extended haplotype
homozygosity score (XPEHH) for each variant.
Parameters
----------
h1 : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array for the first population.
h2 : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array for the second population.
pos : array_like, int, shape (n_variants,)
Variant positions on physical or genetic map.
map_pos : array_like, float, shape (n_variants,)
Variant positions (genetic map distance).
min_ehh: float, optional
Minimum EHH beyond which to truncate integrated haplotype
homozygosity calculation.
include_edges : bool, optional
If True, report scores even if EHH does not decay below `min_ehh`
before reaching the edge of the data.
gap_scale : int, optional
Rescale distance between variants if gap is larger than this value.
max_gap : int, optional
Do not report scores if EHH spans a gap larger than this number of
base pairs.
is_accessible : array_like, bool, optional
Genome accessibility array. If provided, distance between variants
will be computed as the number of accessible bases between them.
use_threads : bool, optional
If True use multiple threads to compute.
Returns
-------
score : ndarray, float, shape (n_variants,)
Unstandardized XPEHH scores.
Notes
-----
This function will calculate XPEHH for all variants. To exclude variants
below a given minor allele frequency, filter the input haplotype arrays
before passing to this function.
This function returns NaN for any EHH calculations where haplotype
homozygosity does not decay below `min_ehh` before reaching the first or
last variant. To disable this behaviour, set `include_edges` to True.
Note that the unstandardized score is returned. Usually these scores are
then standardized genome-wide.
Haplotype arrays from the two populations may have different numbers of
haplotypes.
See Also
--------
standardize
"""
# check inputs
h1 = asarray_ndim(h1, 2)
check_integer_dtype(h1)
h2 = asarray_ndim(h2, 2)
check_integer_dtype(h2)
pos = asarray_ndim(pos, 1)
check_dim0_aligned(h1, h2, pos)
# compute gaps between variants for integration
gaps = compute_ihh_gaps(pos, map_pos, gap_scale, max_gap, is_accessible)
# setup kwargs
kwargs = dict(min_ehh=min_ehh, include_edges=include_edges)
if use_threads and multiprocessing.cpu_count() > 1:
# use multiple threads
# setup threadpool
pool = ThreadPool(min(4, multiprocessing.cpu_count()))
# scan forward
res1_fwd = pool.apply_async(ihh_scan, (h1, gaps), kwargs)
res2_fwd = pool.apply_async(ihh_scan, (h2, gaps), kwargs)
# scan backward
res1_rev = pool.apply_async(ihh_scan, (h1[::-1], gaps[::-1]), kwargs)
res2_rev = pool.apply_async(ihh_scan, (h2[::-1], gaps[::-1]), kwargs)
# wait for both to finish
pool.close()
pool.join()
# obtain results
ihh1_fwd = res1_fwd.get()
ihh2_fwd = res2_fwd.get()
ihh1_rev = res1_rev.get()
ihh2_rev = res2_rev.get()
# cleanup
pool.terminate()
else:
# compute without threads
# scan forward
ihh1_fwd = ihh_scan(h1, gaps, **kwargs)
ihh2_fwd = ihh_scan(h2, gaps, **kwargs)
# scan backward
ihh1_rev = ihh_scan(h1[::-1], gaps[::-1], **kwargs)
ihh2_rev = ihh_scan(h2[::-1], gaps[::-1], **kwargs)
# handle reverse scans
ihh1_rev = ihh1_rev[::-1]
ihh2_rev = ihh2_rev[::-1]
# compute unstandardized score
ihh1 = ihh1_fwd + ihh1_rev
ihh2 = ihh2_fwd + ihh2_rev
score = np.log(ihh1 / ihh2)
return score
def mean_pairwise_difference_between(ac1, ac2, an1=None, an2=None, fill=np.nan):
"""Calculate for each variant the mean number of pairwise differences
between chromosomes sampled from two different populations.
Parameters
----------
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array from the second population.
an1 : array_like, int, shape (n_variants,), optional
Allele numbers for the first population. If not provided, will be
calculated from `ac1`.
an2 : array_like, int, shape (n_variants,), optional
Allele numbers for the second population. If not provided, will be
calculated from `ac2`.
fill : float
Use this value where there are no pairs to compare (e.g.,
all allele calls are missing).
