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 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 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 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 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 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 windowed_diversity(pos, ac, size=None, start=None, stop=None, step=None,
windows=None, is_accessible=None, fill=np.nan):
"""Estimate nucleotide diversity 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
-------
pi : ndarray, float, shape (n_windows,)
Nucleotide diversity 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
--------
>>> 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, windows, n_bases, counts = allel.windowed_diversity(
... pos, ac, size=10, start=1, stop=31
... )
>>> pi
array([0.11666667, 0.21666667, 0.09090909])
>>> windows
array([[ 1, 10],
[11, 20],
[21, 31]])
>>> n_bases
array([10, 10, 11])
>>> counts
array([3, 4, 2])
"""
# check inputs
if not isinstance(pos, SortedIndex):
pos = SortedIndex(pos, copy=False)
is_accessible = asarray_ndim(is_accessible, 1, allow_none=True)
# masking inaccessible sites from pos and ac
pos, ac = mask_inaccessible(is_accessible, pos, ac)
# calculate mean pairwise difference
mpd = mean_pairwise_difference(ac, fill=0)
# sum differences 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
pi, n_bases = per_base(mpd_sum, windows, is_accessible=is_accessible,
fill=fill)
return pi, windows, n_bases, counts