Returns
-------
mpd : ndarray, float, shape (n_variants,)
Notes
-----
The values returned by this function can be summed over a genome
region and divided by the number of accessible bases to estimate
nucleotide divergence between two populations, a.k.a. *Dxy*.
Examples
--------
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> allel.stats.mean_pairwise_difference_between(ac1, ac2)
array([ 0. , 0.5 , 1. , 0.5 , 0. , 1. , 0.75, nan])
See Also
--------
sequence_divergence, windowed_divergence
"""
# This function calculates the mean number of pairwise differences
# between haplotypes from two different populations, generalising to any
# number of alleles.
# check inputs
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
check_dim0_aligned(ac1, ac2)
ac1, ac2 = ensure_dim1_aligned(ac1, ac2)
# total number of haplotypes sampled from each population
if an1 is None:
an1 = np.sum(ac1, axis=1)
else:
an1 = asarray_ndim(an1, 1)
check_dim0_aligned(ac1, an1)
if an2 is None:
an2 = np.sum(ac2, axis=1)
else:
an2 = asarray_ndim(an2, 1)
check_dim0_aligned(ac2, an2)
# total number of pairwise comparisons for each variant
n_pairs = an1 * an2
# number of pairwise comparisons where there is no difference:
# sum of (ac1 * ac2) for each allele (i.e., number of ways to
# choose the same allele twice)
n_same = np.sum(ac1 * ac2, axis=1)
# number of pairwise differences
n_diff = n_pairs - n_same
# mean number of pairwise differences, accounting for cases where
# there are no pairs
with ignore_invalid():
mpd = np.where(n_pairs > 0, n_diff / n_pairs, fill)
return mpd
def sequence_diversity(pos, ac, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide diversity within a given region, which is the
average proportion of sites (including monomorphic sites not present in the
data) that differ between randomly chosen pairs of chromosomes.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based). Defaults to the first position.
stop : int, optional
The position at which to stop (1-based). Defaults to the last position.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
pi : ndarray, float, shape (n_windows,)
Nucleotide diversity.
Notes
-----
If start and/or stop are not provided, uses the difference between the last
and the first position as a proxy for the total number of sites, which can
overestimate the sequence diversity.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> pi = allel.sequence_diversity(pos, ac, start=1, stop=31)
>>> pi
0.13978494623655915
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac = asarray_ndim(ac, 2)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1:stop])
pi = mpd_sum / n_bases
return pi
def plot_sfs(s, yscale='log', bins=None, n=None,
clip_endpoints=True, label=None, plot_kwargs=None,
ax=None):
"""Plot a site frequency spectrum.
Parameters
----------
s : array_like, int, shape (n_chromosomes,)
Site frequency spectrum.
yscale : string, optional
Y axis scale.
bins : int or array_like, int, optional
Allele count bins.
n : int, optional
Number of chromosomes sampled. If provided, X axis will be plotted
as allele frequency, otherwise as allele count.
clip_endpoints : bool, optional
If True, do not plot first and last values from frequency spectrum.
label : string, optional
Label for data series in plot.
plot_kwargs : dict-like
Additional keyword arguments, passed through to ax.plot().
ax : axes, optional
Axes on which to draw. If not provided, a new figure will be created.
Returns
-------
ax : axes
The axes on which the plot was drawn.
"""
import matplotlib.pyplot as plt
import scipy
# check inputs
s = asarray_ndim(s, 1)
# setup axes
if ax is None:
fig, ax = plt.subplots()
# setup data
if bins is None:
if clip_endpoints:
x = np.arange(1, s.shape[0]-1)
y = s[1:-1]
else:
x = np.arange(s.shape[0])
y = s
else:
if clip_endpoints:
y, b, _ = scipy.stats.binned_statistic(
np.arange(1, s.shape[0]-1),
values=s[1:-1],
bins=bins,
statistic='sum')
else:
y, b, _ = scipy.stats.binned_statistic(
np.arange(s.shape[0]),
values=s,
bins=bins,
statistic='sum')
# use bin midpoints for plotting
x = (b[:-1] + b[1:]) / 2
if n:
# convert allele counts to allele frequencies
x = x / n
ax.set_xlabel('derived allele frequency')
else:
ax.set_xlabel('derived allele count')
# do plotting
if plot_kwargs is None:
plot_kwargs = dict()
ax.plot(x, y, label=label, **plot_kwargs)
# tidy
ax.set_yscale(yscale)
ax.set_ylabel('site frequency')
ax.autoscale(axis='x', tight=True)
return ax
def mean_pairwise_difference(ac, an=None, fill=np.nan):
"""Calculate for each variant the mean number of pairwise differences
between chromosomes sampled from within a single population.
Parameters
----------
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
an : array_like, int, shape (n_variants,), optional
Allele numbers. If not provided, will be calculated from `ac`.
fill : float
Use this value where there are no pairs to compare (e.g.,
all allele calls are missing).
Returns
-------
mpd : ndarray, float, shape (n_variants,)
Notes
-----
The values returned by this function can be summed over a genome
region and divided by the number of accessible bases to estimate
nucleotide diversity, a.k.a. *pi*.
Examples
--------
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1]])
>>> ac = h.count_alleles()
>>> allel.stats.mean_pairwise_difference(ac)
array([ 0. , 0.5 , 0.66666667, 0.5 , 0. ,
0.83333333, 0.83333333, 1. ])
See Also
--------
sequence_diversity, windowed_diversity
"""
# This function calculates the mean number of pairwise differences
# between haplotypes within a single population, generalising to any number
# of alleles.
# check inputs
ac = asarray_ndim(ac, 2)
# total number of haplotypes
if an is None:
an = np.sum(ac, axis=1)
else:
an = asarray_ndim(an, 1)
check_dim0_aligned(ac, an)
# total number of pairwise comparisons for each variant:
# (an choose 2)
n_pairs = an * (an - 1) / 2
# number of pairwise comparisons where there is no difference:
# sum of (ac choose 2) for each allele (i.e., number of ways to
# choose the same allele twice)
n_same = np.sum(ac * (ac - 1) / 2, axis=1)
# number of pairwise differences
n_diff = n_pairs - n_same
# mean number of pairwise differences, accounting for cases where
# there are no pairs
with ignore_invalid():
mpd = np.where(n_pairs > 0, n_diff / n_pairs, fill)
return mpd
def standardize(score):
"""Centre and scale to unit variance."""
score = asarray_ndim(score, 1)
return (score - np.nanmean(score)) / np.nanstd(score)
def sequence_diversity(pos, ac, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide diversity within a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
pi : ndarray, float, shape (n_windows,)
Nucleotide diversity.
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> pi = allel.stats.sequence_diversity(pos, ac, start=1, stop=31)
>>> pi
0.13978494623655915
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac = asarray_ndim(ac, 2)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
pi = mpd_sum / n_bases
return pi
def fig_voight_painting(h,
index=None,
palette='colorblind',
height_factor=0.01,
fig=None):
"""Make a figure of shared haplotype prefixes for both left and right
flanks, centred on some variant of choice.
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
index : int, optional
Index of the variant within the haplotype array to centre on. If not
provided, the middle variant will be used.
palette : string, optional
A Seaborn palette name.
height_factor : float, optional
If no axes provided, determine height of figure by multiplying
height of painting array by this number.
fig : figure
The figure on which to draw. If not provided, a new figure will be
created.
Returns
-------
fig : figure
Notes
-----
N.B., the ordering of haplotypes on the left and right flanks will be
different. This means that haplotypes on the right flank **will not**
correspond to haplotypes on the left flank at the same vertical position.
"""
import matplotlib.pyplot as plt
from matplotlib.gridspec import GridSpec
import seaborn as sns
# check inputs
h = asarray_ndim(h, 2)
if index is None:
# use midpoint
index = h.shape[0] // 2
# divide data into two flanks
hl = h[:index + 1][::-1]
hr = h[index:]
# paint both flanks
pl, il = voight_painting(hl)
pr, ir = voight_painting(hr)
# compute ehh decay for both flanks
el = ehh_decay(hl, truncate=False)
er = ehh_decay(hr, truncate=False)
# setup figure
# fixed height for EHH decay subplot
h_ehh = plt.rcParams['figure.figsize'][1] // 3
# add height for paintings
h_painting = height_factor * h.shape[1]
if fig is None:
w = plt.rcParams['figure.figsize'][0]
h = h_ehh + h_painting
fig = plt.figure(figsize=(w, h))
# setup gridspec
gs = GridSpec(2,
2,
width_ratios=[hl.shape[0], hr.shape[0]],
height_ratios=[h_painting, h_ehh])
# plot paintings
ax = fig.add_subplot(gs[0, 0])
sns.despine(ax=ax, left=True, bottom=True)
plot_voight_painting(pl, palette=palette, flank='left', ax=ax)
ax = fig.add_subplot(gs[0, 1])
sns.despine(ax=ax, left=True, bottom=True)
plot_voight_painting(pr, palette=palette, flank='right', ax=ax)
# plot ehh
ax = fig.add_subplot(gs[1, 0])
sns.despine(ax=ax, offset=3)
x = np.arange(el.shape[0])
y = el
ax.fill_between(x, 0, y)
ax.set_ylim(0, 1)
ax.set_yticks([0, 1])
ax.set_ylabel('EHH')
ax.invert_xaxis()
ax = fig.add_subplot(gs[1, 1])
sns.despine(ax=ax, left=True, right=False, offset=3)
ax.yaxis.tick_right()
ax.set_ylim(0, 1)
ax.set_yticks([0, 1])
x = np.arange(er.shape[0])
y = er
ax.fill_between(x, 0, y)
# tidy up
fig.tight_layout()
return fig
def sequence_divergence(pos, ac1, ac2, an1=None, an2=None, start=None, stop=None, is_accessible=None):
"""Estimate nucleotide divergence between two populations within a
given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy = sequence_divergence(pos, ac1, ac2, start=1, stop=31)
>>> dxy
0.12096774193548387
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
ac1 = asarray_ndim(ac1, 2)
ac2 = asarray_ndim(ac2, 2)
if an1 is not None:
an1 = asarray_ndim(an1, 1)
if an2 is not None:
an2 = asarray_ndim(an2, 1)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# handle start/stop
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac1 = ac1[loc]
ac2 = ac2[loc]
if an1 is not None:
an1 = an1[loc]
if an2 is not None:
an2 = an2[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# calculate mean pairwise difference between the two populations
mpd = mean_pairwise_difference_between(ac1, ac2, an1=an1, an2=an2, fill=0)
# sum differences over variants
mpd_sum = np.sum(mpd)
# calculate value per base, N.B., expect pos is 1-based
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
dxy = mpd_sum / n_bases
return dxy
def ihs(h,
pos,
map_pos=None,
min_ehh=0.05,
min_maf=0.05,
include_edges=False,
gap_scale=20000,
max_gap=200000,
is_accessible=None,
use_threads=True):
"""Compute the unstandardized integrated haplotype score (IHS) for each
variant, comparing integrated haplotype homozygosity between the
reference (0) and alternate (1) alleles.
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
pos : array_like, int, shape (n_variants,)
Variant positions (physical distance).
map_pos : array_like, float, shape (n_variants,)
Variant positions (genetic map distance).
min_ehh: float, optional
Minimum EHH beyond which to truncate integrated haplotype
homozygosity calculation.
min_maf : float, optional
Do not compute integrated haplotype homozogysity for variants with
minor allele frequency below this value.
include_edges : bool, optional
If True, report scores even if EHH does not decay below `min_ehh`
before reaching the edge of the data.
gap_scale : int, optional
Rescale distance between variants if gap is larger than this value.
max_gap : int, optional
Do not report scores if EHH spans a gap larger than this number of
base pairs.
is_accessible : array_like, bool, optional
Genome accessibility array. If provided, distance between variants
will be computed as the number of accessible bases between them.
use_threads : bool, optional
If True use multiple threads to compute.
Returns
-------
score : ndarray, float, shape (n_variants,)
Unstandardized IHS scores.
Notes
-----
This function will calculate IHS for all variants. To exclude variants
below a given minor allele frequency, filter the input haplotype array
before passing to this function.
This function computes IHS comparing the reference and alternate alleles.
These can be polarised by switching the sign for any variant where the
reference allele is derived.
This function returns NaN for any IHS calculations where haplotype
homozygosity does not decay below `min_ehh` before reaching the first or
last variant. To disable this behaviour, set `include_edges` to True.
Note that the unstandardized score is returned. Usually these scores are
then standardized in different allele frequency bins.
See Also
--------
standardize_by_allele_count
"""
# check inputs
h = asarray_ndim(h, 2)
check_integer_dtype(h)
pos = asarray_ndim(pos, 1)
check_dim0_aligned(h, pos)
# compute gaps between variants for integration
gaps = compute_ihh_gaps(pos, map_pos, gap_scale, max_gap, is_accessible)
# setup kwargs
kwargs = dict(min_ehh=min_ehh,
min_maf=min_maf,
include_edges=include_edges)
if use_threads and multiprocessing.cpu_count() > 1:
# run with threads
# create pool
pool = ThreadPool(2)
# scan forward
result_fwd = pool.apply_async(ihh01_scan, (h, gaps), kwargs)
# scan backward
result_rev = pool.apply_async(ihh01_scan, (h[::-1], gaps[::-1]),
kwargs)
# wait for both to finish
pool.close()
pool.join()
# obtain results
ihh0_fwd, ihh1_fwd = result_fwd.get()
ihh0_rev, ihh1_rev = result_rev.get()
# cleanup
pool.terminate()
else:
# run without threads
# scan forward
ihh0_fwd, ihh1_fwd = ihh01_scan(h, gaps, **kwargs)
# scan backward
ihh0_rev, ihh1_rev = ihh01_scan(h[::-1], gaps[::-1], **kwargs)
# handle reverse scan
ihh0_rev = ihh0_rev[::-1]
ihh1_rev = ihh1_rev[::-1]
# compute unstandardized score
ihh0 = ihh0_fwd + ihh0_rev
ihh1 = ihh1_fwd + ihh1_rev
score = np.log(ihh1 / ihh0)
return score
def windowed_divergence(
pos, ac1, ac2, size=None, start=None, stop=None, step=None, windows=None, is_accessible=None, fill=np.nan
):
"""Estimate nucleotide divergence between two populations in windows
over a single chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
Dxy : ndarray, float, shape (n_windows,)
Nucleotide divergence in each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
Examples
--------
Simplest case, two haplotypes in each population::
>>> import allel
>>> h = allel.HaplotypeArray([[0, 0, 0, 0],
... [0, 0, 0, 1],
... [0, 0, 1, 1],
... [0, 1, 1, 1],
... [1, 1, 1, 1],
... [0, 0, 1, 2],
... [0, 1, 1, 2],
... [0, 1, -1, -1],
... [-1, -1, -1, -1]])
>>> ac1 = h.count_alleles(subpop=[0, 1])
>>> ac2 = h.count_alleles(subpop=[2, 3])
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> dxy, windows, n_bases, counts = windowed_divergence(
... pos, ac1, ac2, size=10, start=1, stop=31
... )
>>> dxy
array([ 0.15 , 0.225, 0. ])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 31]])
>>> n_bases
array([10, 10, 11])
>>> counts
array([3, 4, 2])
"""
# check inputs
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# calculate mean pairwise divergence
mpd = mean_pairwise_difference_between(ac1, ac2, fill=0)
# sum in windows
mpd_sum, windows, counts = windowed_statistic(
pos, values=mpd, statistic=np.sum, size=size, start=start, stop=stop, step=step, windows=windows, fill=0
)
# calculate value per base
dxy, n_bases = per_base(mpd_sum, windows, is_accessible=is_accessible, fill=fill)
return dxy, windows, n_bases, counts
def nsl(h, use_threads=True):
"""Compute the unstandardized number of segregating sites by length (nSl)
for each variant, comparing the reference and alternate alleles,
after Ferrer-Admetlla et al. (2014).
Parameters
----------
h : array_like, int, shape (n_variants, n_haplotypes)
Haplotype array.
use_threads : bool, optional
If True use multiple threads to compute.
Returns
-------
score : ndarray, float, shape (n_variants,)
Notes
-----
This function will calculate nSl for all variants. To exclude variants
below a given minor allele frequency, filter the input haplotype array
before passing to this function.
This function computes nSl by comparing the reference and alternate
alleles. These can be polarised by switching the sign for any variant where
the reference allele is derived.
This function does nothing about nSl calculations where haplotype
homozygosity extends up to the first or last variant. There may be edge
effects.
Note that the unstandardized score is returned. Usually these scores are
then standardized in different allele frequency bins.
See Also
--------
standardize_by_allele_count
"""
# check inputs
h = asarray_ndim(h, 2)
check_integer_dtype(h)
# # check there are no invariant sites
# ac = h.count_alleles()
# assert np.all(ac.is_segregating()), 'please remove non-segregating sites'
if use_threads and multiprocessing.cpu_count() > 1:
# create pool
pool = ThreadPool(2)
# scan forward
result_fwd = pool.apply_async(nsl01_scan, args=(h, ))
# scan backward
result_rev = pool.apply_async(nsl01_scan, args=(h[::-1], ))
# wait for both to finish
pool.close()
pool.join()
# obtain results
nsl0_fwd, nsl1_fwd = result_fwd.get()
nsl0_rev, nsl1_rev = result_rev.get()
else:
# scan forward
nsl0_fwd, nsl1_fwd = nsl01_scan(h)
# scan backward
nsl0_rev, nsl1_rev = nsl01_scan(h[::-1])
# handle backwards
nsl0_rev = nsl0_rev[::-1]
nsl1_rev = nsl1_rev[::-1]
# compute unstandardized score
nsl0 = nsl0_fwd + nsl0_rev
nsl1 = nsl1_fwd + nsl1_rev
score = np.log(nsl1 / nsl0)
return score
def windowed_df(
pos, ac1, ac2, size=None, start=None, stop=None, step=None, windows=None, is_accessible=None, fill=np.nan
):
"""Calculate the density of fixed differences between two populations in
windows over a single chromosome/contig.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac1 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the first population.
ac2 : array_like, int, shape (n_variants, n_alleles)
Allele counts array for the second population.
size : int, optional
The window size (number of bases).
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
step : int, optional
The distance between start positions of windows. If not given,
defaults to the window size, i.e., non-overlapping windows.
windows : array_like, int, shape (n_windows, 2), optional
Manually specify the windows to use as a sequence of (window_start,
window_stop) positions, using 1-based coordinates. Overrides the
size/start/stop/step parameters.
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
fill : object, optional
The value to use where a window is completely inaccessible.
Returns
-------
df : ndarray, float, shape (n_windows,)
Per-base density of fixed differences in each window.
windows : ndarray, int, shape (n_windows, 2)
The windows used, as an array of (window_start, window_stop) positions,
using 1-based coordinates.
n_bases : ndarray, int, shape (n_windows,)
Number of (accessible) bases in each window.
counts : ndarray, int, shape (n_windows,)
Number of variants in each window.
See Also
--------
allel.model.locate_fixed_differences
"""
# check inputs
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# locate fixed differences
loc_df = locate_fixed_differences(ac1, ac2)
# count number of fixed differences in windows
n_df, windows, counts = windowed_statistic(
pos,
values=loc_df,
statistic=np.count_nonzero,
size=size,
start=start,
stop=stop,
step=step,
windows=windows,
fill=0,
)
# calculate value per base
df, n_bases = per_base(n_df, windows, is_accessible=is_accessible, fill=fill)
return df, windows, n_bases, counts
def recarray_from_hdf5_group(*args, **kwargs):
"""Load a recarray from columns stored as separate datasets with an
HDF5 group.
Either provide an h5py group as a single positional argument,
or provide two positional arguments giving the HDF5 file path and the
group node path within the file.
The following optional parameters may be given.
Parameters
----------
start : int, optional
Index to start loading from.
stop : int, optional
Index to finish loading at.
condition : array_like, bool, optional
A 1-dimensional boolean array of the same length as the columns of the
table to load, indicating a selection of rows to load.
"""
import h5py
h5f = None
if len(args) == 1:
group = args[0]
elif len(args) == 2:
file_path, node_path = args
h5f = h5py.File(file_path, mode='r')
try:
group = h5f[node_path]
except Exception as e:
h5f.close()
raise e
else:
raise ValueError('bad arguments; expected group or (file_path, '
'node_path), found %s' % repr(args))
try:
if not isinstance(group, h5py.Group):
raise ValueError('expected group, found %r' % group)
# determine dataset names to load
available_dataset_names = [
n for n in group.keys() if isinstance(group[n], h5py.Dataset)
]
names = kwargs.pop('names', available_dataset_names)
names = [str(n) for n in names] # needed for PY2
for n in names:
if n not in set(group.keys()):
raise ValueError('name not found: %s' % n)
if not isinstance(group[n], h5py.Dataset):
raise ValueError('name does not refer to a dataset: %s, %r' %
(n, group[n]))
# check datasets are aligned
datasets = [group[n] for n in names]
length = datasets[0].shape[0]
for d in datasets[1:]:
if d.shape[0] != length:
raise ValueError('datasets must be of equal length')
# determine start and stop parameters for load
start = kwargs.pop('start', 0)
stop = kwargs.pop('stop', length)
# check condition
condition = kwargs.pop('condition', None) # type: np.ndarray
condition = asarray_ndim(condition, 1, allow_none=True)
if condition is not None and condition.size != length:
raise ValueError('length of condition does not match length '
'of datasets')
# setup output data
dtype = [(n, d.dtype, d.shape[1:]) for n, d in zip(names, datasets)]
ra = np.empty(length, dtype=dtype)
for n, d in zip(names, datasets):
a = d[start:stop]
if condition is not None:
a = np.compress(condition[start:stop], a, axis=0)
ra[n] = a
return ra
finally:
if h5f is not None:
h5f.close()
def watterson_theta(pos, ac, start=None, stop=None, is_accessible=None):
"""Calculate the value of Watterson's estimator over a given region.
Parameters
----------
pos : array_like, int, shape (n_items,)
Variant positions, using 1-based coordinates, in ascending order.
ac : array_like, int, shape (n_variants, n_alleles)
Allele counts array.
start : int, optional
The position at which to start (1-based).
stop : int, optional
The position at which to stop (1-based).
is_accessible : array_like, bool, shape (len(contig),), optional
Boolean array indicating accessibility status for all positions in the
chromosome/contig.
Returns
-------
theta_hat_w : float
Watterson's estimator (theta hat per base).
Examples
--------
>>> import allel
>>> g = allel.GenotypeArray([[[0, 0], [0, 0]],
... [[0, 0], [0, 1]],
... [[0, 0], [1, 1]],
... [[0, 1], [1, 1]],
... [[1, 1], [1, 1]],
... [[0, 0], [1, 2]],
... [[0, 1], [1, 2]],
... [[0, 1], [-1, -1]],
... [[-1, -1], [-1, -1]]])
>>> ac = g.count_alleles()
>>> pos = [2, 4, 7, 14, 15, 18, 19, 25, 27]
>>> theta_hat_w = allel.stats.watterson_theta(pos, ac, start=1, stop=31)
>>> theta_hat_w
0.10557184750733138
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
if not hasattr(ac, "count_segregating"):
ac = AlleleCountsArray(ac, copy=False)
# deal with subregion
if start is not None or stop is not None:
loc = pos.locate_range(start, stop)
pos = pos[loc]
ac = ac[loc]
if start is None:
start = pos[0]
if stop is None:
stop = pos[-1]
# count segregating variants
S = ac.count_segregating()
# assume number of chromosomes sampled is constant for all variants
n = ac.sum(axis=1).max()
# (n-1)th harmonic number
a1 = np.sum(1 / np.arange(1, n))
# calculate absolute value
theta_hat_w_abs = S / a1
# calculate value per base
if is_accessible is None:
n_bases = stop - start + 1
else:
n_bases = np.count_nonzero(is_accessible[start - 1 : stop])
theta_hat_w = theta_hat_w_abs / n_bases
return theta_hat_w
